diff --git a/.kdev4/dune-microstructure.kdev4 b/.kdev4/dune-microstructure.kdev4
index 985d1fbfcc1af74c4c3b08b55f88bcc1a02b2054..c5a0742362e97feaa9e792bc470da6a0ac982c79 100644
--- a/.kdev4/dune-microstructure.kdev4
+++ b/.kdev4/dune-microstructure.kdev4
@@ -6,7 +6,7 @@ Build Directory Count=1
 Current Build Directory Index-Host System=0
 
 [CMake][CMake Build Directory 0]
-Build Directory Path=/home/klaus/Desktop/DUNE2.8/dune-microstructure/build-cmake
+Build Directory Path=/home/klaus/Desktop/DUNE/dune-microstructure/build-cmake
 Build Type=\n
 CMake Binary=/usr/bin/cmake
 CMake Executable=/usr/bin/cmake
@@ -15,26 +15,5 @@ Extra Arguments=
 Install Directory=
 Runtime=Host System
 
-[Launch]
-Launch Configurations=Launch Configuration 0
-
-[Launch][Launch Configuration 0]
-Configured Launch Modes=execute
-Configured Launchers=nativeAppLauncher
-Name=dune-microstructure
-Type=Native Application
-
-[Launch][Launch Configuration 0][Data]
-Arguments=
-Dependencies=@Variant(\x00\x00\x00\t\x00\x00\x00\x00\x01\x00\x00\x00\x0b\x00\x00\x00\x00\x03\x00\x00\x00&\x00d\x00u\x00n\x00e\x00-\x00m\x00i\x00c\x00r\x00o\x00s\x00t\x00r\x00u\x00c\x00t\x00u\x00r\x00e\x00\x00\x00\x06\x00s\x00r\x00c\x00\x00\x00&\x00d\x00u\x00n\x00e\x00-\x00m\x00i\x00c\x00r\x00o\x00s\x00t\x00r\x00u\x00c\x00t\x00u\x00r\x00e)
-Dependency Action=Build
-EnvironmentGroup=
-Executable=file:///home/klaus/Desktop/DUNE2.8/dune-microstructure
-External Terminal=konsole --noclose --workdir %workdir -e %exe
-Project Target=dune-microstructure,src,dune-microstructure
-Use External Terminal=false
-Working Directory=file:///home/klaus/Desktop/DUNE2.8/dune-microstructure/build-cmake/src
-isExecutable=false
-
 [Project]
 VersionControlSupport=kdevgit
diff --git a/Matlab-Programs/BMatrix.txt b/Matlab-Programs/BMatrix.txt
deleted file mode 100644
index f90d18cb534ed11ef80f6b57e5724c9d21532774..0000000000000000000000000000000000000000
--- a/Matlab-Programs/BMatrix.txt
+++ /dev/null
@@ -1,3 +0,0 @@
-1 1 -0.375507808365302675
-1 2 -0.59999999999997744
-1 3 6.94558662207737461e-10
diff --git a/Matlab-Programs/Minimization.mlx b/Matlab-Programs/Minimization.mlx
index 196d9336e6866a510b2b3e76fa6ae315db54fbfd..a3d7d63b716b1cbba2b3632cb03663743f42df9a 100644
Binary files a/Matlab-Programs/Minimization.mlx and b/Matlab-Programs/Minimization.mlx differ
diff --git a/Matlab-Programs/Minimization_Script.m b/Matlab-Programs/Minimization_Script.m
index ac68cef9b79be992e699cc10418afb307e3b10cc..3a5c6a5ee84f6fada0bcfddbcd0d17fe16fc0513 100644
--- a/Matlab-Programs/Minimization_Script.m
+++ b/Matlab-Programs/Minimization_Script.m
@@ -1,6 +1,11 @@
 clear all
 clc
 
+
+% status = system('mkdir mynew')
+% command = './build-cmake/src/dune-microstructure ./inputs/cellsolver.parset';
+% system(['set PATH=' '/home/klaus/Desktop/DUNE/dune-microstructure' ';' command ]);
+
 % --- Change PolynomialDisplayStyle ----
 % sympref('PolynomialDisplayStyle','ascend');
 % sympref('AbbreviateOutput',false);
@@ -9,140 +14,233 @@ syms f_plus(v1,v2,q1,q2,q3,b1,b2,b3)
 assume( q1 > 0)
 assume( q2 > 0)
 assume( q3 > 0)
-% assume(q3 == q1);
-assume(q3 >= q1)
-assume(q2 >= q3)
-
+assume( q3 >= q1)
+assume( q2 >= q3)
 
 v = [v1; v2];
 
-%should be sqrt(2) instead of 2!
+%should be sqrt(2) instead of 2
+
+fprintf('Functions to be minimized')
 f_plus(v1,v2,q1,q2,q3,b1,b2,b3) = q1*v1^4 + q2*v2^4+2*q3*v1^2*v2^2-2*(q1*b1*v1^2+ q2*b2*v2^2+sqrt(2)*q3*b3*v1*v2);
 f_minus(v1,v2,q1,q2,q3,b1,b2,b3) = q1*v1^4 + q2*v2^4+2*q3*v1^2*v2^2+2*(q1*b1*v1^2+ q2*b2*v2^2+sqrt(2)*q3*b3*v1*v2);
 
 
 % ---- Fix parameters
-% f_plus = subs(f_plus,b3,0)  % set b3
-% f_plus = subs(f_plus,q3,q1)
-
-% f_plus = subs(f_plus,q1,40);
-% f_plus = subs(f_plus,q3,63.9);
-% f_plus = subs(f_plus,q2,34.9);
-% f_plus = subs(f_plus,b1,4);
-% f_plus = subs(f_plus,b2,2.4);
-% f_plus = subs(f_plus,b3,2.4);
-
-% f_plus = subs(f_plus,q1,40);
-% f_plus = subs(f_plus,q3,20);
-% f_plus = subs(f_plus,q2,50);
-% f_plus = subs(f_plus,b1,5);
-% f_plus = subs(f_plus,b2,6);
-% f_plus = subs(f_plus,b3,7);
-
-f_plus = subs(f_plus,q1,40);
-f_plus = subs(f_plus,q3,63.9);
-f_plus = subs(f_plus,q2,70);
-rndm1 = randi([1 20],1,1);
-rndm2 = randi([1 20],1,1);
-rndm3 = randi([1 20],1,1);
-f_plus = subs(f_plus,b1,rndm1);
-f_plus = subs(f_plus,b2,rndm2);
-f_plus = subs(f_plus,b3,rndm3);
-
-
-f_minus = subs(f_minus,q1,40);
-f_minus = subs(f_minus,q3,63.9);
-f_minus = subs(f_minus,q2,70);
-f_minus = subs(f_minus,b1,rndm1);
-f_minus = subs(f_minus,b2,rndm2);
-f_minus = subs(f_minus,b3,rndm3);
-
-
-% Compute Gradient 
+
+% 1. Import effective quantities from CellSolver-Code:
+Qmat = spconvert(load('QMatrix.txt'));
+Qmat = full(Qmat)
+
+Bmat = spconvert(load('BMatrix.txt'));
+Bmat = full(Bmat)
+
+
+% Substitute effective quantitites
+f_plus = subs(f_plus,q1,Qmat(1,1));
+f_plus = subs(f_plus,q3,Qmat(3,3));
+f_plus = subs(f_plus,q2,Qmat(2,2));
+f_plus = subs(f_plus,b1,Bmat(1));
+f_plus = subs(f_plus,b2,Bmat(2));
+f_plus = subs(f_plus,b3,Bmat(3));
+% f_plus = subs(f_plus,b3,0);
+% 
+f_minus = subs(f_minus,q1,Qmat(1,1));
+f_minus = subs(f_minus,q3,Qmat(3,3));
+f_minus = subs(f_minus,q2,Qmat(2,2));
+f_minus = subs(f_minus,b1,Bmat(1));
+f_minus = subs(f_minus,b2,Bmat(2));
+f_minus = subs(f_minus,b3,Bmat(3));  
+% % f_minus = subs(f_minus,b3,0);         
+
+% 2. Substitute specific values:
+
+%%%Compare with 'ClassifyMin-Code'
+% % Compare with 'ClassifyMin-Code'
+% mu_1 = 1;
+% rho_1 = 1;
+% % --- type 1 Situation:
+% % beta = 2;
+% % alpha = 2;
+% % theta = 1/4;
+% % --- type 2 Situation:
+% % beta = 3.0714;
+% % alpha = -20;
+% % theta = 0.3;
+% % --- type 3 Situation:
+% % beta = 2.2857;
+% % alpha = -20;
+% % theta = 0.3;
+% 
+% % interesting: 
+% alpha = 18.3673;
+% beta = 8.57143;
+% theta= 0.913265;
+% 
+% % alpha = 2.85714;
+% % beta = 7;
+% % theta= 0.3;
+% 
+% 
+% 
+% set_mu_gamma = 'q1';
+% % set_mu_gamma = 'q2';
+% print_output = false;
+% 
+% q1i = mu_1.*(beta./(theta+(1-theta).*beta))
+% q2i = mu_1.*((1-theta)+theta.*beta)
+% q3i = q1i
+% % b1i = (mu_1*rho_1/4).*(beta./(theta+(1-theta).*beta)).*(1-theta.*(1+alpha))
+% % b2i =  mu_1.*(rho_1/8).*(1-theta.*(1+beta.*alpha))
+% b3i = 0
+% 
+% %TEST (new)
+% b1i = (3*rho_1/2).*beta.*(1-theta.*(1+alpha));
+% b2i = (3*rho_1/(4*((1-theta)+theta.*beta))).*(1-theta.*(1+beta.*alpha));
+% 
+% f_plus = subs(f_plus,q1,q1i);
+% f_plus = subs(f_plus,q3,q3i);
+% f_plus = subs(f_plus,q2,q2i);
+% f_plus = subs(f_plus,b1,b1i);
+% f_plus = subs(f_plus,b2,b2i);
+% f_plus = subs(f_plus,b3,b3i)
+% 
+% f_minus = subs(f_minus,q1,q1i);
+% f_minus = subs(f_minus,q3,q3i);
+% f_minus = subs(f_minus,q2,q2i);
+% f_minus = subs(f_minus,b1,b1i);
+% f_minus = subs(f_minus,b2,b2i);
+% f_minus = subs(f_minus,b3,b3i)
+% 
+% 
+% 
+% [A,angle,V] = classifyMIN(mu_1,rho_1,alpha,beta,theta,set_mu_gamma,print_output)
+
+% Substitute random values...
+% rndm1 = randi([1 20],1,1);
+% rndm2 = randi([1 20],1,1);
+% rndm3 = randi([1 20],1,1);
+% f_plus = subs(f_plus,b1,rndm1);
+% f_plus = subs(f_plus,b2,rndm2);
+% f_plus = subs(f_plus,b3,rndm3);
+
+% Compute the Gradients 
 df_plusx = diff(f_plus,v1);
 df_plusy = diff(f_plus,v2);
 
 df_minusx = diff(f_minus,v1);
 df_minusy = diff(f_minus,v2);
 
-
+% Setup Equations Grad(f) = 0 
 eq1 = df_plusx == 0;
 eq2 = df_plusy == 0;
-eqns = [eq1, eq2]
+eqns = [eq1, eq2];
 
 eq3 = df_minusx == 0;
 eq4 = df_minusy == 0;
-eqns_minus = [eq3, eq4]
+eqns_minus = [eq3, eq4];
+
+
+% Symbolically Solve Equations: 
 
+% More robust (works even for values b_3 ~ 1e-08 ): 
+S = solve(eqns,v1,v2,'MaxDegree' , 5);  
+S_minus = solve(eqns_minus,v1,v2,'MaxDegree' , 5);
+
+%Tests:
+% S = solve(eqns,v1,v2,'MaxDegree' , 5, 'Real', true);
+% S_minus = solve(eqns_minus,v1,v2,'MaxDegree' , 5, 'Real', true);
 
-S = solve(eqns,v1,v2,'MaxDegree' , 5, 'Real', true);
-S_minus = solve(eqns_minus,v1,v2,'MaxDegree' , 5, 'Real', true);
-% S = solve(eqns,v1,v2,'MaxDegree' , 5);
 % S = solve(eqns,v1,v2,'MaxDegree' , 5, 'IgnoreAnalyticConstraints',true);
 % S = solve(eqns,v1,v2,'MaxDegree' , 5, 'IgnoreAnalyticConstraints',true, 'Real', true);
 % S = solve(eqns)
 
-
 A = S.v1;
 B = S.v2;
 A_minus = S_minus.v1;
 B_minus = S_minus.v2;
 % A = simplify(A);
 % B = simplify(B)
-% S_minus = solve(eqns_minus,v1,v2);
-% S_minus.v1
-% S_minus.v2
-
-%---------- TEST ---------------------
-% r = subs(subs(df_plusx,v1,A(3)),v2,B(3));
-fprintf('Testing equation grad(f) = 0  with stationary points')
-double(subs(subs(df_plusx,v1,A(1)),v2,B(1)))
-double(subs(subs(df_plusx,v1,A(2)),v2,B(2)))
-double(subs(subs(df_plusx,v1,A(3)),v2,B(3)))
-% ------------------------------------
-
-
-
-
-
-fprintf('print stationary points of f_plus:')
-double(A)
-double(B)
-fprintf('print stationary points of f_minus:')
-double(A_minus)
-double(B_minus)
 
+%---------- TEST if Grad(f) = 0 ---------------------
+% fprintf('Testing equation grad(f) = 0  with stationary points')
+% 
+% for i = 1:size(A,1)
+%     fprintf('Testing %d.point (f_plus): ',i )
+%     [ double(subs(subs(df_plusx,v1,A(i)),v2,B(i))), double(subs(subs(df_plusy,v1,A(i)),v2,B(i))) ]
+% end
+% for i = 1:size(A_minus,1)
+%     fprintf('Testing %d.point (f_minus): ',i )
+%     [double(subs(subs(df_minusx,v1,A_minus(i)),v2,B_minus(i))), double(subs(subs(df_minusy,v1,A_minus(i)),v2,B_minus(i)))]
+% end
+% ------------------------------------
 
-% determine global Minimizer from stationary points:
-fprintf('function values at stationary points:')
+fprintf('stationary points of f_plus:')
+A = double(A);                                     %safe symbolic values
+B = double(B);
+fprintf('stationary points of f_minus:')
+A_minus = double(A_minus);
+B_minus = double(B_minus);
+
+% Extract only Real-Solutions
+fprintf('real stationary points of f_plus:')
+tmp1 = A(imag(A)==0 & imag(B) == 0);
+tmp2 = B(imag(A)==0 & imag(B) == 0);
+A = tmp1;
+B = tmp2;
+% A(abs(imag(A)) <1e-3  & abs(imag(B)) <1e-3 )
+SP_Plus = [A,B]
+
+fprintf('real stationary points of f_minus:')
+tmp1 = A_minus(imag(A_minus)==0 & imag(B_minus) == 0);
+tmp2 = B_minus(imag(A_minus)==0 & imag(B_minus) == 0);
+A_minus = tmp1;
+B_minus = tmp2;
+% A_minus(abs(imag(A_minus)) <1e-3  & abs(imag(B_minus)) <1e-3 )
+SP_Minus = [A_minus,B_minus]
+
+% Determine global Minimizer from stationary points:
+fprintf('function values at stationary points (f_plus):')
 T = arrayfun(@(v1,v2) double(f_plus(v1,v2,q1,q2,q3,b1,b2,b3)),A,B,'UniformOutput', false)
 T = cell2mat(T);
-Min_plus = min(T, [], 'all')
+% Min_plus = min(T, [], 'all')
+[Min_plus,MinIdx_plus] = min(T, [], 'all', 'linear');  
 
-
-% determine global Minimizer from stationary points:
-fprintf('function values at stationary points:')
+fprintf('function values at stationary points (f_minus):')
 T_minus = arrayfun(@(v1,v2) double(f_minus(v1,v2,q1,q2,q3,b1,b2,b3)),A_minus,B_minus,'UniformOutput', false)
 T_minus = cell2mat(T_minus);
-Min_minus = min(T_minus, [], 'all')
-
-globalMinimizerValue = min(Min_plus,Min_minus)
-
-% Plot function
+% Min_minus = min(T_minus, [], 'all')
+[Min_minus,MinIdx_minus] = min(T_minus, [], 'all', 'linear');   
+
+[globalMinimizerValue,GlobalIdx] = min([Min_plus,Min_minus]);
+ 
+if GlobalIdx == 1     %Min_plus
+    GlobalMinimizer = SP_Plus(MinIdx_plus,:);
+    sign = 1.0;
+elseif GlobalIdx == 2  %Min_minus 
+    GlobalMinimizer = SP_Minus(MinIdx_minus,:);
+    sign = -1.0;
+end
+
+fprintf('Global Minimizer:(%d,%d)', GlobalMinimizer(1),GlobalMinimizer(2) )
+fprintf('Global Minimizer Value : %d', globalMinimizerValue )
+
+% Plot functions
 fsurf(@(x,y) f_plus(x,y,q1,q2,q3,b1,b2,b3))
 hold on 
 plot3(A,B,T,'g*')
+%Plot GlobalMinimizer:
+hold on 
+plot3(GlobalMinimizer(1),GlobalMinimizer(2),globalMinimizerValue, 'o', 'Color','c')
 % view(90,0)
 % view(2)
 
-
 figure
 fsurf(@(x,y) f_minus(x,y,q1,q2,q3,b1,b2,b3))
 hold on
-plot3(A_minus,B_minus,T,'g*')
-
-
-
+plot3(A_minus,B_minus,T_minus,'g*')
+hold on 
+plot3(GlobalMinimizer(1),GlobalMinimizer(2),globalMinimizerValue, 'o', 'Color','c')
 
 
 %Write to txt-File
@@ -150,10 +248,113 @@ fileID = fopen('txt.txt','w');
 fprintf(fileID,'%s' , latex(S.v1));
 fclose(fileID);
 
-
-
-
-
+ 
+
+%%%Compare with 'ClassifyMin-Code'
+fprintf('----------------compare with ClassifyMIN----------------')
+fprintf('Output Minimizer Matrix from symbolic Minimization')
+
+sign*GlobalMinimizer'*GlobalMinimizer %sign correct?   should do this with symbolic Values! TODO
+% GlobalMinimizer'*GlobalMinimizer
+
+%check with higher Precision:
+% vpa(GlobalMinimizer'*GlobalMinimizer)
+
+
+% % 
+% % %Output from Classify Min:
+% % [A,angle,type,K] = classifyMIN(mu_1,rho_1,alpha,beta,theta,set_mu_gamma,print_output);
+% % fprintf('Output Minimizer Matrix from ClassifyMIN')
+% % 
+% % % [A(1) sign*sqrt(A(1)*A(2)) ; sign*sqrt(A(1)*A(2)) A(2)]  %sign correct?
+% % [A(1) sqrt(A(1)*A(2)) ; sqrt(A(1)*A(2)) A(2)]  %sign correct?
+% % 
+% % %check with higher Precision:
+% % % vpa([A(1) sqrt(A(1)*A(2)) ; sqrt(A(1)*A(2)) A(2)])
+% % 
+% % 
+% % e = [sqrt(A(1)), sqrt(A(2))];      %TODO .. this might be complex?!
+% % 
+% % norm = sqrt((A(1)+A(2)));
+% % 
+% % e = e./norm;
+% % 
+% % K*(e'*e)
+% % 
+% % % e'*e
+% % % K
+% % 
+% % fprintf('angle: %d', angle)
+% % fprintf('Type: %d', type)
+
+
+
+%% Compare with "Task2" 
+% fprintf('----------------compare with Task2----------------')
+% 
+% B = [b1i b3i; b3i b2i];
+% x = 0:0.01:2*pi;
+% 
+% y1 = arrayfun(@(alpha)compute_F(alpha,B,q1i,q2i,q3i),x,'UniformOutput', false);
+% y1 = cell2mat(y1);
+% 
+% 
+% figure 
+% plot(x,y1,'b')
+% hold on 
+% 
+% fun = @(a) compute_F(a,B,q1i,q2i,q3i);
+% [alphaMin,f] = fminunc(fun,0)
+% [alphaMin,f] = fminunc(fun,3)        % Different initial value
+% plot(alphaMin,f,'*')
+% 
+% %compute radius
+% rMin = compute_r(alphaMin,B,q1i,q2i,q3i)
+% 
+% %compute Minimizer:
+% v_alpha = [cos(alphaMin);sin(alphaMin)];
+% 
+% 
+% 
+% G = rMin.*(v_alpha*v_alpha')
+
+
+%%Determine Minimizer Type (in general case)
+% % T = [GlobalMinimizer' e1']
+% % det(T)  % also works?
+% %  
+% % 
+% % % symbolically : 
+% % 
+% % if GlobalIdx == 1     %Min_plus
+% %     A_sym = S.v1;
+% %     B_sym = S.v2
+% %     Index = MinIdx_plus;
+% % elseif GlobalIdx == 2  %Min_minus 
+% %     A_sym = S_minus.v1;
+% %     B_sym = S_minus.v2;
+% %     Index = MinIdx_minus;
+% % end
+% % 
+% % % Check Determinant symbolically?!?! 
+% % 
+% % g_sym = [A_sym(Index) B_sym(Index)]
+% % G_sym = g_sym'*g_sym
+% % 
+% % e1 = [1 0];
+% % e2 = [0 1];
+% % 
+% % % check alignment with e1
+% % % if .... 
+% % det([g_sym' e1'])
+% % % ... bending in e1 direction
+% % % check alignment with e2
+% % % if..
+% % det([g_sym' e2'])
+% % double(det([g_sym' e2']))
+% % % bending in e2 direction
+% % %Else 
+% % %.... 
 
 
 
diff --git a/Matlab-Programs/PhaseDiagrams.mlx b/Matlab-Programs/PhaseDiagrams.mlx
index 442621dedd7e8bb67ba0b65d289dca9cf144ccff..7e27b8bfff5acf86e08c65c356092134a349980f 100644
Binary files a/Matlab-Programs/PhaseDiagrams.mlx and b/Matlab-Programs/PhaseDiagrams.mlx differ
diff --git a/Matlab-Programs/QMatrix.txt b/Matlab-Programs/QMatrix.txt
deleted file mode 100644
index 93c6dfab22b0fb116a35458cff4c09fae26d535d..0000000000000000000000000000000000000000
--- a/Matlab-Programs/QMatrix.txt
+++ /dev/null
@@ -1,9 +0,0 @@
-1 1 1.90510815738902228
-1 2 2.60132454317226442e-26
-1 3 -4.93750948541723109e-11
-2 1 -5.99537621698159769e-27
-2 2 2.08333333333341164
-2 3 -2.82386576263450663e-18
-3 1 -2.16574525495542866e-10
-3 2 -2.82386567902393238e-18
-3 3 1.92269764555762257
diff --git a/Matlab-Programs/classifyMIN.m b/Matlab-Programs/classifyMIN.m
index 5ec2594fa8ef98c0db1ba4e9ec5b10a20f7d53c4..3f36a2c467886e782a7dcb1c90deff09a0e3b576 100755
--- a/Matlab-Programs/classifyMIN.m
+++ b/Matlab-Programs/classifyMIN.m
@@ -38,12 +38,12 @@ q3 = mu_gamma(b,t);
 % assert((q1 > 0 ) & (q2 > 0 ) & (q3 > 0), 'At least one of q1,q2 or q3 is not positive' )
 
 
-% Compute components of B_eff
-b1 = (mu_1*rho_1/4).*(b./(t+(1-t).*b)).*(1-t.*(1+a));
-b2 =  mu_1.*(rho_1/8).*(1-t.*(1+b.*a));
+% Compute components of B_eff (old)
+% b1 = (mu_1*rho_1/4).*(b./(t+(1-t).*b)).*(1-t.*(1+a));
+% b2 =  mu_1.*(rho_1/8).*(1-t.*(1+b.*a));
 
 %TEST (new)
-b1 = (3*rho_1/2).*b.*(1-t.*(1+a));
+b1 =  (3*rho_1/2).*b.*(1-t.*(1+a));
 b2 =  (3*rho_1./(4.*((1-t)+t.*b))).*(1-t.*(1+b.*a));
 
 
@@ -169,20 +169,109 @@ end
 
 
 % Compute a3 from a1 % a2
-a3 = sqrt(2*a1*a2);
+a3 = sqrt(2*a1*a2);                    % WRONG ? 
 
 
 
 
 % compute angle between [sqrt(a1) , sqrt(a2)] and e1:
 % angle = atan2(sqrt(a2),sqrt(a1));
+
+v = [sqrt(a1), sqrt(a2)];
+e1 = [1 0];
+
 if (type == 3 )
-   angle = atan2(a2,a1);
+%    angle = atan2(a2,a1);
+%    angle = acos(v*e1/(sqrt(a1+a2)));
 else
    angle = 0;
 end
 % angle = atan2(norm(cross(a,b)), dot(a,b))
 
+% Try to compute angle of Matrices
+
+E1 = [1 0;0 0 ];
+% V = [a1 sqrt(a1*a2)/sqrt(2); sqrt(a1*a2)/sqrt(2) a2]; % This ?? NO
+
+V = [a1 sqrt(a1*a2); sqrt(a1*a2) a2];         % This!
+
+% CHECK
+% U = trace(V'*E1)/(sqrt(trace(V'*V))*sqrt(trace(E1'*E1)))   
+% if abs(U) > 1
+%    fprintf('value greater 1') 
+% end
+
+
+% angle = atan2(sqrt(abs(a2)), sqrt(abs(a1)));   % does this make sense? 
+
+
+
+% angle = acos(trace(V'*E1)/(sqrt(trace(V'*V))*sqrt(trace(E1'*E1))));    %angle in radians
+% angle = acos(trace(V'*E1)/(sqrt(trace(V'*V))*sqrt(trace(E1'*E1))))/pi * 180; % angle in degrees
+
+
+% CHECK does case (0,-b) ever happen?  Yes 
+% if  (q2*b2^2 > q1*b1^2 && b2 < 0)
+%     fprintf('point lies on negative half of y-axis'); 
+% end
+
+
+
+% CHECK if Minimizer ever lies inside lambda ... YES 
+% if  (a1 ~= 0 && a2 ~= 0)
+%     fprintf('minimizer lies inside lambda'); 
+% end
+
+
+% Alternative atan2d(y,x): returns angle in degrees 
+
+
+% CHECK
+e = [sqrt(a1), sqrt(a2)];        % Might be complex...
+norm = sqrt(a1+a2);              % Might be complex...
+e = e./norm;
+angle = atan2(e(2), e(1));   %TEST
+
+if (imag(e(1))~= 0 || imag(e(2))~=0)
+   fprintf('complex vector e'); 
+end
+
+% if (imag(norm)~=0)
+%    fprintf('complex norm'); % happens a lot .. 
+% end
+
+
+% do it this way to avoid complex numbers: 
+e = [sqrt((a1/(a1+a2))), sqrt((a2/(a1+a2)))];    % always positive under sqrt here .. basically takes absolute value here
+angle = atan2(e(2), e(1)); 
+
+
+if (imag(e(1))~= 0 || imag(e(2))~=0)
+   fprintf('complex vector e'); 
+end
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% TEST  -------------------
+% the magnitude kappa of the vector does not matter for the angle ..
+% In order to also get negative angles just use:
+% atan2(a2,a1) 
+
+% angle = atan2(a2,a1);         %% FEHLER : muss [sqrt(a1) sqrt(a2)] betrachten..
+% angle = atan2(sqrt(a2),sqrt(a1));  % Inputs must be real... 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+% angle2 = acos(e(1)/(sqrt(e(1)^2 + e(2)^2) ));
+% if angle ~= angle2
+%    interesting = 1; 
+% end
+
+% if (angle ~= 0 | angle ~= 3.1416)
+%    fprintf('angle not zero or pi.. plot type')
+%    type  
+%    angle
+% end
 
 %compute Kappa? 
 % fprintf('Output Kappa:')
diff --git a/Matlab-Programs/plotBeff.mlx b/Matlab-Programs/plotBeff.mlx
index 32562683181f97166a2aeee4dc5c4071645268c0..1f5b30055f865b716cc709f858780d7a1c73aee5 100644
Binary files a/Matlab-Programs/plotBeff.mlx and b/Matlab-Programs/plotBeff.mlx differ
diff --git a/Matlab-Programs/txt.txt b/Matlab-Programs/txt.txt
deleted file mode 100644
index 9f084d89ea0d1caa1412409af116f686d900e2bb..0000000000000000000000000000000000000000
--- a/Matlab-Programs/txt.txt
+++ /dev/null
@@ -1 +0,0 @@
-\left(\begin{array}{c} \frac{2476481930565655\,\sqrt{2}\,\sqrt{\frac{7236321}{513284}-\frac{90489364076808055029099312\,\sqrt{73011132837436776744575999668362869808\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}-50337392659754784557384084350662671\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{2/3}+2630010951307735848\,\sqrt{805988923034412626385945162553118395785305}+15098162394174825647557249560747700608744}-62387727378614246819519\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}\,\sqrt{73011132837436776744575999668362869808\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}-50337392659754784557384084350662671\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{2/3}+2630010951307735848\,\sqrt{805988923034412626385945162553118395785305}+15098162394174825647557249560747700608744}+2169106763648607037448\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{2/3}\,\sqrt{73011132837436776744575999668362869808\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}-50337392659754784557384084350662671\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{2/3}+2630010951307735848\,\sqrt{805988923034412626385945162553118395785305}+15098162394174825647557249560747700608744}-1084553381824303518724\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}\,\sqrt{\frac{2169106763648607037448\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{2/3}-62387727378614246819519\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}+90489364076808055029099312}{1084553381824303518724\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}}}\,\sqrt{-\frac{411785266187684483115013018801761512433206452075313127077544\,\sqrt{\frac{22622341019202013757274828}{271138345456075879681\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}}+2\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}-\frac{3788817572159}{65865116164}}-111520498974074812466515182290068769048594814721898561225904\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}+76887605058380361711501131344236721718108169343073828023\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{2/3}+8950700537173950699474115226947926504\,\sqrt{805988923034412626385945162553118395785305}\,\sqrt{\frac{22622341019202013757274828}{271138345456075879681\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}}+2\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{2187673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37736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}+76887605058380361711501131344236721718108169343073828023\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{2/3}+8950700537173950699474115226947926504\,\sqrt{805988923034412626385945162553118395785305}\,\sqrt{\frac{22622341019202013757274828}{271138345456075879681\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}}+2\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}-\frac{3788817572159}{65865116164}}-1538031129882303371646823345410352858641651541697995618320\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}\,\sqrt{\frac{22622341019202013757274828}{271138345456075879681\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}}+2\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}-\frac{3788817572159}{65865116164}}+16935646475695605713506954032500091913111194620506369490\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{2/3}\,\sqrt{\frac{22622341019202013757274828}{271138345456075879681\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}}+2\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}-\frac{3788817572159}{65865116164}}+414174835296574096940990442846306573203402344369024\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{4/3}\,\sqrt{\frac{22622341019202013757274828}{271138345456075879681\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}}+2\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}-\frac{3788817572159}{65865116164}}-4017197408101699179435052119313143176424\,\sqrt{805988923034412626385945162553118395785305}-311199428002124515362917427982565568\,\sqrt{805988923034412626385945162553118395785305}\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}\,\sqrt{\frac{22622341019202013757274828}{271138345456075879681\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}}+2\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}-\frac{3788817572159}{65865116164}}-23061614555946679442195315529794967892415503959611221162504872}{59163142998964508\,\sqrt{\frac{22622341019202013757274828}{271138345456075879681\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}}+2\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}-\frac{3788817572159}{65865116164}}}}}{2169106763648607037448\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}\,\sqrt{\frac{22622341019202013757274828}{271138345456075879681\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}}+2\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}-\frac{3788817572159}{65865116164}}\,\sqrt{73011132837436776744575999668362869808\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{1/3}-50337392659754784557384084350662671\,{\left(\frac{2561945191461\,\sqrt{805988923034412626385945162553118395785305}}{1704844437736186534870734449}+\frac{1887270299271853205944656195093462576093}{218767343094745192341147515230129}\right)}^{2/3}+2630010951307735848\,\sqrt{805988923034412626385945162553118395785305}+15098162394174825647557249560747700608744}}\right)}^{7/2}}{57697562236314309552} \end{array}\right)
\ No newline at end of file
diff --git a/dune-microstructure.kdev4 b/dune-microstructure.kdev4
deleted file mode 100644
index deb877a1db8588964e5c8b3e77e12a0c7f64b598..0000000000000000000000000000000000000000
--- a/dune-microstructure.kdev4
+++ /dev/null
@@ -1,4 +0,0 @@
-[Project]
-CreatedFrom=CMakeLists.txt
-Manager=KDevCMakeManager
-Name=dune-microstructure
diff --git a/dune/microstructure/matrix_operations.hh b/dune/microstructure/matrix_operations.hh
index c67423e6369ea1a3dc19de60ec612ccdf74a284a..018e09a70312d4c32d1f88aa9d0b86216ca0b4d0 100644
--- a/dune/microstructure/matrix_operations.hh
+++ b/dune/microstructure/matrix_operations.hh
@@ -17,6 +17,19 @@ namespace MatrixOperations {
 	        Id[i][i]=1.0;
 	    return Id;
 	}
+	
+	
+    static double norm(VectorRT v){
+		return sqrt(pow(v[0],2) + pow(v[1],2) + pow(v[2],2));
+	}
+
+	static double norm(MatrixRT M){
+		return sqrt(
+			  pow(M[0][0],2) + pow(M[0][1],2) + pow(M[0][2],2)
+			+ pow(M[1][0],2) + pow(M[1][1],2) + pow(M[1][2],2)
+			+ pow(M[2][0],2) + pow(M[2][1],2) + pow(M[2][2],2));
+	}
+	
 
 	static MatrixRT sym (MatrixRT M) { // 1/2 (M^T + M)
     	MatrixRT ret(0);
@@ -80,6 +93,25 @@ namespace MatrixOperations {
 		return t1 + t2;
 	}
 
+    // --- Generalization: Define Quadratic QuadraticForm
+    
+    static double QuadraticForm(const double mu, const double lambda, const MatrixRT M){
+        
+        auto tmp1 = sym(M);
+        double tmp2 = norm(tmp1);
+        return lambda*std::pow(trace(M),2) + 2*mu*pow( tmp2 ,2);
+//         return lambda*std::pow(trace(M),2) + 2*mu*pow( norm( sym(M) ),2);
+    }
+
+    
+	static double generalizedDensity(const double mu, const double lambda, MatrixRT F, MatrixRT G){
+     /// Write this whole File as a Class that uses lambda,mu as members ? 
+        
+     // Define L via Polarization-Identity from QuadratifForm
+     // <LF,G> := (1/2)*(Q(F+G) - Q(F) - Q(G) ) 
+        return (1.0/2.0)*(QuadraticForm(mu,lambda,F+G) - QuadraticForm(mu,lambda,F) - QuadraticForm(mu,lambda,G) );
+    }
+
 	static MatrixRT matrixSqrt(MatrixRT M){
 		std::cout << "matrixSqrt not implemented!!!" << std::endl;//implement this
 		return M;
@@ -97,16 +129,7 @@ namespace MatrixOperations {
 		return cos(phi)*x1 + sin(phi)*x2 > 0;
 	}
 
-	static double norm(VectorRT v){
-		return sqrt(pow(v[0],2) + pow(v[1],2) + pow(v[2],2));
-	}
 
-	static double norm(MatrixRT M){
-		return sqrt(
-			  pow(M[0][0],2) + pow(M[0][1],2) + pow(M[0][2],2)
-			+ pow(M[1][0],2) + pow(M[1][1],2) + pow(M[1][2],2)
-			+ pow(M[2][0],2) + pow(M[2][1],2) + pow(M[2][2],2));
-	}
 
 	/*
 	template<double phi>
diff --git a/dune/microstructure/prestrain_material_geometry.hh b/dune/microstructure/prestrain_material_geometry.hh
index 2ceacb0e89613a710395c1f3d85031e57f56f682..8e429bf0683bdfa3e3db803d3388329f78d2cd39 100644
--- a/dune/microstructure/prestrain_material_geometry.hh
+++ b/dune/microstructure/prestrain_material_geometry.hh
@@ -35,7 +35,7 @@ public:
 
     FuncScalar getMu(ParameterTree parameters){
 
-    	std::string imp =  parameters.get<std::string>("material_implementation");
+    	std::string imp = parameters.get<std::string>("material_implementation", "analytical_Example");
     	//std::array<std::string,5> imps({"homogen_poisson" "bilayer_poisson" "chess_poisson" "3Dchess_poisson" "vertical_bilayer_poisson"});
         
     	double phi = M_PI*parameters.get<double>("material_angle", 0.0)/180; //TODO 
@@ -48,8 +48,7 @@ public:
     	if (imp == "homogeneous"){    
 		    double mu     = parameters.get<double>("mu", 10);
 
-		    auto muTerm = [mu] (const Domain& z) {
-		      return mu;};
+		    auto muTerm = [mu] (const Domain& z) {return mu;};
 		    
 			return muTerm;
 		}
@@ -59,7 +58,6 @@ public:
 		    double mu2 = beta*mu1;
 		    
 		   auto muTerm = [mu1, mu2, theta] (const Domain& z) {
-               
 //                     std::cout << "Analytical-MU is used" << std::endl;
                     if (abs(z[0]) >= (theta/2.0))                                                   
                         return mu1;
@@ -120,6 +118,8 @@ public:
                 FieldVector<double,3> s = {x[0]+domainShift, x[1]+domainShift, x[2]+domainShift};
 //                 std::cout << "matrixMaterial-MU is used" << std::endl;
                 
+                double output;
+                
                 // determine if point is in upper/lower Layer
                 if ( 0  <= s[2] && s[2] <= 1.0/2.0) // upper Layer
                 {
@@ -134,10 +134,13 @@ public:
 //                             printvector(std::cout, Fcenter, "Fcenter" , "--");
 //                             
                             if(sqrt(pow(s[0]-Fcenter[0],2)+pow(s[2]-Fcenter[1],2)) <= rF )
-                                return mu2;                                                         //richtig so? Fiber hat tendenziell größeres mu? 
+                                output = mu2;
+//                                 return mu2;                                                         //richtig so? Fiber hat tendenziell größeres mu? 
                             else
-                                return mu1;
+                                output = mu1;
+//                                 return mu1;
                         }
+                        else {}
                     }
                 }
                 else  // lower Layer
@@ -153,14 +156,17 @@ public:
 //                             printvector(std::cout, Fcenter, "Fcenter" , "--");
                             
                             if(sqrt(pow(s[0]-Fcenter[0],2)+pow(s[2]-Fcenter[1],2)) <= rF )
-                                return mu2;                                                         //richtig so? Fiber hat tendenziell größeres mu? 
+                                output = mu2;
+//                                 return mu2;                                                         //richtig so? Fiber hat tendenziell größeres mu? 
                             else
-                                return mu1;
+                                output = mu1;
+//                                 return mu1;
                         }
+                        else{}
                     }
 
                 }
-
+                return output;
             };
             return muTerm;
         }
@@ -186,6 +192,7 @@ public:
                 // shift x to domain [0,1]^3
                 FieldVector<double,3> s = {x[0]+domainShift, x[1]+domainShift, x[2]+domainShift};
 //                 std::cout << "matrixMaterial-MU is used" << std::endl;
+                double output;
                 
                 // determine if point is in upper/lower Layer
                 if ( 0  <= s[2] && s[2] <= 1.0/2.0) // upper Layer
@@ -201,9 +208,11 @@ public:
 //                             printvector(std::cout, Fcenter, "Fcenter" , "--");
 //                             
                             if(std::max( abs(s[0]-Fcenter[0]), abs(s[2]-Fcenter[1])  ) <= rF )
-                                return mu2;                                                         //richtig so? Fiber hat tendenziell größeres mu? 
+                                output = mu2;
+//                                 return mu2;                                                         //richtig so? Fiber hat tendenziell größeres mu? 
                             else
-                                return mu1;
+                                output = mu1;
+//                                 return mu1;
                         }
                     }
                 }
@@ -220,14 +229,15 @@ public:
 //                             printvector(std::cout, Fcenter, "Fcenter" , "--");
                             
                             if(std::max( abs(s[0]-Fcenter[0]), abs(s[2]-Fcenter[1])  ) <= rF )
-                                return mu2;                                                         //richtig so? Fiber hat tendenziell größeres mu? 
+                                output = mu2;
+//                                 return mu2;                                                         //richtig so? Fiber hat tendenziell größeres mu? 
                             else
-                                return mu1;
+                                output = mu1;
+//                                 return mu1;
                         }
                     }
-
                 }
-
+                return output;
             };
             return muTerm;
         }
@@ -237,10 +247,11 @@ public:
 		    double mu2 = beta*mu1;
 		    
 		    auto muTerm = [mu1, mu2, phi] (const Domain& z) {
-		      if ( isInRotatedPlane(phi, z[dim-2], z[dim-1])  )
+		      if (isInRotatedPlane(phi, z[dim-2], z[dim-1]))
 		        return mu1;
 		      else
-		        return mu2; };
+		        return mu2; 
+            };
 		    
 			return muTerm;
 		}
@@ -363,7 +374,7 @@ public:
 	FuncScalar getLambda(ParameterTree parameters)
     {
 
-		std::string imp =  parameters.get<std::string>("material_implementation");
+		std::string imp = parameters.get<std::string>("material_implementation", "analytical_Example");
 		//std::array<std::string,5> imps({"homogen_poisson" "bilayer_poisson" "chess_poisson" "3Dchess_poisson" "vertical_bilayer_poisson"});
     	//int i_imp =  parameters.get<int>("impnumber");
     	//std::string imp =  imps[i_imp];
@@ -437,6 +448,7 @@ public:
             int nF    = parameters.get<int>("nF", 2);    //number of Fibers in each Layer
             double rF = parameters.get<double>("rF", 0.5*(width/(2.0*nF)) );   //default: half of the max-fiber-radius mrF = (width/(2.0*nF)) 
             
+            
 
             assert( (2*rF)*nF <= width && (height/4)+rF <= height); //check that fibers are not bigger than Domain
             
@@ -449,6 +461,7 @@ public:
                 // shift x to domain [0,1]^3
                 FieldVector<double,3> s = {x[0]+domainShift, x[1]+domainShift, x[2]+domainShift};
 //                 std::cout << "matrixMaterial-MU is used" << std::endl;
+                double output;
                 
                 // determine if point is in upper/lower Layer
                 if ( 0  <= s[2] && s[2] <= 1.0/2.0) // upper Layer
@@ -464,9 +477,11 @@ public:
 //                             printvector(std::cout, Fcenter, "Fcenter" , "--");
 //                             
                             if(sqrt(pow(s[0]-Fcenter[0],2)+pow(s[2]-Fcenter[1],2)) <= rF )
-                                return lambda2;                                                         //richtig so? Fiber hat tendenziell größeres mu? 
+                                output = lambda2;
+//                                 return lambda2;                                                         //richtig so? Fiber hat tendenziell größeres mu? 
                             else
-                                return lambda1;
+                                output = lambda1;
+//                                 return lambda1;
                         }
                     }
                 }
@@ -483,14 +498,16 @@ public:
 //                             printvector(std::cout, Fcenter, "Fcenter" , "--");
                             
                             if(sqrt(pow(s[0]-Fcenter[0],2)+pow(s[2]-Fcenter[1],2)) <= rF )
-                                return lambda2;                                                         //richtig so? Fiber hat tendenziell größeres mu? 
+                                output = lambda2;
+//                                 return lambda2;                                                         //richtig so? Fiber hat tendenziell größeres mu? 
                             else
-                                return lambda1;
+                                output = lambda1;
+//                                 return lambda1;
                         }
                     }
 
                 }
-
+                return output;
             };
             return lambdaTerm;
         }
@@ -503,8 +520,6 @@ public:
             int nF    = parameters.get<int>("nF", 2);    //number of Fibers in each Layer
             double rF = parameters.get<double>("rF", 0.5*(width/(2.0*nF)) );   //default: half of the max-fiber-radius mrF = (width/(2.0*nF)) 
             
-            
-            
             assert( (2*rF)*nF <= width && (height/4)+rF <= height); //check that fibers are not bigger than Domain
             
             auto lambdaTerm = [lambda1,lambda2, theta,nF,rF,height,width] (const Domain& x)                
@@ -516,6 +531,7 @@ public:
                 // shift x to domain [0,1]^3
                 FieldVector<double,3> s = {x[0]+domainShift, x[1]+domainShift, x[2]+domainShift};
 //                 std::cout << "matrixMaterial-MU is used" << std::endl;
+                double output;
                 
                 // determine if point is in upper/lower Layer
                 if ( 0  <= s[2] && s[2] <= 1.0/2.0) // upper Layer
@@ -531,9 +547,11 @@ public:
 //                             printvector(std::cout, Fcenter, "Fcenter" , "--");
 //                             
                             if(std::max( abs(s[0]-Fcenter[0]), abs(s[2]-Fcenter[1])  ) <= rF )
-                                return lambda2;                                                         //richtig so? Fiber hat tendenziell größeres mu? 
+                                output = lambda2;
+//                                 return lambda2;                                                         //richtig so? Fiber hat tendenziell größeres mu? 
                             else
-                                return lambda1;
+                                output = lambda1;
+//                                 return lambda1;
                         }
                     }
                 }
@@ -550,14 +568,15 @@ public:
 //                             printvector(std::cout, Fcenter, "Fcenter" , "--");
                             
                             if(std::max( abs(s[0]-Fcenter[0]), abs(s[2]-Fcenter[1])  ) <= rF )
-                                return lambda2;                                                         //richtig so? Fiber hat tendenziell größeres mu? 
+                                output = lambda2;
+//                                 return lambda2;                                                         //richtig so? Fiber hat tendenziell größeres mu? 
                             else
-                                return lambda1;
+                                output = lambda1;
+//                                 return lambda1;
                         }
                     }
-
                 }
-
+                return output;
             };
             return lambdaTerm;
         }
@@ -708,7 +727,7 @@ public:
 
 
 
-
+// TODO  add log here? 
 
 
 
@@ -758,7 +777,7 @@ public:
             {             
                 if (abs(x[0]) > (theta/2)  && x[2] > 0)
                     return MatrixRT{{p1, 0.0 , 0.0}, {0.0, p1, 0.0}, {0.0, 0.0, p1}};
-                if (abs(x[0]) < (theta/2)  && x[2] < 0)
+                else if (abs(x[0]) < (theta/2)  && x[2] < 0)
                     return MatrixRT{{p2, 0.0 , 0.0}, {0.0, p2, 0.0}, {0.0, 0.0, p2}};
                 else
                     return MatrixRT{{0.0, 0.0 , 0.0}, {0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}};
@@ -818,6 +837,8 @@ public:
                 double domainShift = 0.0;
                 // shift x to domain [0,1]^3
                 FieldVector<double,3> s = {x[0]+domainShift, x[1]+domainShift, x[2]+domainShift};
+                
+                MatrixRT output;
 
                 // determine if point is in upper/lower Layer
                 if ((0.0 <= s[2] && s[2] <= 1.0/2.0)) // upperLayer
@@ -830,9 +851,11 @@ public:
                             FieldVector<double,2> Fcenter = { (1.0/(2.0*nF))+((1.0/double(nF))*i)-(1.0/2.0) , 1.0/4.0};
 //                             
                             if(sqrt(pow(s[0]-Fcenter[0],2)+pow(s[2]-Fcenter[1],2)) <= rF )
-                                return MatrixRT{{p1, 0.0 , 0.0}, {0.0, p1, 0.0}, {0.0, 0.0, p1}};
+                                output = MatrixRT{{p1, 0.0 , 0.0}, {0.0, p1, 0.0}, {0.0, 0.0, p1}};
+//                                 return MatrixRT{{p1, 0.0 , 0.0}, {0.0, p1, 0.0}, {0.0, 0.0, p1}};
                             else
-                                return MatrixRT{{0.0, 0.0 , 0.0}, {0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}};
+                                output = MatrixRT{{0.0, 0.0 , 0.0}, {0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}};
+//                                 return MatrixRT{{0.0, 0.0 , 0.0}, {0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}};
 //                                 return MatrixRT{{p2, 0.0 , 0.0}, {0.0, p2, 0.0}, {0.0, 0.0, p2}};
                         }
                     }
@@ -847,19 +870,22 @@ public:
                             FieldVector<double,2> Fcenter = { (1.0/(2.0*nF))+((1.0/double(nF))*i)-(1.0/2.0) , -1.0/4.0};
     
                             if(sqrt(pow(s[0]-Fcenter[0],2)+pow(s[2]-Fcenter[1],2)) <= rF )
-                                return MatrixRT{{p1, 0.0 , 0.0}, {0.0, p1, 0.0}, {0.0, 0.0, p1}};
+                                output = MatrixRT{{p1, 0.0 , 0.0}, {0.0, p1, 0.0}, {0.0, 0.0, p1}};
+//                                 return MatrixRT{{p1, 0.0 , 0.0}, {0.0, p1, 0.0}, {0.0, 0.0, p1}};
                             else
-                                return MatrixRT{{0.0, 0.0 , 0.0}, {0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}};
+                                output = MatrixRT{{0.0, 0.0 , 0.0}, {0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}};
+//                                 return MatrixRT{{0.0, 0.0 , 0.0}, {0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}};
 //                                 return MatrixRT{{p2, 0.0 , 0.0}, {0.0, p2, 0.0}, {0.0, 0.0, p2}};
                         }
                     }
 
                 }
-
+                return output;
             };
             std::cout <<" Prestrain Type: matrix_material"<< std::endl;
             return B;
         }
+        
         else if (imp == "matrix_material_squares")   // Matrix material with prestrained Fiber inclusions
         {
             int nF    = parameters.get<int>("nF", 3);    //number of Fibers in each Layer
@@ -874,6 +900,8 @@ public:
                 double domainShift = 0.0;
                 // shift x to domain [0,1]^3
                 FieldVector<double,3> s = {x[0]+domainShift, x[1]+domainShift, x[2]+domainShift};
+                
+                MatrixRT output;
 
                 // determine if point is in upper/lower Layer
                 if ((0.0 <= s[2] && s[2] <= 1.0/2.0)) // upperLayer
@@ -886,9 +914,11 @@ public:
                             FieldVector<double,2> Fcenter = { (1.0/(2.0*nF))+((1.0/double(nF))*i)-(1.0/2.0) , 1.0/4.0};
 //                             
                             if(std::max( abs(s[0]-Fcenter[0]), abs(s[2]-Fcenter[1])  ) <= rF )
-                                return MatrixRT{{p1, 0.0 , 0.0}, {0.0, p1, 0.0}, {0.0, 0.0, p1}};
+                                output = MatrixRT{{p1, 0.0 , 0.0}, {0.0, p1, 0.0}, {0.0, 0.0, p1}};
+//                                 return MatrixRT{{p1, 0.0 , 0.0}, {0.0, p1, 0.0}, {0.0, 0.0, p1}};
                             else
-                                return MatrixRT{{0.0, 0.0 , 0.0}, {0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}};
+                                output = MatrixRT{{0.0, 0.0 , 0.0}, {0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}};
+//                                 return MatrixRT{{0.0, 0.0 , 0.0}, {0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}};
 //                                 return MatrixRT{{p2, 0.0 , 0.0}, {0.0, p2, 0.0}, {0.0, 0.0, p2}};
                         }
                     }
@@ -903,15 +933,17 @@ public:
                             FieldVector<double,2> Fcenter = { (1.0/(2.0*nF))+((1.0/double(nF))*i)-(1.0/2.0) , -1.0/4.0};
     
                             if(std::max( abs(s[0]-Fcenter[0]), abs(s[2]-Fcenter[1])  ) <= rF )
-                                return MatrixRT{{p1, 0.0 , 0.0}, {0.0, p1, 0.0}, {0.0, 0.0, p1}};
+                                output = MatrixRT{{p1, 0.0 , 0.0}, {0.0, p1, 0.0}, {0.0, 0.0, p1}};
+//                                 return MatrixRT{{p1, 0.0 , 0.0}, {0.0, p1, 0.0}, {0.0, 0.0, p1}};
                             else
-                                return MatrixRT{{0.0, 0.0 , 0.0}, {0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}};
+                                output = MatrixRT{{0.0, 0.0 , 0.0}, {0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}};
+//                                 return MatrixRT{{0.0, 0.0 , 0.0}, {0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}};
 //                                 return MatrixRT{{p2, 0.0 , 0.0}, {0.0, p2, 0.0}, {0.0, 0.0, p2}};
                         }
                     }
 
                 }
-
+                return output;
             };
             std::cout <<" Prestrain Type: matrix_material"<< std::endl;
             return B;
@@ -922,6 +954,8 @@ public:
             
         }
         // TODO ANISOTROPIC PRESSURE
+        
+
     }
     
     
diff --git a/dune/microstructure/prestrainimp.hh b/dune/microstructure/prestrainimp.hh
index a3b68f0ac447e22c71d26f880cef65fbe58f5ed0..443de31641e6406e5702a52621ab49606ddb0d07 100644
--- a/dune/microstructure/prestrainimp.hh
+++ b/dune/microstructure/prestrainimp.hh
@@ -49,7 +49,7 @@ public:
     	if (imp==1)
     	{
 
-            Func2Tensor B1_ = [this] (const Domain& x) {              // ISOTROPIC PRESSURE
+            Func2Tensor B1_ = [this] (const Domain& x) {              //  ISOTROPIC PRESSURE
                 if (abs(x[0]) > (theta/2)  && x[2] > 0)
                     return MatrixRT{{p1, 0.0 , 0.0}, {0.0, p1, 0.0}, {0.0, 0.0, p1}};
                 if (abs(x[0]) < (theta/2)  && x[2] < 0)
@@ -63,7 +63,7 @@ public:
         }
         else if (imp==2)
         {
-            Func2Tensor B2_ = [this] (const Domain& x) {              // ISOTROPIC PRESSURE
+            Func2Tensor B2_ = [this] (const Domain& x) {              // Bilayer with one rectangular Fiber & ISOTROPIC PRESSURE    
 
                 if (abs(x[0]) < (theta/2) && x[2] < 0 && x[2] > -(1.0/2.0) )
                     return MatrixRT{{p1, 0.0 , 0.0}, {0.0, p1, 0.0}, {0.0, 0.0, p1}};
diff --git a/inputs/cellsolver.parset b/inputs/cellsolver.parset
index 42b9e10fe0b1121156c4be9fea1fd07994dd123f..464c4fe6628e5a0747096b1f8bacc8a515243e7c 100644
--- a/inputs/cellsolver.parset
+++ b/inputs/cellsolver.parset
@@ -2,8 +2,8 @@
 
 #path for logfile
 #outputPath = "../../outputs/output.txt"
-outputPath = "/home/klaus/Desktop/DUNE/dune-microstructure/outputs/output.txt"
-
+#outputPath = "/home/klaus/Desktop/DUNE/dune-microstructure/outputs/output.txt"
+#outputPath = "/home/klaus/Desktop/DUNE/dune-microstructure/outputs"
 
 #############################################
 #  Debug Output
@@ -31,7 +31,7 @@ cellDomain = 1
 ########################################################################
 
 #numLevels =  1 3   # computes all levels from first to second entry
-numLevels = 2 2     # computes all levels from first to second entry
+numLevels = 3 3     # computes all levels from first to second entry
 #numLevels = 1 6
 
 
@@ -55,7 +55,7 @@ numLevels = 2 2     # computes all levels from first to second entry
 
 #gamma=50.0
 #gamma=1.0
-gamma=51.0
+gamma=0.01
 
 #############################################
 #  Material parameters
@@ -71,11 +71,14 @@ lambda1 = 0.0
 #lambda1 = 20.0 
 #lambda1 = 5.0 
 
+####  material_implementation("analytical_Example") ? 
+
+
 material_implementation = "analytical_Example"
-#material_implementation = "isotropic_bilayer"
+#material_implementation ="isotropic_bilayer"
 
-#material_implementation = "matrix_material_circles"
-#material_implementation = "matrix_material_squares"
+#material_implementation ="matrix_material_circles"
+#material_implementation ="matrix_material_squares"
 
 #material_implementation = "circle_fiber"    #TEST
 #material_implementation = "square_fiber"    #TEST
@@ -114,31 +117,14 @@ height = 1.0
 # Prestrain Types: 
 
 #1 Isotropic Pressure
-    Func2Tensor B1_ = [this] (const Domain& x) {              // ISOTROPIC PRESSURE
-                if (abs(x[0]) > (theta/2)  && x[2] > 0)
-                    return MatrixRT{{p1, 0.0 , 0.0}, {0.0, p1, 0.0}, {0.0, 0.0, p1}};
-                if (abs(x[0]) < (theta/2)  && x[2] < 0)
-                    return MatrixRT{{p2, 0.0 , 0.0}, {0.0, p2, 0.0}, {0.0, 0.0, p2}};
-                else
-                    return MatrixRT{{0.0, 0.0 , 0.0}, {0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}};
-
-            };
-
-
-
-#2 Isotropic Pressure
-
-Func2Tensor B2_ = [this] (const Domain& x) {              // ISOTROPIC PRESSURE
-
-                if (abs(x[0]) < (theta/2) && x[2] < 0 && x[2] > -(1.0/2.0) )
-                    return MatrixRT{{p1, 0.0 , 0.0}, {0.0, p1, 0.0}, {0.0, 0.0, p1}};
-                else
-                    return MatrixRT{{0.0, 0.0 , 0.0}, {0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}};
-
-
-            };
-
-
+#    Func2Tensor B1_ = [this] (const Domain& x) {              // ISOTROPIC PRESSURE
+#                if (abs(x[0]) > (theta/2)  && x[2] > 0)
+#                    return MatrixRT{{p1, 0.0 , 0.0}, {0.0, p1, 0.0}, {0.0, 0.0, p1}};
+#                if (abs(x[0]) < (theta/2)  && x[2] < 0)
+#                    return MatrixRT{{p2, 0.0 , 0.0}, {0.0, p2, 0.0}, {0.0, 0.0, p2}};
+#                else
+#                    return MatrixRT{{0.0, 0.0 , 0.0}, {0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}};
+#            };
 
 
 #############################################
@@ -151,8 +137,8 @@ set_IntegralZero = true
 #arbitraryLocalIndex = 7
 #arbitraryElementNumber = 3
 
-arbitraryLocalIndex = 0
-arbitraryElementNumber = 0
+#arbitraryLocalIndex = 0
+#arbitraryElementNumber = 0
 
 
 #############################################
diff --git a/outputs/debugLog.txt b/outputs/debugLog.txt
deleted file mode 100644
index e69de29bb2d1d6434b8b29ae775ad8c2e48c5391..0000000000000000000000000000000000000000
diff --git a/outputs/output.txt b/outputs/output.txt
index 5800dd61c928f56f450a2aab60b5de00506d71d7..9fb153f078416fb83b087c1ff1c7b9b159f12c34 100644
--- a/outputs/output.txt
+++ b/outputs/output.txt
@@ -1,57 +1,69 @@
-prestrain imp: 2
-rho1 = 1
-rho2 = 2
-alpha: 2
-gamma: 50
-Number of Elements in each direction: [15,15,15]
+----- Input Parameters -----: 
+alpha: 5
+gamma: 0.01
+theta: 0.25
 beta: 2
 material parameters: 
 mu1: 10
 mu2: 20
 lambda1: 0
-lambda2:0
-size of FiniteElementBasis: 10800
+lambda2: 0
+----------------------------: 
+Number of Elements in each direction: [8,8,8]
+size of FiniteElementBasis: 1728
+Solver-type used:  CG-Solver
+---------- OUTPUT ----------
+ --------------------
 Corrector-Matrix M_1: 
--8.73326e-10 3.3873e-09 0
-3.3873e-09 -9.35729e-22 0
+-4.7875e-09 1.11201e-09 0
+1.11201e-09 -1.65324e-21 0
 0 0 0
 
  --------------------
 Corrector-Matrix M_2: 
--1.20023e-25 -9.12937e-18 0
--9.12937e-18 1.96361e-17 0
+1.04621e-25 -1.08615e-20 0
+-1.08615e-20 -9.4846e-18 0
 0 0 0
 
  --------------------
 Corrector-Matrix M_3: 
--1.352e-11 -3.15777e-12 0
--3.15777e-12 -3.55246e-18 0
+1.94872e-09 -9.19575e-10 0
+-9.19575e-10 2.93022e-20 0
 0 0 0
 
+ --------------------
+Effective Matrix Q: 
+2.08099 -5.09371e-24 2.86003e-10
+7.68785e-25 2.08333 -5.64259e-22
+-7.27118e-09 -5.65834e-22 2.08306
 
-Solution of Corrector problems:
-Computed Matrix Q: 
-1.97452 3.06664e-22 1.73925e-11
--2.77279e-25 2.16049 1.34612e-18
--8.52488e-12 1.3461e-18 1.97454
-
-Computed prestrain B_hat: 
--0.922995 -1.48056 -1.03062e-07
-Computed prestrain B_eff: 
--0.467452 -0.68529 -5.21975e-08
-computed q1: 1.97452
-computed q2: 2.16049
-computed q3: 1.97454
-computed b1: -0.467452
-computed b2: -0.68529
-computed b3: -5.21975e-08
-computed b1_hat: -0.922995
-computed b2_hat: -1.48056
-computed b3_hat: -1.03062e-07
- --- analytic solutions: --- 
-b1 : -0.882353
-b2 : -1.5
-b3 : 0
-q1 : 1.96078
-q2 : 2.16667
+--- Prestrain Output --- 
+B_hat: -1.24298 -1.25 2.78718e-08
+B_eff: -0.597302 -0.6 1.12953e-08 (Effective Prestrain)
+------------------------ 
+q1: 2.08099
+q2: 2.08333
+q3: 2.08306
+effective b1: -0.597302
+effective b2: -0.6
+effective b3: 1.12953e-08
+b1_hat: -1.24298
+b2_hat: -1.25
+b3_hat: 2.78718e-08
+mu_gamma=2.08306
+----- print analytic solutions -----
+b1_hat_ana : -0.714286
+b2_hat_ana : -1.25
+b3_hat_ana : 0
+b1_eff_ana : -0.375
+b2_eff_ana : -0.6
+b3_eff_ana : 0
+q1_ana : 1.90476
+q2_ana : 2.08333
 q3 should be between q1 and q2
+   Levels    |  L2SymError  |    Order     |  L2SymNorm   | L2SNorm_ana  |    L2Norm    | 
+------------------------------------------------------------------------------------------
+     3       & 7.09613e-02  & 0.00000e+00  & 8.19784e-03  & 7.14286e-02  & 5.58336e-03  & 
+  Levels     | |q1_ana-q1|  | |q2_ana-q2|  |      q3      | |b1_ana-b1|  | |b2_ana-b2|  | |b3_ana-b3|  | 
+---------------------------------------------------------------------------------------------------------
+     3       & 1.76231e-01  & 8.88178e-15  & 2.08306e+00  & 2.22302e-01  & 2.44249e-15  & 1.12953e-08  & 
diff --git a/outputs/output20x20x20.txt b/outputs/output20x20x20.txt
deleted file mode 100644
index 24404acda473b1d76a8abc20d6f9f503c038fa53..0000000000000000000000000000000000000000
--- a/outputs/output20x20x20.txt
+++ /dev/null
@@ -1,57 +0,0 @@
-prestrain imp: 2
-rho1 = 1
-rho2 = 2
-alpha: 2
-gamma: 50
-Number of Elements in each direction: [20,20,20]
-beta: 2
-material parameters: 
-mu1: 10
-mu2: 20
-lambda1: 0
-lambda2:0
-size feBasis: 25200
-Corrector-Matrix M_1: 
-1.923e-10 8.39184e-10 0
-8.39184e-10 5.15403e-21 0
-0 0 0
-
- --------------------
-Corrector-Matrix M_2: 
-2.39727e-23 -4.18818e-17 0
--4.18818e-17 4.08491e-18 0
-0 0 0
-
- --------------------
-Corrector-Matrix M_3: 
-2.71269e-11 -2.81909e-12 0
--2.81909e-12 -1.6844e-17 0
-0 0 0
-
-
-Solution of Corrector problems:
-Computed Matrix Q: 
-1.96078 3.32328e-21 2.38035e-11
-1.20763e-25 2.16667 1.18138e-18
-1.23313e-11 1.18136e-18 1.9608
-
-Computed prestrain B_hat: 
--0.882353 -1.5 -7.19027e-08
-Computed prestrain B_eff: 
--0.45 -0.692308 -3.66673e-08
-computed q1: 1.96078
-computed q2: 2.16667
-computed q3: 1.9608
-computed b1: -0.45
-computed b2: -0.692308
-computed b3: -3.66673e-08
-computed b1_hat: -0.882353
-computed b2_hat: -1.5
-computed b3_hat: -7.19027e-08
- --- analytic solutions: --- 
-b1 : -0.882353
-b2 : -1.5
-b3 : 0
-q1 : 1.96078
-q2 : 2.16667
-q3 should be between q1 and q2
diff --git a/src/.dune-microstructure.cc.kate-swp b/src/.dune-microstructure.cc.kate-swp
deleted file mode 100644
index ab134f664ac0f18ef9713f78c53389e793de0692..0000000000000000000000000000000000000000
Binary files a/src/.dune-microstructure.cc.kate-swp and /dev/null differ
diff --git a/src/dune-microstructure.cc b/src/dune-microstructure.cc
index 639d22e39a5e0dbb0d2a9a50fbcd452039c25c45..d820b453d1197dcf8689aebb83363d84b2296ab1 100644
--- a/src/dune-microstructure.cc
+++ b/src/dune-microstructure.cc
@@ -852,11 +852,17 @@ int main(int argc, char *argv[])
 
   // Output setter
 //   std::string outputPath = parameterSet.get("outputPath", "../../outputs/output.txt");
-  std::string outputPath = parameterSet.get("outputPath", "/home/klaus/Desktop/DUNE/dune-microstructure/outputs/output.txt");
+//   std::string outputPath = parameterSet.get("outputPath", "/home/klaus/Desktop/DUNE/dune-microstructure/outputs/output.txt");
+  std::string outputPath = parameterSet.get("outputPath", "/home/klaus/Desktop/DUNE/dune-microstructure/outputs");
+//   std::string MatlabPath = parameterSet.get("MatlabPath", "/home/klaus/Desktop/DUNE/dune-microstructure/Matlab-Programs");
 //     std::string outputPath = "/home/klaus/Desktop/DUNE/dune-microstructure/outputs/output.txt";
   std::fstream log;
-  log.open(outputPath ,std::ios::out);
+  log.open(outputPath + "/output.txt" ,std::ios::out);
 
+  std::cout << "outputPath:" << outputPath << std::endl;
+  
+//   parameterSet.report(log); // short Alternativ
+  
   
   constexpr int dim = 3;
   constexpr int dimWorld = 3;
@@ -897,15 +903,16 @@ int main(int argc, char *argv[])
   auto prestrainImp = PrestrainImp(); //NEW 
   auto B_Term = prestrainImp.getPrestrain(parameterSet);
 
+  log << "----- Input Parameters -----: " << std::endl;
 //   log << "prestrain imp: " <<  prestraintype << "\nrho1 = " << rho1 << "\nrho2 = " << rho2  << std::endl;
   log << "alpha: " << alpha << std::endl;
-  log << "OUTPUT GAMMA-----: " << std::endl;
   log << "gamma: " << gamma << std::endl;
   log << "theta: " << theta << std::endl;
   log << "beta: " << beta << std::endl;
   log << "material parameters: " << std::endl;
   log << "mu1: " << mu1 << "\nmu2: " << mu2 << std::endl;
-  log << "lambda1: " << lambda1 <<"\nlambda2:" << lambda2 << std::endl;
+  log << "lambda1: " << lambda1 <<"\nlambda2: " << lambda2 << std::endl;
+  log << "----------------------------: " << std::endl;
 
   ///////////////////////////////////
   // Generate the grid
@@ -930,7 +937,6 @@ int main(int argc, char *argv[])
   ///////////////////////////////////
   // Create Data Storage
   ///////////////////////////////////
-  
   // Storage:: #1 level #2 L2SymError #3 L2SymErrorOrder #4  L2Norm(sym) #5 L2Norm(sym-analytic) #6 L2Norm(phi_1)
   std::vector<std::variant<std::string, size_t , double>> Storage_Error;
   
@@ -1165,7 +1171,7 @@ int main(int argc, char *argv[])
         solver.apply(x_2, load_alpha2, statistics);
         std::cout << "solve linear system for x_3.\n";
         solver.apply(x_3, load_alpha3, statistics);
-        log << "Solver-type used: " <<"\n CG-Solver" << std::endl;
+        log << "Solver-type used: " <<" CG-Solver" << std::endl;
     }
     ////////////////////////////////////////////////////////////////////////////////////
 
@@ -1196,7 +1202,7 @@ int main(int argc, char *argv[])
         solver.apply(x_1, load_alpha1, statistics);
         solver.apply(x_2, load_alpha2, statistics);
         solver.apply(x_3, load_alpha3, statistics);
-        log << "Solver-type used: " <<"\n GMRES-Solver" << std::endl;
+        log << "Solver-type used: " <<" GMRES-Solver" << std::endl;
     }
     ////////////////////////////////////////////////////////////////////////////////////
     else if ( Solvertype == 3)// QR - SOLVER
@@ -1212,7 +1218,7 @@ int main(int argc, char *argv[])
         sPQR.apply(x_1, load_alpha1, statisticsQR);
         sPQR.apply(x_2, load_alpha2, statisticsQR);
         sPQR.apply(x_3, load_alpha3, statisticsQR);
-        log << "Solver-type used: " <<"\n QR-Solver" << std::endl;
+        log << "Solver-type used: " <<" QR-Solver" << std::endl;
     }
     //     printvector(std::cout, load_alpha1BS, "load_alpha1 before SOLVER", "--" );
     //     printvector(std::cout, load_alpha1, "load_alpha1 AFTER SOLVER", "--" );
@@ -1259,12 +1265,14 @@ int main(int argc, char *argv[])
     printmatrix(std::cout, M_1, "Corrector-Matrix M_1", "--");
     printmatrix(std::cout, M_2, "Corrector-Matrix M_2", "--");
     printmatrix(std::cout, M_3, "Corrector-Matrix M_3", "--");
+    log << "---------- OUTPUT ----------" << std::endl;
+    log << " --------------------" << std::endl;
     log << "Corrector-Matrix M_1: \n" << M_1 << std::endl;
     log << " --------------------" << std::endl;
     log << "Corrector-Matrix M_2: \n" << M_2 << std::endl;
     log << " --------------------" << std::endl;
     log << "Corrector-Matrix M_3: \n" << M_3 << std::endl;
-
+    log << " --------------------" << std::endl;
 
     ////////////////////////////////////////////////////////////////////////////
     // Substract Integral-mean
@@ -1305,9 +1313,10 @@ int main(int argc, char *argv[])
     /////////////////////////////////////////////////////////
     // Write Solution (Corrector Coefficients) in Logs
     /////////////////////////////////////////////////////////
-    log << "\nSolution of Corrector problems:\n";
+//     log << "\nSolution of Corrector problems:\n";
     if(write_corrector_phi1)
     {
+        log << "\nSolution of Corrector problems:\n";
         log << "\n Corrector_phi1:\n";
         log << x_1 << std::endl;
     }
@@ -1377,7 +1386,7 @@ int main(int argc, char *argv[])
             }
         }
     printmatrix(std::cout, Q, "Matrix Q", "--");
-    log << "Computed Matrix Q: " << std::endl;
+    log << "Effective Matrix Q: " << std::endl;
     log << Q << std::endl;
 
     // compute B_hat
@@ -1392,8 +1401,10 @@ int main(int argc, char *argv[])
             std::cout << "check this Contribution: " << (coeffContainer[a]*tmp2) << std::endl;  //see orthotropic.tex
         }
     }
-    log << "Computed prestrain B_hat: " << std::endl;
-    log << B_hat << std::endl;
+
+//     log << B_hat << std::endl;
+//     log << "Prestrain B_hat: " << std::endl;
+//     log << B_hat << std::endl;
 
     std::cout << "check this Contribution: " << (coeffContainer[2]*tmp2) << std::endl;  //see orthotropic.tex
 
@@ -1402,17 +1413,23 @@ int main(int argc, char *argv[])
     //////////////////////////////
     FieldVector<double, 3> Beff;
     Q.solve(Beff,B_hat);
-    log << "Computed prestrain B_eff: " << std::endl;
-    log << Beff << std::endl;
+    
+    log << "--- Prestrain Output --- " << std::endl;
+    log << "B_hat: " << B_hat << std::endl;
+    log << "B_eff: " << Beff <<  " (Effective Prestrain)" << std::endl;
+    log << "------------------------ " << std::endl;
+//     log << Beff << std::endl;
+//     log << "Effective Prestrain B_eff: " << std::endl;
+//     log << Beff << std::endl;
 //     printvector(std::cout, Beff, "Beff", "--");
 
-    auto q1_c = Q[0][0];
-    auto q2_c = Q[1][1];
-    auto q3_c = Q[2][2];
+    auto q1 = Q[0][0];
+    auto q2 = Q[1][1];
+    auto q3 = Q[2][2];
     
-    std::cout<< "q1_c: " << q1_c << std::endl;
-    std::cout<< "q2_c: " << q2_c << std::endl;
-    std::cout<< "q3_c: " << q3_c << std::endl;
+    std::cout<< "q1 : " << q1 << std::endl;
+    std::cout<< "q2 : " << q2 << std::endl;
+    std::cout<< "q3 : " << q3 << std::endl;
 //     std::cout<< "b1hat_c: " << B_hat[0] << std::endl;
 //     std::cout<< "b2hat_c: " << B_hat[1] << std::endl;
 //     std::cout<< "b3hat_c: " << B_hat[2] << std::endl;
@@ -1425,33 +1442,33 @@ int main(int argc, char *argv[])
     std::cout << "Theta: " << theta << std::endl;
     std::cout << "Gamma: " << gamma << std::endl;
     std::cout << "Number of Elements in each direction: " << nElements << std::endl;
-    log << "computed q1: " << q1_c << std::endl;
-    log << "computed q2: " << q2_c << std::endl;
-    log << "computed q3: " << q3_c << std::endl;
-    log << "mu_gamma=" << q3_c << std::endl;           // added for Python-Script
-    log << "computed b1: " << Beff[0] << std::endl;
-    log << "computed b2: " << Beff[1] << std::endl;
-    log << "computed b3: " << Beff[2] << std::endl;
-    log << "computed b1_hat: " << B_hat[0] << std::endl;
-    log << "computed b2_hat: " << B_hat[1] << std::endl;
-    log << "computed b3_hat: " << B_hat[2] << std::endl;
+    log << "q1: " << q1 << std::endl;
+    log << "q2: " << q2 << std::endl;
+    log << "q3: " << q3 << std::endl;
     
+    log << "effective b1: " << Beff[0] << std::endl;
+    log << "effective b2: " << Beff[1] << std::endl;
+    log << "effective b3: " << Beff[2] << std::endl;
+    log << "b1_hat: " << B_hat[0] << std::endl;
+    log << "b2_hat: " << B_hat[1] << std::endl;
+    log << "b3_hat: " << B_hat[2] << std::endl;
+    log << "mu_gamma=" << q3 << std::endl;           // added for Python-Script
 
     //////////////////////////////////////////////////////////////
     // Define Analytic Solutions
     //////////////////////////////////////////////////////////////
     // double b1 = (mu1*p1/4)*(beta/(theta+(1-theta)*beta))*(1-theta*(1+alpha));
     // double b2 = (mu1*p1/8)*(1-theta*(1+beta*alpha));
-    double b1_hat = (-(theta/4.0)*mu1*mu2)/(theta*mu1+(1.0-theta)*mu2);
-    double b2_hat = -(theta/4.0)*mu2;
-    double b3_hat = 0.0;
+    double b1_hat_ana = (-(theta/4.0)*mu1*mu2)/(theta*mu1+(1.0-theta)*mu2);
+    double b2_hat_ana = -(theta/4.0)*mu2;
+    double b3_hat_ana = 0.0;
    
-    double b1_eff = (-3.0/2.0)*theta;
-    double b2_eff = (-3.0/2.0)*(theta*mu2)/(mu1*(1-theta)+mu2*theta);
-    double b3_eff = 0.0;
+    double b1_eff_ana = (-3.0/2.0)*theta;
+    double b2_eff_ana = (-3.0/2.0)*(theta*mu2)/(mu1*(1-theta)+mu2*theta);
+    double b3_eff_ana = 0.0;
     
-    double q1 = ((mu1*mu2)/6.0)/(theta*mu1+ (1.0- theta)*mu2);
-    double q2 = ((1.0-theta)*mu1+theta*mu2)/6.0;
+    double q1_ana = ((mu1*mu2)/6.0)/(theta*mu1+ (1.0- theta)*mu2);
+    double q2_ana = ((1.0-theta)*mu1+theta*mu2)/6.0;
     
     
     
@@ -1462,34 +1479,34 @@ int main(int argc, char *argv[])
     
     std::cout << ((3.0*p1)/2.0)*beta*(1-(theta*(1+alpha)))   << std::endl;  // TODO ERROR in paper ?? 
 
-    std::cout << " --- print analytic solutions --- " << std::endl;
-    std::cout << "b1_hat : " << b1_hat << std::endl;
-    std::cout << "b2_hat : " << b2_hat << std::endl;
-    std::cout << "b3_hat : " << b3_hat << std::endl;
-    std::cout << "b1_eff : " << b1_eff << std::endl;
-    std::cout << "b2_eff : " << b2_eff << std::endl;
-    std::cout << "b3_eff : " << b3_eff << std::endl;
+    std::cout << "----- print analytic solutions -----" << std::endl;
+    std::cout << "b1_hat_ana : " << b1_hat_ana << std::endl;
+    std::cout << "b2_hat_ana : " << b2_hat_ana << std::endl;
+    std::cout << "b3_hat_ana : " << b3_hat_ana << std::endl;
+    std::cout << "b1_eff_ana : " << b1_eff_ana << std::endl;
+    std::cout << "b2_eff_ana : " << b2_eff_ana << std::endl;
+    std::cout << "b3_eff_ana : " << b3_eff_ana << std::endl;
     
-    std::cout << "q1 : "     << q1 << std::endl;
-    std::cout << "q2 : "     << q2 << std::endl;
+    std::cout << "q1_ana : "     << q1_ana << std::endl;
+    std::cout << "q2_ana : "     << q2_ana << std::endl;
     std::cout << "q3 should be between q1 and q2"  << std::endl;
-    log << " --- analytic solutions: --- " << std::endl;
-    log << "b1_hat : " << b1_hat << std::endl;
-    log << "b2_hat : " << b2_hat << std::endl;
-    log << "b3_hat : " << b3_hat << std::endl;
-    log << "b1_eff : " << b1_eff << std::endl;
-    log << "b2_eff : " << b2_eff << std::endl;
-    log << "b3_eff : " << b3_eff << std::endl;
-    log << "q1 : "     << q1 << std::endl;
-    log << "q2 : "     << q2 << std::endl;
+    log << "----- print analytic solutions -----" << std::endl;
+    log << "b1_hat_ana : " << b1_hat_ana << std::endl;
+    log << "b2_hat_ana : " << b2_hat_ana << std::endl;
+    log << "b3_hat_ana : " << b3_hat_ana << std::endl;
+    log << "b1_eff_ana : " << b1_eff_ana << std::endl;
+    log << "b2_eff_ana : " << b2_eff_ana << std::endl;
+    log << "b3_eff_ana : " << b3_eff_ana << std::endl;
+    log << "q1_ana : "     << q1_ana << std::endl;
+    log << "q2_ana : "     << q2_ana << std::endl;
     log << "q3 should be between q1 and q2"  << std::endl;
     
-    Storage_Quantities.push_back(std::abs(q1 - q1_c));
-    Storage_Quantities.push_back(std::abs(q2 - q2_c));
-    Storage_Quantities.push_back( q3_c );
-    Storage_Quantities.push_back(std::abs(b1_eff - Beff[0]));
-    Storage_Quantities.push_back(std::abs(b2_eff - Beff[1]));
-    Storage_Quantities.push_back(std::abs(b3_eff - Beff[2]));
+    Storage_Quantities.push_back(std::abs(q1_ana - q1));
+    Storage_Quantities.push_back(std::abs(q2_ana - q2));
+    Storage_Quantities.push_back( q3 );
+    Storage_Quantities.push_back(std::abs(b1_eff_ana - Beff[0]));
+    Storage_Quantities.push_back(std::abs(b2_eff_ana - Beff[1]));
+    Storage_Quantities.push_back(std::abs(b3_eff_ana - Beff[2]));
 
     auto symPhi_1_analytic = [mu1, mu2, theta, muTerm] (const Domain& x) {
                         return MatrixRT{{  (((mu1*mu2)/((theta*mu1 +(1-theta)*mu2)*muTerm(x))) - 1)*x[2] , 0.0, 0.0}, {0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}};
@@ -1501,31 +1518,31 @@ int main(int argc, char *argv[])
 
     if(write_L2Error)
     {
-        std::cout << " ----- L2ErrorSym ----" << std::endl;
+//         std::cout << " ----- L2ErrorSym ----" << std::endl;
         auto L2SymError = computeL2SymError(Basis_CE,phi_1,gamma,symPhi_1_analytic);
-        std::cout << "L2SymError: " << L2SymError << std::endl;
-        std::cout << " -----------------" << std::endl;
+//         std::cout << "L2SymError: " << L2SymError << std::endl;
+//         std::cout << " -----------------" << std::endl;
 
-        std::cout << " ----- L2NORMSym ----" << std::endl;
+//         std::cout << " ----- L2NORMSym ----" << std::endl;
         auto L2Norm_Symphi = computeL2SymError(Basis_CE,phi_1,gamma,zeroFunction);                           
-        std::cout << "L2-Norm(Symphi_1): " << L2Norm_Symphi << std::endl;           
+//         std::cout << "L2-Norm(Symphi_1): " << L2Norm_Symphi << std::endl;           
         VectorCT zeroVec;
         zeroVec.resize(Basis_CE.size());
         zeroVec = 0;
         auto L2Norm_SymAnalytic = computeL2SymError(Basis_CE,zeroVec ,gamma, symPhi_1_analytic);
-        std::cout << "L2-Norm(SymAnalytic): " << L2Norm_SymAnalytic << std::endl;
-        std::cout << " -----------------" << std::endl;
+//         std::cout << "L2-Norm(SymAnalytic): " << L2Norm_SymAnalytic << std::endl;
+//         std::cout << " -----------------" << std::endl;
 
-        std::cout << " ----- L2NORM ----" << std::endl;
+//         std::cout << " ----- L2NORM ----" << std::endl;
         auto L2Norm = computeL2Norm(Basis_CE,phi_1);
-        std::cout << "L2Norm(phi_1): "  << L2Norm << std::endl;
-        std::cout << " -----------------" << std::endl;
+//         std::cout << "L2Norm(phi_1): "  << L2Norm << std::endl;
+//         std::cout << " -----------------" << std::endl;
         
         
         
-        log << "L2-Error (symmetric Gradient phi_1):" << L2SymError << std::endl;
-        log << "L2-Norm(Symphi_1): "    << L2Norm_Symphi<< std::endl;
-        log << "L2-Norm(SymAnalytic): " << L2Norm_SymAnalytic << std::endl;
+//         log << "L2-Error (symmetric Gradient phi_1):" << L2SymError << std::endl;
+//         log << "L2-Norm(Symphi_1): "    << L2Norm_Symphi<< std::endl;
+//         log << "L2-Norm(SymAnalytic): " << L2Norm_SymAnalytic << std::endl;
 
         double EOC = 0.0;
         Storage_Error.push_back(L2SymError);
@@ -1553,17 +1570,14 @@ int main(int argc, char *argv[])
   //////////////////////////////////////////////////////////////////////////////////////////////
   // Write Data to Matlab / Optimization-Code
   //////////////////////////////////////////////////////////////////////////////////////////////
-
-//   writeMatrixToMatlab(Q, "matlab.txt");
-  writeMatrixToMatlab(Q, "../../Matlab-Programs/QMatrix.txt");
-  
+//   writeMatrixToMatlab(Q, "../../Matlab-Programs/QMatrix.txt");
+  writeMatrixToMatlab(Q, outputPath + "/QMatrix.txt");
   
   // write effective Prestrain in Matrix for Output
-  
   FieldMatrix<double,1,3> BeffMat;
-  
   BeffMat[0] = Beff;
-  writeMatrixToMatlab(BeffMat, "../../Matlab-Programs/BMatrix.txt");
+//   writeMatrixToMatlab(BeffMat, "../../Matlab-Programs/BMatrix.txt");
+  writeMatrixToMatlab(BeffMat, outputPath + "/BMatrix.txt");
   
   //////////////////////////////////////////////////////////////////////////////////////////////
   // Write result to VTK file
@@ -1581,7 +1595,8 @@ int main(int argc, char *argv[])
   vtkWriter.addVertexData(
     correctorFunction_3,
     VTK::FieldInfo("Corrector phi_3 level"+ std::to_string(level) , VTK::FieldInfo::Type::vector, dim));
-  vtkWriter.write( VTKOutputName  + "-level"+ std::to_string(level));
+//   vtkWriter.write( VTKOutputName  + "-level"+ std::to_string(level));
+  vtkWriter.pwrite( VTKOutputName  + "-level"+ std::to_string(level), outputPath, "");
   std::cout << "wrote data to file: " + VTKOutputName + "-level" + std::to_string(level) << std::endl;      
 
   
@@ -1693,20 +1708,20 @@ int main(int argc, char *argv[])
 
     //////////////// OUTPUT QUANTITIES TABLE //////////////
     std::cout << center("Levels ",tableWidth)       << " | "
-              << center("|q1-q1_c|",tableWidth)       << " | "
-              << center("|q2-q2_c|",tableWidth)       << " | "
+              << center("|q1_ana-q1|",tableWidth)       << " | "
+              << center("|q2_ana-q2|",tableWidth)       << " | "
               << center(" q3_c",tableWidth)           << " | "
-              << center("|b1-b1_c|",tableWidth)       << " | "
-              << center("|b2-b2_c|",tableWidth)       << " | "
-              << center("|b3-b3_c|",tableWidth)       << " | " << "\n";
+              << center("|b1_ana-b1|",tableWidth)       << " | "
+              << center("|b2_ana-b2|",tableWidth)       << " | "
+              << center("|b3_ana-b3|",tableWidth)       << " | " << "\n";
     std::cout << std::string(tableWidth*7 + 3*7, '-') << "\n";
     log       << center("Levels ",tableWidth)       << " | "
-              << center("|q1-q1_c|",tableWidth)       << " | "
-              << center("|q2-q2_c|",tableWidth)       << " | "
-              << center(" q3_c",tableWidth)           << " | "
-              << center("|b1-b1_c|",tableWidth)       << " | "
-              << center("|b2-b2_c|",tableWidth)       << " | "
-              << center("|b3-b3_c|",tableWidth)       << " | " << "\n";
+              << center("|q1_ana-q1|",tableWidth)       << " | "
+              << center("|q2_ana-q2|",tableWidth)       << " | "
+              << center(" q3",tableWidth)           << " | "
+              << center("|b1_ana-b1|",tableWidth)       << " | "
+              << center("|b2_ana-b2|",tableWidth)       << " | "
+              << center("|b3_ana-b3|",tableWidth)       << " | " << "\n";
     log       << std::string(tableWidth*7 + 3*7, '-') << "\n";
     
     int StorageCount2 = 0;
@@ -1721,8 +1736,6 @@ int main(int argc, char *argv[])
             log << std::endl;
         }
     }
-    log << "OUTPUT GAMMA-----: " << std::endl;
-    log << "gamma: " << gamma << std::endl;
 
     log.close();
 }