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Aland, Sebastian
amdis
Commits
5a71c46a
Commit
5a71c46a
authored
Sep 05, 2012
by
Praetorius, Simon
Browse files
Coefficients for rosenbrock methods corrected
parent
c1eca4e2
Changes
1
Hide whitespace changes
Inline
Side-by-side
AMDiS/src/time/RosenbrockMethod.cc
View file @
5a71c46a
...
...
@@ -47,21 +47,21 @@ namespace AMDiS {
createData
();
// b
1
(2) = 0.5
// b
1
(1) = 1-b
1
(2) = 0.5
// alpha(2,1) = 1/(2*b
1
(2)) = 1
// b(2) = 0.5
// b(1) = 1-b(2) = 0.5
// alpha(2,1) = 1/(2*b(2)) = 1
// gamma = 1+1/sqrt(2) = 1.707...
// gamma(2,1) = -gamma/b
1
(2) = -3.41421356237309
// b
2
(1) = 1
// b
2
(2) = 0
// gamma(2,1) = -gamma/b(2) = -3.41421356237309
// b
_
(1) = 1
// b
_
(2) = 0
a
[
0
][
0
]
=
0.0
;
a
[
1
][
0
]
=
5.857864376269050e-01
;
a
[
1
][
1
]
=
a
[
1
][
0
]
;
a
[
1
][
1
]
=
1.0
;
c
[
0
][
0
]
=
gamma
;
c
[
1
][
0
]
=
-
1.171572875253810e+00
;
c
[
1
][
1
]
=
c
[
1
][
0
]
+
gamma
;
c
[
1
][
1
]
=
-
gamma
;
m1
[
0
]
=
8.786796564403575e-01
;
m1
[
1
]
=
2.928932188134525e-01
;
...
...
@@ -87,11 +87,11 @@ namespace AMDiS {
a
[
2
][
0
]
=
1.605996252195329e+00
;
a
[
2
][
2
]
=
0.7
;
c
[
0
][
0
]
=
0.435866521508459
;
c
[
1
][
0
]
=
8.874044410657833e-01
;
c
[
0
][
0
]
=
gamma
;
c
[
1
][
0
]
=
8.874044410657833e-01
;
c
[
1
][
1
]
=
0.604455284065559
;
c
[
2
][
0
]
=
2.398747971635036e+01
;
c
[
2
][
1
]
=
5.263722371562129e+00
;
c
[
2
][
0
]
=
2.398747971635036e+01
;
c
[
2
][
1
]
=
5.263722371562129e+00
;
c
[
2
][
2
]
=
6.37978879934488
;
m1
[
0
]
=
2.236727045296590e+00
;
...
...
@@ -114,26 +114,26 @@ namespace AMDiS {
createData
();
a
[
0
][
0
]
=
0.0
;
a
[
1
][
0
]
=
1.26794919243112
;
a
[
1
][
0
]
=
1.26794919243112
3
;
a
[
1
][
1
]
=
1.0
;
a
[
2
][
0
]
=
1.26794919243112
;
a
[
2
][
0
]
=
1.26794919243112
3
;
a
[
2
][
1
]
=
0.0
;
a
[
2
][
2
]
=
1.0
;
c
[
0
][
0
]
=
0.788675134594813
;
c
[
1
][
0
]
=
-
1.6076951545867
4
;
c
[
1
][
1
]
=
-
0.211324865405187
;
c
[
2
][
0
]
=
-
3.46410161513775
;
c
[
2
][
1
]
=
-
1.7320508075688
8
;
c
[
2
][
2
]
=
-
1.0773502691896
3
;
c
[
0
][
0
]
=
gamma
;
c
[
1
][
0
]
=
-
1.6076951545867
36
;
c
[
1
][
1
]
=
-
0.211324865405187
1
;
c
[
2
][
0
]
=
-
3.46410161513775
5
;
c
[
2
][
1
]
=
-
1.7320508075688
77
;
c
[
2
][
2
]
=
-
1.0773502691896
26
;
m1
[
0
]
=
2.0
;
m1
[
1
]
=
0.577350269189625
;
m1
[
2
]
=
0.422649730810374
;
m1
[
1
]
=
0.577350269189625
8
;
m1
[
2
]
=
0.422649730810374
2
;
m2
[
0
]
=
2.11324865405187
;
m2
[
0
]
=
2.11324865405187
1
;
m2
[
1
]
=
1.0
;
m2
[
2
]
=
0.422649730810374
;
m2
[
2
]
=
0.422649730810374
2
;
MSG
(
"Rosenbrock scheme Ros3p
\n
"
);
}
...
...
@@ -143,26 +143,25 @@ namespace AMDiS {
{
order
=
4
;
stages
=
6
;
gamma
=
2.5e-01
;
gamma
=
0.25
;
createData
();
a
[
0
][
0
]
=
0.0
;
a
[
1
][
0
]
=
3.0
;
//
a[1][1] =
a
[
1
][
1
]
=
0.75
;
a
[
2
][
0
]
=
1.831036793486759e+00
;
a
[
2
][
1
]
=
4.955183967433795e-01
;
//
a[2][2] =
a
[
2
][
2
]
=
0.21
;
a
[
3
][
0
]
=
2.304376582692669e+00
;
a
[
3
][
1
]
=
-
5.249275245743001e-02
;
a
[
3
][
2
]
=
-
1.176798761832782e+00
;
//
a[3][3] =
a
[
3
][
3
]
=
0.63
;
a
[
4
][
0
]
=
-
7.170454962423025e+00
;
a
[
4
][
1
]
=
-
4.741636671481786e+00
;
a
[
4
][
2
]
=
-
1.631002631330971e+01
;
a
[
4
][
3
]
=
-
1.062004044111401e+00
;
//
a[4][4] =
a
[
4
][
4
]
=
1.0
;
a
[
5
][
0
]
=
-
7.170454962423025e+00
;
a
[
5
][
1
]
=
-
4.741636671481785e+00
;
a
[
5
][
2
]
=
-
1.631002631330971e+01
;
...
...
@@ -171,27 +170,26 @@ namespace AMDiS {
a
[
5
][
5
]
=
1.0
;
c
[
0
][
0
]
=
gamma
;
c
[
1
][
0
]
=
-
1.200000000000000e+01
;
//
c[1][1] =
4.0
;
c
[
1
][
1
]
=
-
0.5
;
c
[
2
][
0
]
=
-
8.791795173947035e+00
;
c
[
2
][
1
]
=
-
2.207865586973518e+00
;
//
c[2][2] =
4.0
;
c
[
2
][
2
]
=
-
0.023504
;
c
[
3
][
0
]
=
1.081793056857153e+01
;
c
[
3
][
1
]
=
6.780270611428266e+00
;
c
[
3
][
2
]
=
1.953485944642410e+01
;
//
c[3][3] =
4.0
;
c
[
3
][
3
]
=
-
0.0362
;
c
[
4
][
0
]
=
3.419095006749677e+01
;
c
[
4
][
1
]
=
1.549671153725963e+01
;
c
[
4
][
2
]
=
5.474760875964130e+01
;
c
[
4
][
3
]
=
1.416005392148534e+01
;
//
c[4][4] =
4
.0;
c
[
4
][
4
]
=
0
.0
;
c
[
5
][
0
]
=
3.462605830930533e+01
;
c
[
5
][
1
]
=
1.530084976114473e+01
;
c
[
5
][
2
]
=
5.699955578662667e+01
;
c
[
5
][
3
]
=
1.840807009793095e+01
;
c
[
5
][
4
]
=
-
5.714285714285717e+00
;
//
c[5][5] =
4
.0;
c
[
5
][
5
]
=
0
.0
;
m1
[
0
]
=
-
7.170454962423026e+00
;
m1
[
1
]
=
-
4.741636671481786e+00
;
...
...
@@ -206,7 +204,6 @@ namespace AMDiS {
m2
[
3
]
=
-
1.062004044111401e+00
;
m2
[
4
]
=
1.0
;
WARNING
(
"You have to fill the diagonals of the coeffcients to use time derivatives of your operators!
\n
"
);
MSG
(
"Rosenbrock scheme Rodasp
\n
"
);
}
...
...
@@ -220,34 +217,34 @@ namespace AMDiS {
createData
();
a
[
0
][
0
]
=
0.0
;
a
[
1
][
0
]
=
1.14714018013952
;
a
[
1
][
0
]
=
1.14714018013952
1
;
a
[
1
][
1
]
=
0.5
;
a
[
2
][
0
]
=
1.
32930341703716
;
a
[
2
][
0
]
=
1.
785764587181959
;
a
[
2
][
1
]
=
0.442124760965983
;
a
[
2
][
2
]
=
0.75
;
a
[
3
][
0
]
=
-
2.
19977665049954
;
a
[
3
][
1
]
=
4.55821087656518
;
a
[
3
][
2
]
=
-
1.3736155449064
5
;
a
[
3
][
0
]
=
2.
506239510951673
;
a
[
3
][
1
]
=
4.55821087656518
2
;
a
[
3
][
2
]
=
-
1.3736155449064
49
;
a
[
3
][
3
]
=
1.0
;
c
[
0
][
0
]
=
gamma
;
c
[
1
][
0
]
=
-
0.
26318611857810
7
;
c
[
1
][
1
]
=
0.
385866521508459
;
c
[
2
][
0
]
=
-
3.
35635061779949
;
c
[
1
][
0
]
=
-
2
.
6318611857810
65
;
c
[
1
][
1
]
=
-
0.
064133478491541
;
c
[
2
][
0
]
=
-
3.
011310475541004
;
c
[
2
][
1
]
=
0.334203214637756
;
c
[
2
][
2
]
=
-
0.145563307177156
;
c
[
3
][
0
]
=
-
2.6183067448488
;
c
[
3
][
1
]
=
-
1.0899412381571
6
;
c
[
3
][
2
]
=
-
1.71836543021444
;
c
[
3
][
0
]
=
-
3.743590594301783
;
c
[
3
][
1
]
=
-
1.0899412381571
58
;
c
[
3
][
2
]
=
-
1.71836543021444
2
;
c
[
3
][
3
]
=
-
0.135847884055848
;
m1
[
0
]
=
-
1.24823690752574
;
m1
[
1
]
=
3.9534178869996
;
m1
[
2
]
=
-
1.21522771421847
;
m1
[
3
]
=
1.1654174474593
1
;
m1
[
0
]
=
2.833375148827832
;
m1
[
1
]
=
3.9534178869996
03
;
m1
[
2
]
=
-
1.21522771421847
2
;
m1
[
3
]
=
1.1654174474593
07
;
m2
[
0
]
=
0.919998349829964
;
m2
[
1
]
=
1.77038079363523
;
m2
[
0
]
=
2.747785798103605
;
m2
[
1
]
=
1.77038079363523
3
;
m2
[
2
]
=
0.257316038155499
;
m2
[
3
]
=
0.343556220548095
;
...
...
@@ -264,36 +261,36 @@ namespace AMDiS {
createData
();
a
[
0
][
0
]
=
0.0
;
a
[
1
][
0
]
=
1.14714018013952
;
a
[
1
][
0
]
=
1.14714018013952
1
;
a
[
1
][
1
]
=
0.5
;
a
[
2
][
0
]
=
-
0.79265181178863
;
a
[
2
][
1
]
=
3.48693217206767
;
a
[
2
][
0
]
=
2.807348188211369
;
a
[
2
][
1
]
=
3.48693217206767
1
;
a
[
2
][
2
]
=
1.0
;
a
[
3
][
0
]
=
-
0.79265181178863
;
a
[
3
][
1
]
=
3.48693217206767
;
a
[
3
][
0
]
=
a
[
2
][
0
]
;
a
[
3
][
1
]
=
a
[
2
][
1
]
;
a
[
3
][
2
]
=
0.0
;
a
[
3
][
3
]
=
1.0
;
c
[
0
][
0
]
=
gamma
;
c
[
1
][
0
]
=
-
0.
26318611857810
7
;
c
[
1
][
1
]
=
0.
385866521508459
;
c
[
2
][
0
]
=
-
1.40507848232679
;
c
[
2
][
1
]
=
6.1810410213404
1
;
c
[
2
][
2
]
=
1.20849664917601
;
c
[
3
][
0
]
=
4.99718323859189
;
c
[
3
][
1
]
=
-
6.5459726524397
3
;
c
[
1
][
0
]
=
-
2
.
6318611857810
65
;
c
[
1
][
1
]
=
-
0.
064133478491541
;
c
[
2
][
0
]
=
4.976389977276388
;
c
[
2
][
1
]
=
6.1810410213404
08
;
c
[
2
][
2
]
=
1.20849664917601
0
;
c
[
3
][
0
]
=
-
1.761050184345382
;
c
[
3
][
1
]
=
-
6.5459726524397
27
;
c
[
3
][
2
]
=
-
0.539706236424999
;
c
[
3
][
3
]
=
0.0
;
m1
[
0
]
=
-
0.792651811788631
;
m1
[
1
]
=
3.48693217206767
;
m1
[
0
]
=
2.807348188211369
;
m1
[
1
]
=
3.48693217206767
2
;
m1
[
2
]
=
0.0
;
m1
[
3
]
=
1.0
;
m2
[
0
]
=
6.5561019882493
6
;
m2
[
1
]
=
-
5.9432993417113
2
;
m2
[
0
]
=
0.42008425852292
6
;
m2
[
1
]
=
-
5.9432993417113
17
;
m2
[
2
]
=
0.360559439940373
;
m2
[
3
]
=
-
3.34373891242489
;
m2
[
3
]
=
-
3.34373891242489
0
;
MSG
(
"Rosenbrock scheme ROSI2P2
\n
"
);
}
...
...
@@ -319,7 +316,7 @@ namespace AMDiS {
c
[
0
][
0
]
=
gamma
;
c
[
1
][
0
]
=
-
4.58856072055827
;
c
[
1
][
1
]
=
-
0.435866521508468
;
c
[
1
][
1
]
=
-
gamma
;
c
[
2
][
0
]
=
-
4.56739138878308
;
c
[
2
][
1
]
=
-
0.0683107605436897
;
c
[
2
][
2
]
=
-
0.418867127163069
;
...
...
@@ -363,7 +360,7 @@ namespace AMDiS {
c
[
0
][
0
]
=
gamma
;
c
[
1
][
0
]
=
-
4.58856072055827
;
c
[
1
][
1
]
=
-
0.435866521508468
;
c
[
1
][
1
]
=
-
gamma
;
c
[
2
][
0
]
=
48.3965596116246
;
c
[
2
][
1
]
=
16.132186537208
;
c
[
2
][
2
]
=
6.56544000523295
;
...
...
@@ -404,9 +401,9 @@ namespace AMDiS {
a
[
2
][
1
]
=
0.0
;
a
[
2
][
2
]
=
0.5
;
c
[
0
][
0
]
=
0.788675134594813
;
c
[
0
][
0
]
=
gamma
;
c
[
1
][
0
]
=
-
2.53589838486225
;
c
[
1
][
1
]
=
-
0.788675134594813
;
c
[
1
][
1
]
=
-
gamma
;
c
[
2
][
0
]
=
-
1.62740473580836
;
c
[
2
][
1
]
=
-
0.274519052838329
;
c
[
2
][
2
]
=
-
0.0528312163512967
;
...
...
@@ -446,9 +443,9 @@ namespace AMDiS {
a
[
3
][
2
]
=
2.29428036027904
;
a
[
3
][
3
]
=
1.0
;
c
[
0
][
0
]
=
0.435866521508459
;
c
[
0
][
0
]
=
gamma
;
c
[
1
][
0
]
=
-
4.58856072055809
;
c
[
1
][
1
]
=
-
0.435866521508459
;
c
[
1
][
1
]
=
-
gamma
;
c
[
2
][
0
]
=
-
4.18476048231916
;
c
[
2
][
1
]
=
0.285192017355496
;
c
[
2
][
2
]
=
-
0.413333376233886
;
...
...
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