IntegratorExport* createDiagonallyIRK4Export( UserInteraction* _userInteraction,
const std::string &_commonHeaderName)
{
const double alpha = 1.137158042603258;
DMatrix AA(3,3);
DVector bb(3);
DVector cc(3);
AA(0,0) = (1.0+alpha)/2.0; AA(0,1) = 0.0; AA(0,2) = 0.0;
AA(1,0) = -alpha/2.0; AA(1,1) = (1.0+alpha)/2.0; AA(1,2) = 0.0;
AA(2,0) = 1.0+alpha; AA(2,1) = -(1.0+2.0*alpha); AA(2,2) = (1.0+alpha)/2.0;
bb(0) = 1.0/(6.0*alpha*alpha);
bb(1) = 1.0-1.0/(3.0*alpha*alpha);
bb(2) = 1.0/(6.0*alpha*alpha);
cc(0) = (1.0+alpha)/2.0;
cc(1) = 1.0/2.0;
cc(2) = (1.0-alpha)/2.0;
DiagonallyImplicitRKExport* integrator = createDiagonallyImplicitRKExport(_userInteraction, _commonHeaderName);
integrator->initializeButcherTableau(AA, bb, cc);
return integrator;
}
IntegratorExport* createDiagonallyIRK5Export( UserInteraction* _userInteraction,
const String &_commonHeaderName)
{
Matrix AA(5,5);
Vector bb(5);
Vector cc(5);
AA(0,0) = (6.0-sqrt(6.0))/10.0; AA(0,1) = 0.0; AA(0,2) = 0.0; AA(0,3) = 0.0; AA(0,4) = 0.0;
AA(1,0) = (5.0*sqrt(6.0)-6.0)/14.0; AA(1,1) = (6.0-sqrt(6.0))/10.0; AA(1,2) = 0.0; AA(1,3) = 0.0; AA(1,4) = 0.0;
AA(2,0) = (607.0*sqrt(6.0)+888.0)/2850.0; AA(2,1) = (126.0-161.0*sqrt(6.0))/1425.0; AA(2,2) = (6.0-sqrt(6.0))/10.0; AA(2,3) = 0.0; AA(2,4) = 0.0;
AA(3,0) = (3153.0-3082.0*sqrt(6.0))/14250.0; AA(3,1) = (3213.0+1148.0*sqrt(6.0))/28500.0; AA(3,2) = (88.0*sqrt(6.0)-267.0)/500.0; AA(3,3) = (6.0-sqrt(6.0))/10.0; AA(3,4) = 0.0;
AA(4,0) = (14638.0*sqrt(6.0)-32583.0)/71250.0; AA(4,1) = (364.0*sqrt(6.0)-17199.0)/142500.0; AA(4,2) = (1329.0-544.0*sqrt(6.0))/2500.0; AA(4,3) = (131.0*sqrt(6.0)-96.0)/625.0; AA(4,4) = (6.0-sqrt(6.0))/10.0;
bb(0) = 0.0;
bb(1) = 0.0;
bb(2) = 1.0/9.0;
bb(3) = (16.0-sqrt(6.0))/36.0;
bb(4) = (16.0+sqrt(6.0))/36.0;
cc(0) = (6.0-sqrt(6.0))/10.0;
cc(1) = (6.0+9.0*sqrt(6.0))/35.0;
cc(2) = 1.0;
cc(3) = (4.0-sqrt(6.0))/10.0;
cc(4) = (4.0+sqrt(6.0))/10.0;
DiagonallyImplicitRKExport* integrator = createDiagonallyImplicitRKExport(_userInteraction, _commonHeaderName);
integrator->initializeButcherTableau(AA, bb, cc);
return integrator;
}
IntegratorExport* createDiagonallyIRK3Export( UserInteraction* _userInteraction,
const String &_commonHeaderName)
{
Matrix AA(2,2);
Vector bb(2);
Vector cc(2);
AA(0,0) = 1.0/2.0+1.0/(2.0*sqrt(3.0)); AA(0,1) = 0.0;
AA(1,0) = -1.0/sqrt(3.0); AA(1,1) = 1.0/2.0+1.0/(2.0*sqrt(3.0));
bb(0) = 1.0/2.0;
bb(1) = 1.0/2.0;
cc(0) = 1.0/2.0+1.0/(2.0*sqrt(3.0));
cc(1) = 1.0/2.0-1.0/(2.0*sqrt(3.0));
DiagonallyImplicitRKExport* integrator = createDiagonallyImplicitRKExport(_userInteraction, _commonHeaderName);
integrator->initializeButcherTableau(AA, bb, cc);
return integrator;
}