IntegratorExport* createGaussLegendre2Export( UserInteraction* _userInteraction,
const std::string &_commonHeaderName)
{
DMatrix AA(1,1);
DVector bb(1);
DVector cc(1);
AA(0,0) = 1.0/2.0;
bb(0) = 1.0;
cc(0) = 1.0/2.0;
ImplicitRungeKuttaExport* integrator = createImplicitRungeKuttaExport(_userInteraction, _commonHeaderName);
integrator->initializeButcherTableau(AA, bb, cc);
return integrator;
}
IntegratorExport* createGaussLegendre4Export( UserInteraction* _userInteraction,
const String &_commonHeaderName)
{
Matrix AA(2,2);
Vector bb(2);
Vector cc(2);
AA(0,0) = 1.0/4.0; AA(0,1) = (1.0/4.0+sqrt(3.0)/6.0);
AA(1,0) = (1.0/4.0-sqrt(3.0)/6.0); AA(1,1) = 1.0/4.0;
bb(0) = 1.0/2.0;
bb(1) = 1.0/2.0;
cc(0) = 1.0/2.0+sqrt(3.0)/6.0;
cc(1) = 1.0/2.0-sqrt(3.0)/6.0;
ImplicitRungeKuttaExport* integrator = createImplicitRungeKuttaExport(_userInteraction, _commonHeaderName);
integrator->initializeButcherTableau(AA, bb, cc);
return integrator;
}
IntegratorExport* createGaussLegendre6Export( UserInteraction* _userInteraction,
const std::string &_commonHeaderName)
{
DMatrix AA(3,3);
DVector bb(3);
DVector cc(3);
AA(0,0) = 5.0/36.0;
AA(0,1) = 2.0/9.0-1.0/15.0*sqrt(15.0);
AA(0,2) = 5.0/36.0-1.0/30.0*sqrt(15.0);
AA(1,0) = 5.0/36.0+1.0/24.0*sqrt(15.0);
AA(1,1) = 2.0/9.0;
AA(1,2) = 5.0/36.0-1.0/24.0*sqrt(15.0);
AA(2,0) = 5.0/36.0+1.0/30.0*sqrt(15.0);
AA(2,1) = 2.0/9.0+1.0/15.0*sqrt(15.0);
AA(2,2) = 5.0/36.0;
bb(0) = 5.0/18.0;
bb(1) = 4.0/9.0;
bb(2) = 5.0/18.0;
cc(0) = 1.0/2.0-sqrt(15.0)/10.0;
cc(1) = 1.0/2.0;
cc(2) = 1.0/2.0+sqrt(15.0)/10.0;
// SIMPLIFIED NEWTON:
DMatrix _eig(2,2);
_eig(0,0) = 3.677814645373912; _eig(0,1) = 3.508761919567443; // the second column is the imaginary part
_eig(1,0) = 4.644370709252173; _eig(1,1) = 0.0;
DMatrix _simplified_transf1(3,3);
_simplified_transf1(0,0) = -18.636486890695167; _simplified_transf1(0,1) = -15.250990917842101; _simplified_transf1(0,2) = 3.156971624093098;
_simplified_transf1(1,0) = -27.017033488529613; _simplified_transf1(1,1) = 7.134863930477463; _simplified_transf1(1,2) = 1.101474723408009;
_simplified_transf1(2,0) = 28.095293818520428; _simplified_transf1(2,1) = 5.341817943917859; _simplified_transf1(2,2) = 2.027127483041268;
DMatrix _simplified_transf2(3,3);
_simplified_transf2(0,0) = -0.077948357550038; _simplified_transf2(0,1) = -0.056982523211087; _simplified_transf2(0,2) = 0.071464556714801;
_simplified_transf2(1,0) = 0.050295169925554; _simplified_transf2(1,1) = 0.299699605816585; _simplified_transf2(1,2) = 0.117700617809852;
_simplified_transf2(2,0) = 0.947801449544836; _simplified_transf2(2,1) = 0.0; _simplified_transf2(2,2) = 0.990474321575646;
// SINGLE NEWTON:
double _single_tau = 0.202740066519113;
DVector _lower_triang(3);
_lower_triang(0) = 1.291180015430378; _lower_triang(1) = -1.430998974529736; _lower_triang(2) = 2.108070244672127;
DMatrix _single_transf1(3,3);
_single_transf1(0,0) = 1.000000000000000; _single_transf1(0,1) = 0.358037439038676; _single_transf1(0,2) = -0.031545235223924;
_single_transf1(1,0) = -1.291180015430378; _single_transf1(1,1) = 0.537709213937389; _single_transf1(1,2) = 0.059994748344832;
_single_transf1(2,0) = 1.430998974529736; _single_transf1(2,1) = -1.595719036564529; _single_transf1(2,2) = 0.914248574982086;
DMatrix _single_transf2(3,3);
_single_transf2(0,0) = 1.0; _single_transf2(0,1) = -0.358037439038676; _single_transf2(0,2) = 0.038442529688880;
_single_transf2(1,0) = 0.0; _single_transf2(1,1) = 1.0; _single_transf2(1,2) = -0.019264171041652;
_single_transf2(2,0) = 0.0; _single_transf2(2,1) = 0.0; _single_transf2(2,2) = 1.0;
ImplicitRungeKuttaExport* integrator = createImplicitRungeKuttaExport(_userInteraction, _commonHeaderName);
integrator->initializeButcherTableau(AA, bb, cc);
integrator->setEigenvalues(_eig);
integrator->setSimplifiedTransformations(_simplified_transf1, _simplified_transf2);
integrator->setSingleTransformations(_single_tau, _lower_triang, _single_transf1, _single_transf2);
return integrator;
}