int main (int argc, char* argv[]) {
if(argc != 2){
cerr << "USAGE: " << argv[0] << " Jmax (= max. level of sparse grid)" << endl;
exit(1);
}
//===============================================================//
//========= PROBLEM SETUP =======================//
//===============================================================//
int d = 2;
int d_ = 2;
int j0 = 2;
size_t Jmax = atoi(argv[1]);
//getchar();
/// Basis initialization
TrialBasis_Time basis_per(d,d_,j0);
TestBasis_Time basis_int(d,d_,j0);
Basis_Space basis_intbc(d,0);
basis_intbc.enforceBoundaryCondition<DirichletBC>();
Basis2D_Trial basis2d_trial(basis_per,basis_intbc);
Basis2D_Test basis2d_test(basis_int,basis_intbc);
/// Initialization of operator
// Bilinear Forms
Convection1D_Time ConvectionBil_t(basis_per, basis_int);
Identity1D_Time IdentityBil_t(basis_per, basis_int);
Identity1D_Space IdentityBil_x(basis_intbc, basis_intbc);
Laplace1D_Space LaplaceBil_x(basis_intbc, basis_intbc);
RefConvection1D_Time RefConvectionBil_t(basis_per.refinementbasis, basis_int.refinementbasis);
RefIdentity1D_Time RefIdentityBil_t(basis_per.refinementbasis, basis_int.refinementbasis);
RefIdentity1D_Space RefIdentityBil_x(basis_intbc.refinementbasis, basis_intbc.refinementbasis);
RefLaplace1D_Space RefLaplaceBil_x(basis_intbc.refinementbasis, basis_intbc.refinementbasis);
// Transposed Bilinear Forms
TranspConvection1D_Time TranspConvectionBil_t(basis_per, basis_int);
TranspIdentity1D_Time TranspIdentityBil_t(basis_per, basis_int);
TranspIdentity1D_Space TranspIdentityBil_x(basis_intbc, basis_intbc);
TranspLaplace1D_Space TranspLaplaceBil_x(basis_intbc, basis_intbc);
RefTranspConvection1D_Time RefTranspConvectionBil_t(basis_per.refinementbasis, basis_int.refinementbasis);
RefTranspIdentity1D_Time RefTranspIdentityBil_t(basis_per.refinementbasis, basis_int.refinementbasis);
RefTranspIdentity1D_Space RefTranspIdentityBil_x(basis_intbc.refinementbasis, basis_intbc.refinementbasis);
RefTranspLaplace1D_Space RefTranspLaplaceBil_x(basis_intbc.refinementbasis, basis_intbc.refinementbasis);
/// Initialization of local operator
LOp_Conv1D_Time lOp_Conv1D_t(basis_int, basis_per, RefConvectionBil_t, ConvectionBil_t);
LOp_Id1D_Time lOp_Id1D_t (basis_int, basis_per, RefIdentityBil_t, IdentityBil_t);
LOp_Id1D_Space lOp_Id1D_x (basis_intbc, basis_intbc, RefIdentityBil_x, IdentityBil_x);
LOp_Lapl1D_Space lOp_Lapl1D_x(basis_intbc, basis_intbc, RefLaplaceBil_x, LaplaceBil_x);
LOpT_Conv1D_Time lOpT_Conv1D_t(basis_per, basis_int, RefTranspConvectionBil_t, TranspConvectionBil_t);
LOpT_Id1D_Time lOpT_Id1D_t (basis_per, basis_int, RefTranspIdentityBil_t, TranspIdentityBil_t);
LOpT_Id1D_Space lOpT_Id1D_x (basis_intbc, basis_intbc, RefTranspIdentityBil_x, TranspIdentityBil_x);
LOpT_Lapl1D_Space lOpT_Lapl1D_x(basis_intbc, basis_intbc, RefTranspLaplaceBil_x, TranspLaplaceBil_x);
LOp_Conv_Id_2D localConvectionIdentityOp2D(lOp_Conv1D_t, lOp_Id1D_x);
LOp_Id_Lapl_2D localIdentityLaplaceOp2D(lOp_Id1D_t, lOp_Lapl1D_x);
LOpT_Conv_Id_2D transpLocalConvectionIdentityOp2D(lOpT_Conv1D_t, lOpT_Id1D_x);
LOpT_Id_Lapl_2D transpLocalIdentityLaplaceOp2D(lOpT_Id1D_t, lOpT_Lapl1D_x);
localConvectionIdentityOp2D.setJ(9);
localIdentityLaplaceOp2D.setJ(9);
transpLocalConvectionIdentityOp2D.setJ(9);
transpLocalIdentityLaplaceOp2D.setJ(9);
// Use CompoundLocalOperator2D
COp_Heat localOperator2D(localConvectionIdentityOp2D,localIdentityLaplaceOp2D);
COpT_Heat transpLocalOperator2D(transpLocalConvectionIdentityOp2D,transpLocalIdentityLaplaceOp2D);
// Use FlexibleCompoundLocalOperator2D
// vector<AbstractLocalOperator2D<T>* > localOperatorVec, transpLocalOperatorVec;
// localOperatorVec.push_back(&localConvectionIdentityOp2D);
// localOperatorVec.push_back(&localIdentityLaplaceOp2D);
// transpLocalOperatorVec.push_back(&transpLocalConvectionIdentityOp2D);
// transpLocalOperatorVec.push_back(&transpLocalIdentityLaplaceOp2D);
// FlexibleCompoundLocalOperator2D localOperator2D(localOperatorVec);
// FlexibleCompoundLocalOperator2D transpLocalOperator2D(transpLocalOperatorVec);
/// Initialization of preconditioner
LeftPrec2D leftPrec(basis2d_test);
RightPrec2D rightPrec(basis2d_trial);
NoPrec2D noPrec;
/// Initialization of rhs
/// Right Hand Side:
/// No Singular Supports in both dimensions
DenseVectorT sing_support_x;
DenseVectorT sing_support_t(n+1);
for(size_t i = 0; i <= n; ++i){
sing_support_t(i+1) = i*l;
}
/// Forcing Functions
SeparableFunction2D<T> F_fct(f_t, sing_support_t, f_x, sing_support_x);
/// Peaks: points and corresponding coefficients
/// (heights of jumps in derivatives)
FullColMatrixT nodeltas;
SeparableRhsIntegral2D rhs(basis2d_test, F_fct, nodeltas, nodeltas, 20);
SeparableRhs F(rhs,noPrec);
//===============================================================//
//=============== AWGM =========================================//
//===============================================================//
/* AWGM PG Parameters Default Values
double tol = 5e-03;
double alpha = 0.7;
size_t max_its = 100;
size_t max_basissize = 400000;
bool reset_res = false;
bool print_info = true;
bool verbose = true;
bool plot_solution = false;
bool verbose_extra = false; //(print added wavelet indizes)
size_t hashmapsize_trial = 10;
size_t hashmapsize_test = 10;
std::string info_filename = "awgm_cgls_conv_info.txt";
std::string plot_filename = "awgm_cgls_u_plot";
bool write_intermediary_solutions = false;
std::string intermediary_solutions_filename = "awgm_cgls_u";
*/
/* IS Parameters Default Values
bool adaptive_tol = true;
size_t max_its = 100;
double init_tol = 0.001;
double res_reduction = 0.01;
double absolute_tol = 1e-8;
bool verbose = true;
*/
// MultitreeAWGM with default values
//MT_AWGM multitree_awgm(basis2d_trial, basis2d_test, localOperator2D, transLocalOperator2D,
// F, rightPrec, leftPrec);
// If you want other parameters
AWGM_PG_Parameters awgm_parameters;
IS_Parameters cgls_parameters;
// .... set them here:
awgm_parameters.max_its = 0;
awgm_parameters.tol = 1e-04;
awgm_parameters.plot_solution = false;
awgm_parameters.verbose_extra = false;
awgm_parameters.info_filename = "awgm_ExSaw_SG_mv_conv_info.txt";
awgm_parameters.plot_filename = "awgm_ExSaw_SG_mv_u_plot";
awgm_parameters.write_intermediary_solutions = true;
awgm_parameters.max_basissize = 1000000;
cgls_parameters.adaptive_tol = true;
cgls_parameters.init_tol = 1e-4;
cgls_parameters.res_reduction = 0.01;
cgls_parameters.max_its = 700;
MT_AWGM multitree_awgm(basis2d_trial, basis2d_test, localOperator2D, transpLocalOperator2D,
F, rightPrec, leftPrec, awgm_parameters, cgls_parameters);
multitree_awgm.awgm_params.print();
multitree_awgm.is_params.print();
multitree_awgm.set_sol(dummy);
for(size_t J = 2; J < Jmax; ++J){
stringstream filename;
filename << "awgm_ExSaw_SG_mv_u_J_" << J;
multitree_awgm.awgm_params.intermediary_solutions_filename = filename.str();
/// Initialization of solution vector and initial index sets
Coefficients<Lexicographical,T,Index2D> u;
T gamma = 0.2;
IndexSet<Index2D> LambdaTrial, LambdaTest;
getSparseGridIndexSet(basis2d_trial,LambdaTrial,J,0,gamma);
getSparseGridIndexSet(basis2d_test ,LambdaTest ,J,1,gamma);
Timer time;
time.start();
multitree_awgm.solve(u, LambdaTrial, LambdaTest);
time.stop();
cout << "Solution took " << time.elapsed() << " seconds" << endl;
}
return 0;
}
int main () {
//===============================================================//
//========= PROBLEM SETUP =======================//
//===============================================================//
int d = 2;
int d_ = 2;
int j0 = 2;
//getchar();
/// Basis initialization
TrialBasis_Time basis_per(d,d_,j0);
TestBasis_Time basis_int(d,d_,j0);
Basis_Space basis_intbc(d,0);
basis_intbc.enforceBoundaryCondition<DirichletBC>();
Basis2D_Trial basis2d_trial(basis_per,basis_intbc);
Basis2D_Test basis2d_test(basis_int,basis_intbc);
/// Initialization of operators
DenseVectorT no_singPts;
// Bilinear Forms
Convection1D_Time ConvectionBil_t(basis_per, basis_int);
Identity1D_Time IdentityBil_t(basis_per, basis_int);
Identity1D_Space IdentityBil_x(basis_intbc, basis_intbc);
Laplace1D_Space LaplaceBil_x(basis_intbc, basis_intbc);
Convection1D_Space ConvectionBil_x(basis_intbc, basis_intbc);
RefConvection1D_Time RefConvectionBil_t(basis_per.refinementbasis, basis_int.refinementbasis);
RefIdentity1D_Time RefIdentityBil_t(basis_per.refinementbasis, basis_int.refinementbasis);
RefIdentity1D_Space RefIdentityBil_x(basis_intbc.refinementbasis, basis_intbc.refinementbasis);
RefLaplace1D_Space RefLaplaceBil_x(basis_intbc.refinementbasis, basis_intbc.refinementbasis);
RefConvection1D_Space RefConvectionBil_x(basis_intbc.refinementbasis, basis_intbc.refinementbasis);
// Transposed Bilinear Forms
TranspConvection1D_Time TranspConvectionBil_t(basis_per, basis_int);
TranspIdentity1D_Time TranspIdentityBil_t(basis_per, basis_int);
TranspIdentity1D_Space TranspIdentityBil_x(basis_intbc, basis_intbc);
TranspLaplace1D_Space TranspLaplaceBil_x(basis_intbc, basis_intbc);
TranspConvection1D_Space TranspConvectionBil_x(basis_intbc, basis_intbc);
RefTranspConvection1D_Time RefTranspConvectionBil_t(basis_per.refinementbasis, basis_int.refinementbasis);
RefTranspIdentity1D_Time RefTranspIdentityBil_t(basis_per.refinementbasis, basis_int.refinementbasis);
RefTranspIdentity1D_Space RefTranspIdentityBil_x(basis_intbc.refinementbasis, basis_intbc.refinementbasis);
RefTranspLaplace1D_Space RefTranspLaplaceBil_x(basis_intbc.refinementbasis, basis_intbc.refinementbasis);
RefTranspConvection1D_Space RefTranspConvectionBil_x(basis_intbc.refinementbasis, basis_intbc.refinementbasis);
/// Initialization of local operator
LOp_Conv1D_Time lOp_Conv1D_t (basis_int, basis_per, RefConvectionBil_t, ConvectionBil_t);
LOp_Id1D_Time lOp_Id1D_t (basis_int, basis_per, RefIdentityBil_t, IdentityBil_t);
LOp_Id1D_Space lOp_Id1D_x (basis_intbc, basis_intbc, RefIdentityBil_x, IdentityBil_x);
LOp_Lapl1D_Space lOp_Lapl1D_x (basis_intbc, basis_intbc, RefLaplaceBil_x, LaplaceBil_x);
LOp_Conv1D_Space lOp_Conv1D_x (basis_intbc, basis_intbc, RefConvectionBil_x, ConvectionBil_x);
LOpT_Conv1D_Time lOpT_Conv1D_t(basis_per, basis_int, RefTranspConvectionBil_t, TranspConvectionBil_t);
LOpT_Id1D_Time lOpT_Id1D_t (basis_per, basis_int, RefTranspIdentityBil_t, TranspIdentityBil_t);
LOpT_Id1D_Space lOpT_Id1D_x (basis_intbc, basis_intbc, RefTranspIdentityBil_x, TranspIdentityBil_x);
LOpT_Lapl1D_Space lOpT_Lapl1D_x(basis_intbc, basis_intbc, RefTranspLaplaceBil_x, TranspLaplaceBil_x);
LOpT_Conv1D_Space lOpT_Conv1D_x(basis_intbc, basis_intbc, RefTranspConvectionBil_x, TranspConvectionBil_x);
LOp_Conv_Id_2D localConvectionIdentityOp2D (lOp_Conv1D_t, lOp_Id1D_x);
LOp_Id_Id_2D localIdentityIdentityOp2D (lOp_Id1D_t, lOp_Id1D_x);
LOp_Id_Lapl_2D localIdentityLaplaceOp2D (lOp_Id1D_t, lOp_Lapl1D_x);
LOp_Id_Conv_2D localIdentityConvectionOp2D (lOp_Id1D_t, lOp_Conv1D_x);
LOpT_Conv_Id_2D transpLocalConvectionIdentityOp2D (lOpT_Conv1D_t, lOpT_Id1D_x);
LOpT_Id_Id_2D transpLocalIdentityIdentityOp2D (lOpT_Id1D_t, lOpT_Id1D_x);
LOpT_Id_Lapl_2D transpLocalIdentityLaplaceOp2D (lOpT_Id1D_t, lOpT_Lapl1D_x);
LOpT_Id_Conv_2D transpLocalIdentityConvectionOp2D (lOpT_Id1D_t, lOpT_Conv1D_x);
localConvectionIdentityOp2D.setJ(9);
localIdentityIdentityOp2D.setJ(9);
localIdentityLaplaceOp2D.setJ(9);
localIdentityConvectionOp2D.setJ(9);
transpLocalConvectionIdentityOp2D.setJ(9);
transpLocalIdentityIdentityOp2D.setJ(9);
transpLocalIdentityLaplaceOp2D.setJ(9);
transpLocalIdentityConvectionOp2D.setJ(9);
// Affine Decompositions:
// Left Hand Side -> mu's are _NOT_ evaluated (only global consts!!)
vector<ThetaStructure<ParamType>::ThetaFct> lhs_theta_fcts;
lhs_theta_fcts.push_back(no_theta);
lhs_theta_fcts.push_back(theta_lapl);
lhs_theta_fcts.push_back(theta_conv);
lhs_theta_fcts.push_back(theta_reac);
ThetaStructure<ParamType> lhs_theta(lhs_theta_fcts);
vector<AbstractLocalOperator2D<T>* > lhs_ops, lhs_opsT;
lhs_ops.push_back(&localConvectionIdentityOp2D);
lhs_ops.push_back(&localIdentityLaplaceOp2D);
lhs_ops.push_back(&localIdentityConvectionOp2D);
lhs_ops.push_back(&localIdentityIdentityOp2D);
lhs_opsT.push_back(&transpLocalConvectionIdentityOp2D);
lhs_opsT.push_back(&transpLocalIdentityLaplaceOp2D);
lhs_opsT.push_back(&transpLocalIdentityConvectionOp2D);
lhs_opsT.push_back(&transpLocalIdentityIdentityOp2D);
Affine_Op_2D affine_lhs(lhs_theta, lhs_ops);
Affine_Op_2D affine_lhs_T(lhs_theta, lhs_opsT);
/// Initialization of preconditioner
LeftPrec2D leftPrec(basis2d_test);
RightPrec2D rightPrec(basis2d_trial);
NoPrec2D noPrec;
/// Initialization of rhs
/// Right Hand Side:
/// No Singular Supports in both dimensions
int n = 20;
DenseVectorT sing_support_t(n+1), sing_support_x(n+1);
int i0 = sing_support_t.firstIndex();
for(int i = 0; i <= n; ++i){
sing_support_t(i0 + i) = i/(double)n;
sing_support_x(i0 + i) = i/(double)n;
}
/// Forcing Functions
Function2D<T> F_fct(curve, sing_support_t, sing_support_x);
RhsIntegral2D rhs(basis2d_test, F_fct, 10);
AdaptiveRhs2D F(rhs,noPrec);
//===============================================================//
//=============== AWGM =========================================//
//===============================================================//
/* AWGM PG Parameters Default Values
double tol = 5e-03;
double alpha = 0.7;
size_t max_its = 100;
size_t max_basissize = 400000;
bool reset_res = false;
StableExpansionVersion stable_exp_u = FullExpansion;
StableExpansionVersion stable_exp_res = FullExpansion;
ResidualConstruction res_construction = SimpleStableExpansion;
bool print_info = true;
bool verbose = true;
bool plot_solution = false;
bool verbose_extra = false; //(print added wavelet indizes)
size_t hashmapsize_trial = 10;
size_t hashmapsize_test = 10;
std::string info_filename = "awgm_cgls_conv_info.txt";
std::string plot_filename = "awgm_cgls_u_plot";
bool write_intermediary_solutions = false;
std::string intermediary_solutions_filename = "awgm_cgls_u";
*/
/* IS Parameters Default Values
bool adaptive_tol = true;
size_t max_its = 100;
double init_tol = 0.001;
double res_reduction = 0.01;
double absolute_tol = 1e-8;
bool verbose = true;
*/
// MultitreeAWGM with default values
//MT_AWGM multitree_awgm(basis2d_trial, basis2d_test, localOperator2D, transLocalOperator2D,
// F, rightPrec, leftPrec);
// If you want other parameters
AWGM_PG_Parameters awgm_parameters;
IS_Parameters cgls_parameters;
// .... set them here:
awgm_parameters.tol = 0.0001;
awgm_parameters.stable_exp_u = OnlyTemporalHWExpansion; //WoMixedHWExpansion;
awgm_parameters.stable_exp_res = OnlyTemporalHWExpansion;
awgm_parameters.res_construction = DoubleStableExpansion; // ParallelMTCones
awgm_parameters.plot_solution = false;
awgm_parameters.verbose_extra = true;
awgm_parameters.info_filename = "awgm_ExCDRCurve_mw_DoubleExp_conv_info.txt";
awgm_parameters.plot_filename = "awgm_ExCDRCurve_mw_DoubleExp_u_plot";
awgm_parameters.write_intermediary_solutions = true;
awgm_parameters.intermediary_solutions_filename = "awgm_ExCDRCurve_mw_DoubleExp_u_Iteration";
cgls_parameters.adaptive_tol = true;
cgls_parameters.init_tol = 1e-4;
cgls_parameters.res_reduction = 0.01;
cgls_parameters.max_its = 700;
// MT_AWGM multitree_awgm(basis2d_trial, basis2d_test, localOperator2D, transpLocalOperator2D,
// F, rightPrec, leftPrec, awgm_parameters, cgls_parameters);
MT_AWGM multitree_awgm(basis2d_trial, basis2d_test, affine_lhs, affine_lhs_T,
F, rightPrec, leftPrec, awgm_parameters, cgls_parameters);
// Parameter is ignored anyway!!
ParamType mu = {{0., -9.}};
lhs_theta.set_param(mu);
multitree_awgm.awgm_params.print();
multitree_awgm.is_params.print();
multitree_awgm.set_sol(dummy);
/// Initialization of solution vector and initial index sets
Coefficients<Lexicographical,T,Index2D> u;
T gamma = 0.2;
IndexSet<Index2D> LambdaTrial, LambdaTest;
getSparseGridIndexSet(basis2d_trial,LambdaTrial,2,0,gamma);
getSparseGridIndexSet(basis2d_test ,LambdaTest ,2,1,gamma);
Timer time;
time.start();
multitree_awgm.solve(u, LambdaTrial, LambdaTest);
time.stop();
cout << "Solution took " << time.elapsed() << " seconds" << endl;
saveCoeffVector2D(u, basis2d_trial, "awgm_ExCDRCurve_mw_DoubleExp_u.txt");
return 0;
}