int main()
{
double /* **U, **Unew,err=0.0,*/ sta = 1.0/8.0, stb=1.0/128.0;
int sa = 9, sb = 129, i/*,j*/;
FILE *outs;
init(&U,sa,sa);
init(&Unew,sa,sa);
init(&Ub,sb,sb);
init_cond(&U, sa, sa, sta,sta);
memcpy(&Unew,&U,sizeof(Unew));
for(i = 0; i<1000 /*&& (err>0.001 || err == 0.0)*/; i++)
{
//err = 0.0;
iteration(&U,&Unew, sa,sa, sta,sta);
memcpy(&U,&Unew,sizeof(Unew));
}
outs = fopen("../output/out1.dat", "w");
output_line(U, sa,sa, sta,sta, outs);
fclose(outs);
//init_cond(&Ub, sb, sb, stb,stb);
interpol(&Ub, sb, sb, stb, stb, &U, sa-1, sa-1, sta, sta);
init_cond(&Ub, sb, sb, stb, stb);
outs = fopen("../output/out2.dat", "w");
output_line(Ub, sb,sb, stb,stb, outs);
fclose(outs);
freeArr(&Unew, sa);
//output_line(U, sa,sa, sta,sta);
//output_line(Ub, sb,sb, stb,stb);
//freeArr(&U, sa);
init(&Unew,sb,sb);
init_cond(&Unew, sb, sb, stb, stb);
memcpy(&Unew,&Ub,sizeof(Ub));
//err = 0.0;
for(i = 0; i<1000 /*&& (err>0.0005 || err == 0.0)*/ ; i++)
{
iteration(&Ub,&Unew, sb,sb, stb,stb);
memcpy(&Ub,&Unew,sizeof(Unew));
}
outs = fopen("../output/out3.dat", "w");
output_line(Ub, sb,sb, stb,stb, outs);
fclose(outs);
outs = fopen("../output/out3_mstk.dat", "w");
opt_mstk_line(Ub, sb,sb, stb,stb, outs);
fclose(outs);
//output_line(U, size,size, step,step);
//printf("%f %f %f\n", step*5, step*5, err);
return 0;
}
int kernel_main()
{
printk("Hello kernel!\n");
page_init();
init_cond();
return 0;
}
/**
* Simple Parabolic PDE u' = del squared u
*
* With u = 0 on the boundaries of the unit cube. Subject to the initial
* condition u(0,x,y,z)=sin( PI x)sin( PI y)sin( PI z).
*/
void TestSimpleLinearParabolicSolver3DZeroDirich()
{
// read mesh on [0,1]x[0,1]x[0,1]
TrianglesMeshReader<3,3> mesh_reader("mesh/test/data/cube_136_elements");
TetrahedralMesh<3,3> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
// Instantiate PDE object
HeatEquation<3> pde;
// Boundary conditions - zero dirichlet everywhere on boundary
BoundaryConditionsContainer<3,3,1> bcc;
bcc.DefineZeroDirichletOnMeshBoundary(&mesh);
// Solver
SimpleLinearParabolicSolver<3,3> solver(&mesh,&pde,&bcc);
/*
* Choose initial condition sin(x*pi)*sin(y*pi)*sin(z*pi) as
* this is an eigenfunction of the heat equation.
*/
std::vector<double> init_cond(mesh.GetNumNodes());
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
double x = mesh.GetNode(i)->GetPoint()[0];
double y = mesh.GetNode(i)->GetPoint()[1];
double z = mesh.GetNode(i)->GetPoint()[2];
init_cond[i] = sin(x*M_PI)*sin(y*M_PI)*sin(z*M_PI);
}
Vec initial_condition = PetscTools::CreateVec(init_cond);
double t_end = 0.1;
solver.SetTimes(0, t_end);
solver.SetTimeStep(0.001);
solver.SetInitialCondition(initial_condition);
Vec result = solver.Solve();
ReplicatableVector result_repl(result);
// Check solution is u = e^{-3*t*pi*pi} sin(x*pi)*sin(y*pi)*sin(z*pi), t=0.1
for (unsigned i=0; i<result_repl.GetSize(); i++)
{
double x = mesh.GetNode(i)->GetPoint()[0];
double y = mesh.GetNode(i)->GetPoint()[1];
double z = mesh.GetNode(i)->GetPoint()[2];
double u = exp(-3*t_end*M_PI*M_PI)*sin(x*M_PI)*sin(y*M_PI)*sin(z*M_PI);
TS_ASSERT_DELTA(result_repl[i], u, 0.1);
}
PetscTools::Destroy(initial_condition);
PetscTools::Destroy(result);
}
// Essential (Dirichlet) boundary condition markers.
scalar essential_bc_values(double x, double y)
{
double dx, dy;
return init_cond(x, y, dx, dy);
}
void TestHeatEquationWithSourceWithCoupledOdeSystemIn1dWithZeroNeumann()
{
// Create mesh of domain [0,1]
TrianglesMeshReader<1,1> mesh_reader("mesh/test/data/1D_0_to_1_100_elements");
TetrahedralMesh<1,1> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
// Create PDE system object
HeatEquationWithSourceForCoupledOdeSystem<1> pde;
// Define zero Neumann boundary conditions
BoundaryConditionsContainer<1,1,1> bcc;
ConstBoundaryCondition<1>* p_boundary_condition = new ConstBoundaryCondition<1>(0.0);
TetrahedralMesh<1,1>::BoundaryElementIterator iter = mesh.GetBoundaryElementIteratorBegin();
bcc.AddNeumannBoundaryCondition(*iter, p_boundary_condition);
iter = mesh.GetBoundaryElementIteratorEnd();
iter--;
bcc.AddNeumannBoundaryCondition(*iter, p_boundary_condition);
// Create the correct number of ODE systems
double a = 5.0;
std::vector<AbstractOdeSystemForCoupledPdeSystem*> ode_systems;
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
ode_systems.push_back(new OdeSystemForCoupledHeatEquationWithSource(a));
}
// Create PDE system solver
LinearParabolicPdeSystemWithCoupledOdeSystemSolver<1,1,1> solver(&mesh, &pde, &bcc, ode_systems);
// Test setting end time and timestep
TS_ASSERT_THROWS_THIS(solver.SetTimes(1.0, 0.0), "Start time has to be less than end time");
TS_ASSERT_THROWS_THIS(solver.SetTimeStep(0.0), "Time step has to be greater than zero");
// Set end time and timestep
double t_end = 0.1;
solver.SetTimes(0, t_end);
solver.SetTimeStep(0.001);
// Set initial condition u(x,0) = 1 + cos(pi*x)
std::vector<double> init_cond(mesh.GetNumNodes());
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
double x = mesh.GetNode(i)->GetPoint()[0];
init_cond[i] = 1 + cos(M_PI*x);
}
Vec initial_condition = PetscTools::CreateVec(init_cond);
solver.SetInitialCondition(initial_condition);
// Solve PDE system and store result
Vec result = solver.Solve();
ReplicatableVector result_repl(result);
/*
* Test that solution is given by
*
* u(x,t) = 1 + (1 - exp(-a*t))/a + exp(-pi*pi*t)*cos(pi*x),
* v(x,t) = exp(-a*t),
*
* with t = t_end.
*/
for (unsigned i=0; i<result_repl.GetSize(); i++)
{
double x = mesh.GetNode(i)->GetPoint()[0];
double u = 1 + (1 - exp(-a*t_end))/a + exp(-M_PI*M_PI*t_end)*cos(M_PI*x);
TS_ASSERT_DELTA(result_repl[i], u, 0.1);
double u_from_v = solver.GetOdeSystemAtNode(i)->rGetPdeSolution()[0];
TS_ASSERT_DELTA(result_repl[i], u_from_v, 0.1);
double v = exp(-a*t_end);
TS_ASSERT_DELTA(ode_systems[i]->rGetStateVariables()[0], v, 0.1);
}
// Test the method GetOdeSystemAtNode()
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
TS_ASSERT(solver.GetOdeSystemAtNode(i) != NULL);
TS_ASSERT_DELTA(static_cast<OdeSystemForCoupledHeatEquationWithSource*>(solver.GetOdeSystemAtNode(i))->GetA(), 5.0, 1e-6);
}
// Tidy up
PetscTools::Destroy(initial_condition);
PetscTools::Destroy(result);
}
void TestSolveAndWriteResultsToFileMethod()
{
// Create mesh of the domain [0,1]x[0,1]
TrianglesMeshReader<2,2> mesh_reader("mesh/test/data/square_128_elements");
TetrahedralMesh<2,2> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
// Create PDE system object
HeatEquationForCoupledOdeSystem<2> pde;
// Define zero Dirichlet boundary conditions on entire boundary
BoundaryConditionsContainer<2,2,1> bcc;
bcc.DefineZeroDirichletOnMeshBoundary(&mesh);
// Create the correct number of ODE systems
double a = 5.0;
std::vector<AbstractOdeSystemForCoupledPdeSystem*> ode_systems;
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
ode_systems.push_back(new OdeSystemForCoupledHeatEquation(a));
}
// Create PDE system solver
LinearParabolicPdeSystemWithCoupledOdeSystemSolver<2,2,1> solver(&mesh, &pde, &bcc, ode_systems);
// Set end time and timestep (end time is not a multiple of timestep, for coverage)
double t_end = 0.105;
/*
* Set initial condition
*
* u(x,y,0) = sin(pi*x)*sin(pi*y),
*
* which is an eigenfunction of the heat equation.
*/
std::vector<double> init_cond(mesh.GetNumNodes());
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
double x = mesh.GetNode(i)->GetPoint()[0];
double y = mesh.GetNode(i)->GetPoint()[1];
init_cond[i] = sin(M_PI*x)*sin(M_PI*y);
}
Vec initial_condition = PetscTools::CreateVec(init_cond);
// Need an output folder
TS_ASSERT_THROWS_THIS(solver.SolveAndWriteResultsToFile(),
"SetOutputDirectory() must be called prior to SolveAndWriteResultsToFile()");
solver.SetOutputDirectory("TestHeatEquationForCoupledOdeSystemIn2dWithZeroDirichletWithOutput");
// Need a time interval
TS_ASSERT_THROWS_THIS(solver.SolveAndWriteResultsToFile(),
"SetTimes() must be called prior to SolveAndWriteResultsToFile()");
solver.SetTimes(0, t_end);
// Need a timestep
TS_ASSERT_THROWS_THIS(solver.SolveAndWriteResultsToFile(),
"SetTimeStep() must be called prior to SolveAndWriteResultsToFile()");
solver.SetTimeStep(0.01);
// Need sampling interval
TS_ASSERT_THROWS_THIS(solver.SolveAndWriteResultsToFile(),
"SetSamplingTimeStep() must be called prior to SolveAndWriteResultsToFile()");
solver.SetSamplingTimeStep(0.1);
// Need initial condition
TS_ASSERT_THROWS_THIS(solver.SolveAndWriteResultsToFile(),
"SetInitialCondition() must be called prior to SolveAndWriteResultsToFile()");
solver.SetInitialCondition(initial_condition);
solver.SolveAndWriteResultsToFile();
//#ifdef CHASTE_VTK
///\todo #1967 Check that the file was output and has expected content
//#endif // CHASTE_VTK
// Tidy up
PetscTools::Destroy(initial_condition);
}
void TestHeatEquationWithCoupledOdeSystemIn2dWithZeroDirichlet()
{
// Create mesh of the domain [0,1]x[0,1]
TrianglesMeshReader<2,2> mesh_reader("mesh/test/data/square_4096_elements");
TetrahedralMesh<2,2> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
// Create PDE system object
HeatEquationForCoupledOdeSystem<2> pde;
// Define zero Dirichlet boundary conditions on entire boundary
BoundaryConditionsContainer<2,2,1> bcc;
bcc.DefineZeroDirichletOnMeshBoundary(&mesh);
// Create the correct number of ODE systems
double a = 5.0;
std::vector<AbstractOdeSystemForCoupledPdeSystem*> ode_systems;
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
ode_systems.push_back(new OdeSystemForCoupledHeatEquation(a));
}
// Create PDE system solver
LinearParabolicPdeSystemWithCoupledOdeSystemSolver<2,2,1> solver(&mesh, &pde, &bcc, ode_systems);
// Set end time and timestep
double t_end = 0.01;
solver.SetTimes(0, t_end);
solver.SetTimeStep(0.001);
/*
* Set initial condition
*
* u(x,y,0) = sin(pi*x)*sin(pi*y),
*
* which is an eigenfunction of the heat equation.
*/
std::vector<double> init_cond(mesh.GetNumNodes());
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
double x = mesh.GetNode(i)->GetPoint()[0];
double y = mesh.GetNode(i)->GetPoint()[1];
init_cond[i] = sin(M_PI*x)*sin(M_PI*y);
}
Vec initial_condition = PetscTools::CreateVec(init_cond);
solver.SetInitialCondition(initial_condition);
// Solve PDE system and store result
Vec result = solver.Solve();
ReplicatableVector result_repl(result);
/*
* Test that solution is given by
*
* u(x,y,t) = e^{-2*pi*pi*t} sin(pi*x)*sin(pi*y),
* v(x,y,t) = 1 + (1 - e^{-2*pi*pi*t})*sin(pi*x)*sin(pi*y)*a/(2*pi*pi),
*
* with t = t_end.
*/
for (unsigned i=0; i<result_repl.GetSize(); i++)
{
double x = mesh.GetNode(i)->GetPoint()[0];
double y = mesh.GetNode(i)->GetPoint()[1];
double u = exp(-2*M_PI*M_PI*t_end)*sin(M_PI*x)*sin(M_PI*y);
double v = 1.0 + (a/(2*M_PI*M_PI))*(1 - exp(-2*M_PI*M_PI*t_end))*sin(M_PI*x)*sin(M_PI*y);
TS_ASSERT_DELTA(result_repl[i], u, 0.01);
TS_ASSERT_DELTA(ode_systems[i]->rGetStateVariables()[0], v, 0.01);
}
// Tidy up
PetscTools::Destroy(initial_condition);
PetscTools::Destroy(result);
}
void TestHeatEquationWithCoupledOdeSystemIn1dWithMixed()
{
// Create mesh of domain [0,1]
TrianglesMeshReader<1,1> mesh_reader("mesh/test/data/1D_0_to_1_100_elements");
TetrahedralMesh<1,1> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
// Create PDE system object
HeatEquationForCoupledOdeSystem<1> pde;
// Define non-zero Neumann boundary condition at x=0
BoundaryConditionsContainer<1,1,1> bcc;
ConstBoundaryCondition<1>* p_boundary_condition = new ConstBoundaryCondition<1>(1.0);
TetrahedralMesh<1,1>::BoundaryElementIterator iter = mesh.GetBoundaryElementIteratorBegin();
bcc.AddNeumannBoundaryCondition(*iter, p_boundary_condition);
// Define zero Dirichlet boundary condition at x=1
ConstBoundaryCondition<1>* p_boundary_condition2 = new ConstBoundaryCondition<1>(0.0);
TetrahedralMesh<1,1>::BoundaryNodeIterator node_iter = mesh.GetBoundaryNodeIteratorEnd();
--node_iter;
bcc.AddDirichletBoundaryCondition(*node_iter, p_boundary_condition2);
// Create the correct number of ODE systems
double a = 5.0;
std::vector<AbstractOdeSystemForCoupledPdeSystem*> ode_systems;
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
ode_systems.push_back(new OdeSystemForCoupledHeatEquation(a));
}
// Create PDE system solver
LinearParabolicPdeSystemWithCoupledOdeSystemSolver<1,1,1> solver(&mesh, &pde, &bcc, ode_systems);
// Set end time and timestep
double t_end = 0.1;
solver.SetTimes(0, t_end);
solver.SetTimeStep(0.001);
// Set initial condition u(x,0) = 1 - x
std::vector<double> init_cond(mesh.GetNumNodes());
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
double x = mesh.GetNode(i)->GetPoint()[0];
init_cond[i] = 1 - x;
}
Vec initial_condition = PetscTools::CreateVec(init_cond);
solver.SetInitialCondition(initial_condition);
// Solve PDE system and store result
Vec result = solver.Solve();
ReplicatableVector result_repl(result);
/*
* Test that solution is given by
*
* u(x,t) = 1 - x,
* v(x,t) = 1 + a*(1-x)*t,
*
* with t = t_end.
*/
for (unsigned i=0; i<result_repl.GetSize(); i++)
{
double x = mesh.GetNode(i)->GetPoint()[0];
double u = 1 - x;
TS_ASSERT_DELTA(result_repl[i], u, 0.1);
double v = 1 + a*(1-x)*t_end;
TS_ASSERT_DELTA(ode_systems[i]->rGetStateVariables()[0], v, 0.1);
}
// Tidy up
PetscTools::Destroy(initial_condition);
PetscTools::Destroy(result);
}
// Essential (Dirichlet) boundary condition markers.
scalar essential_bc_values(int ess_bdy_marker, double x, double y)
{
double dx, dy;
return init_cond(x, y, dx, dy);
}
int main()
{
double sta = 1.0/64.;//, stb = 1./512.;
int sa = 65, i;//, sb = 513/*,j*/;
FILE *outs;
init(&U,sa,sa);
init(&Unew,sa,sa);
//init(&Ub,sb,sb);
init_cond(&U, sa, sa, sta,sta);
memcpy(&Unew,&U,sizeof(Unew));
for(i = 0; i<7000; i++)
{
iteration(&U,&Unew, sa,sa, sta,sta);
memcpy(&U,&Unew,sizeof(Unew));
}
printf("step a done\n");
//outs = fopen("../output/out1.dat", "w");
//output_line(U, sa,sa, sta,sta, outs);
//fclose(outs);
//interpol(&Ub, sb, sb, stb, stb, &U, sa-1, sa-1, sta, sta);
//init_cond(&Ub, sb, sb, stb, stb);
//freeArr(&Unew, sa);
//init(&Unew,sb,sb);
//init_cond(&Unew, sb, sb, stb, stb);
//memcpy(&Unew,&Ub,sizeof(Ub));
//for(i = 0; i<500 /*&& (err>0.0005 || err == 0.0)*/ ; i++)
//{
//printf("%d/100\n",i);
//iteration(&Ub,&Unew, sb,sb, stb,stb);
//memcpy(&Ub,&Unew,sizeof(Unew));
//}
outs = fopen("../output/out3.dat", "w");
output_grid(U, sa,sa, sta,sta, outs);
fclose(outs);
printf("pot. output \n");
outs = fopen("../output/press.dat", "w");
output_field_color(U, sa,sa, sta,sta, outs);
fclose(outs);
printf("pressure output\n");
outs = fopen("../output/field.dat", "w");
output_field(U, sa,sa, sta,sta, outs);
fclose(outs);
printf("field output\n");
system("./lines_of_level");
system("./Plot_field");
system("./Plot_col");
system("./Plot");
return 0;
}
// test 2D problem - takes a long time to run.
// solution is incorrect to specified tolerance.
void xTestSimpleLinearParabolicSolver2DNeumannWithSmallTimeStepAndFineMesh()
{
// Create mesh from mesh reader
FemlabMeshReader<2,2> mesh_reader("mesh/test/data/",
"femlab_fine_square_nodes.dat",
"femlab_fine_square_elements.dat",
"femlab_fine_square_edges.dat");
TetrahedralMesh<2,2> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
// Instantiate PDE object
HeatEquation<2> pde;
// Boundary conditions - zero dirichlet on boundary;
BoundaryConditionsContainer<2,2,1> bcc;
TetrahedralMesh<2,2>::BoundaryNodeIterator iter = mesh.GetBoundaryNodeIteratorBegin();
while (iter != mesh.GetBoundaryNodeIteratorEnd())
{
double x = (*iter)->GetPoint()[0];
double y = (*iter)->GetPoint()[1];
ConstBoundaryCondition<2>* p_dirichlet_boundary_condition =
new ConstBoundaryCondition<2>(x);
if (fabs(y) < 0.01)
{
bcc.AddDirichletBoundaryCondition(*iter, p_dirichlet_boundary_condition);
}
if (fabs(y - 1.0) < 0.01)
{
bcc.AddDirichletBoundaryCondition(*iter, p_dirichlet_boundary_condition);
}
if (fabs(x) < 0.01)
{
bcc.AddDirichletBoundaryCondition(*iter, p_dirichlet_boundary_condition);
}
iter++;
}
TetrahedralMesh<2,2>::BoundaryElementIterator surf_iter = mesh.GetBoundaryElementIteratorBegin();
ConstBoundaryCondition<2>* p_neumann_boundary_condition =
new ConstBoundaryCondition<2>(1.0);
while (surf_iter != mesh.GetBoundaryElementIteratorEnd())
{
int node = (*surf_iter)->GetNodeGlobalIndex(0);
double x = mesh.GetNode(node)->GetPoint()[0];
if (fabs(x - 1.0) < 0.01)
{
bcc.AddNeumannBoundaryCondition(*surf_iter, p_neumann_boundary_condition);
}
surf_iter++;
}
// Solver
SimpleLinearParabolicSolver<2,2> solver(&mesh,&pde,&bcc);
// Initial condition u(0,x,y) = sin(0.5*M_PI*x)*sin(M_PI*y)+x
std::vector<double> init_cond(mesh.GetNumNodes());
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
double x = mesh.GetNode(i)->GetPoint()[0];
double y = mesh.GetNode(i)->GetPoint()[1];
init_cond[i] = sin(0.5*M_PI*x)*sin(M_PI*y)+x;
}
Vec initial_condition = PetscTools::CreateVec(init_cond);
double t_end = 0.1;
solver.SetTimes(0, t_end);
solver.SetTimeStep(0.001);
solver.SetInitialCondition(initial_condition);
Vec result = solver.Solve();
ReplicatableVector result_repl(result);
// Check solution is u = e^{-5/4*M_PI*M_PI*t} sin(0.5*M_PI*x)*sin(M_PI*y)+x, t=0.1
for (unsigned i=0; i<result_repl.GetSize(); i++)
{
double x = mesh.GetNode(i)->GetPoint()[0];
double y = mesh.GetNode(i)->GetPoint()[1];
double u = exp((-5/4)*M_PI*M_PI*t_end) * sin(0.5*M_PI*x) * sin(M_PI*y) + x;
TS_ASSERT_DELTA(result_repl[i], u, 0.001);
}
PetscTools::Destroy(result);
PetscTools::Destroy(initial_condition);
}
