void TestVerifyBoundaryCondition2d() throw(Exception)
{
// Create a cell population
CylindricalHoneycombMeshGenerator generator(4, 4, 0, 1.0);
Cylindrical2dMesh* p_mesh = generator.GetCylindricalMesh();
std::vector<unsigned> location_indices = generator.GetCellLocationIndices();
std::vector<CellPtr> cells;
CryptCellsGenerator<FixedDurationGenerationBasedCellCycleModel> cells_generator;
cells_generator.Generate(cells, p_mesh, std::vector<unsigned>(), true);
MeshBasedCellPopulationWithGhostNodes<2> crypt(*p_mesh, cells, location_indices);
// Store the node locations
std::map<Node<2>*, c_vector<double, 2> > node_locations_before;
for (unsigned node_index=0; node_index<p_mesh->GetNumNodes(); node_index++)
{
node_locations_before[crypt.GetNode(node_index)] = crypt.GetNode(node_index)->rGetLocation();
}
// Now move the first cell (which should be on y=0) down a bit
crypt.GetNode(0)->rGetModifiableLocation()[1] = -0.1;
// Create a boundary condition object
CryptSimulationBoundaryCondition<2> boundary_condition(&crypt);
// Before imposing the boundary condition, it should not be satisfied
TS_ASSERT_EQUALS(boundary_condition.VerifyBoundaryCondition(), false);
boundary_condition.ImposeBoundaryCondition(node_locations_before);
// After imposing the boundary condition, it should be satisfied
TS_ASSERT_EQUALS(boundary_condition.VerifyBoundaryCondition(), true);
}
void TestImposeBoundaryConditionWithNoWnt1d() throw(Exception)
{
// Create 1D cell population
unsigned num_cells = 5;
MutableMesh<1,1> mesh;
mesh.ConstructLinearMesh(num_cells-1);
std::vector<CellPtr> cells;
CellsGenerator<FixedDurationGenerationBasedCellCycleModel, 2> cells_generator;
cells_generator.GenerateBasic(cells, mesh.GetNumNodes());
MeshBasedCellPopulation<1> crypt(mesh, cells);
// Store the node locations
std::map<Node<1>*, c_vector<double, 1> > node_locations_before;
for (unsigned node_index=0; node_index<mesh.GetNumNodes(); node_index++)
{
node_locations_before[crypt.GetNode(node_index)] = crypt.GetNode(node_index)->rGetLocation();
}
// Now move the first cell (which should be on x=0, and a stem cell) to the left a bit
AbstractCellPopulation<1>::Iterator cell_iter = crypt.Begin();
// Check is a stem cell
TS_ASSERT_EQUALS(cell_iter->GetCellProliferativeType()->IsType<StemCellProliferativeType>(), true);
// Check initially at x=0
TS_ASSERT_DELTA(crypt.GetLocationOfCellCentre(*cell_iter)[0], 0.0, 1e-6);
// Now move to the left a bit
crypt.GetNode(0)->rGetModifiableLocation()[0] = -0.1;
TS_ASSERT_LESS_THAN(crypt.GetLocationOfCellCentre(*cell_iter)[0], 0.0);
// Pass this cell population to a boundary condition object
CryptSimulationBoundaryCondition<1> boundary_condition(&crypt);
// Impose the boundary condition without a Wnt stimulus
boundary_condition.ImposeBoundaryCondition(node_locations_before);
/*
* The first cell should have been pulled back to x=0 since it is a stem cell and
* there is no Wnt stimulus. It should be unaffected by jiggling, which is not imposed
* in 1D.
*/
TS_ASSERT_DELTA(0.0, crypt.GetLocationOfCellCentre(*cell_iter)[0], 1e-3);
// The nodes should all now be at their original locations
std::map<Node<1>*, c_vector<double, 1> > node_locations_after;
for (unsigned node_index=0; node_index<mesh.GetNumNodes(); node_index++)
{
node_locations_after[crypt.GetNode(node_index)] = crypt.GetNode(node_index)->rGetLocation();
}
for (unsigned node_index=0; node_index<mesh.GetNumNodes(); node_index++)
{
TS_ASSERT_DELTA(node_locations_before[crypt.GetNode(node_index)](0), node_locations_after[crypt.GetNode(node_index)](0), 1e-3);
}
}
void TestImposeBoundaryConditionWithNoWntButWithJiggling() throw(Exception)
{
// Create a cell population
CylindricalHoneycombMeshGenerator generator(4, 4, 0, 1.0);
Cylindrical2dMesh* p_mesh = generator.GetCylindricalMesh();
std::vector<unsigned> location_indices = generator.GetCellLocationIndices();
std::vector<CellPtr> cells;
MAKE_PTR(TransitCellProliferativeType, p_transit_type);
CryptCellsGenerator<FixedDurationGenerationBasedCellCycleModel> cells_generator;
cells_generator.Generate(cells, p_mesh, std::vector<unsigned>(), true);
MeshBasedCellPopulationWithGhostNodes<2> crypt(*p_mesh, cells, location_indices);
// Store the node locations
std::map<Node<2>*, c_vector<double, 2> > node_locations_before;
for (unsigned node_index=0; node_index<p_mesh->GetNumNodes(); node_index++)
{
node_locations_before[crypt.GetNode(node_index)] = crypt.GetNode(node_index)->rGetLocation();
}
// Move the first cell (which should be on y=0, and is a stem cell) down a bit
AbstractCellPopulation<2>::Iterator cell_iter = crypt.Begin();
crypt.GetNode(0)->rGetModifiableLocation()[1] = -0.1;
// Also move the second cell (which should be on y=0, and we make a transit cell)
++cell_iter;
TS_ASSERT_EQUALS(cell_iter->GetCellProliferativeType()->IsType<StemCellProliferativeType>(), true);
cell_iter->SetCellProliferativeType(p_transit_type);
TS_ASSERT_EQUALS(cell_iter->GetCellProliferativeType()->IsType<TransitCellProliferativeType>(), true);
TS_ASSERT_DELTA(crypt.GetLocationOfCellCentre(*cell_iter)[1], 0.0, 1e-6);
crypt.GetNode(1)->rGetModifiableLocation()[1] = -0.1;
TS_ASSERT_LESS_THAN(crypt.GetLocationOfCellCentre(*cell_iter)[1], 0.0);
// Create a boundary condition object
CryptSimulationBoundaryCondition<2> boundary_condition(&crypt);
boundary_condition.SetUseJiggledBottomCells(true);
// Impose the boundary condition without a Wnt stimulus but with jiggled bottom cells
boundary_condition.ImposeBoundaryCondition(node_locations_before);
/*
* The first cell should have been pulled up to y=0 since it is a stem cell and
* there is no Wnt stimulus. It should then be unaffected by the jiggling. The
* second cell should not have been pulled up since it is a stem cell, but should
* then have been moved to above y=0 by the jiggling.
*/
AbstractCellPopulation<2>::Iterator cell_iter2 = crypt.Begin();
TS_ASSERT_DELTA(0.0, crypt.GetLocationOfCellCentre(*cell_iter2)[1], 1e-3);
++cell_iter2;
TS_ASSERT_LESS_THAN(0.0, crypt.GetLocationOfCellCentre(*cell_iter2)[1]);
}
void TestImposeBoundaryConditionWithWntButNoJiggling() throw(Exception)
{
// Create a cell population
CylindricalHoneycombMeshGenerator generator(4, 4, 0, 1.0);
Cylindrical2dMesh* p_mesh = generator.GetCylindricalMesh();
std::vector<unsigned> location_indices = generator.GetCellLocationIndices();
std::vector<CellPtr> cells;
CryptCellsGenerator<FixedDurationGenerationBasedCellCycleModel> cells_generator;
cells_generator.Generate(cells, p_mesh, std::vector<unsigned>(), true);
MeshBasedCellPopulationWithGhostNodes<2> crypt(*p_mesh, cells, location_indices);
// Store the node locations
std::map<Node<2>*, c_vector<double, 2> > node_locations_before;
for (unsigned node_index=0; node_index<p_mesh->GetNumNodes(); node_index++)
{
node_locations_before[crypt.GetNode(node_index)] = crypt.GetNode(node_index)->rGetLocation();
}
// Move the first cell (which should be on y=0) down a bit
AbstractCellPopulation<2>::Iterator cell_iter = crypt.Begin();
crypt.GetNode(0)->rGetModifiableLocation()[1] = -0.1;
c_vector<double, 2> perturbed_location = crypt.GetLocationOfCellCentre(*cell_iter);
// Create a boundary condition object
CryptSimulationBoundaryCondition<2> boundary_condition(&crypt);
boundary_condition.SetUseJiggledBottomCells(false);
// Set up a WntConcentration singleton object
WntConcentration<2>* p_wnt = WntConcentration<2>::Instance();
WntConcentration<2>::Instance()->SetType(LINEAR);
WntConcentration<2>::Instance()->SetCellPopulation(crypt);
WntConcentration<2>::Instance()->SetCryptLength(crypt.GetWidth(1));
TS_ASSERT_EQUALS(p_wnt->IsWntSetUp(), true);
// Impose the boundary condition with a Wnt stimulus but without jiggled bottom cells
boundary_condition.ImposeBoundaryCondition(node_locations_before);
/*
* The first cell should not have been moved by the boundary condition object,
* and hence should remain in its perturbed location.
*/
c_vector<double, 2> location_after = crypt.GetLocationOfCellCentre(*cell_iter);
TS_ASSERT_DELTA(location_after[0], perturbed_location[0], 1e-3);
TS_ASSERT_DELTA(location_after[1], location_after[1], 1e-3);
// Tidy up
WntConcentration<2>::Destroy();
}
void TestImposeBoundaryConditionWithNoWntOrJiggling2d() throw(Exception)
{
// Create a cell population
CylindricalHoneycombMeshGenerator generator(4, 4, 0, 1.0);
Cylindrical2dMesh* p_mesh = generator.GetCylindricalMesh();
std::vector<unsigned> location_indices = generator.GetCellLocationIndices();
std::vector<CellPtr> cells;
CryptCellsGenerator<FixedDurationGenerationBasedCellCycleModel> cells_generator;
cells_generator.Generate(cells, p_mesh, std::vector<unsigned>(), true);
MeshBasedCellPopulationWithGhostNodes<2> crypt(*p_mesh, cells, location_indices);
// Store the node locations
std::map<Node<2>*, c_vector<double, 2> > node_locations_before;
for (unsigned node_index=0; node_index<p_mesh->GetNumNodes(); node_index++)
{
node_locations_before[crypt.GetNode(node_index)] = crypt.GetNode(node_index)->rGetLocation();
}
// Now move the first cell (which should be on y=0) down a bit
AbstractCellPopulation<2>::Iterator cell_iter = crypt.Begin();
TS_ASSERT_DELTA(crypt.GetLocationOfCellCentre(*cell_iter)[1], 0.0, 1e-6);
crypt.GetNode(0)->rGetModifiableLocation()[1] = -0.1;
TS_ASSERT_LESS_THAN(crypt.GetLocationOfCellCentre(*cell_iter)[1], 0.0);
// Create a boundary condition object
CryptSimulationBoundaryCondition<2> boundary_condition(&crypt);
boundary_condition.SetUseJiggledBottomCells(false);
// Impose the boundary condition without a Wnt stimulus or jiggled bottom cells
boundary_condition.ImposeBoundaryCondition(node_locations_before);
// The first cell should have been moved back by the boundary condition object
TS_ASSERT_DELTA(crypt.GetLocationOfCellCentre(*cell_iter)[1], 0.0, 1e-4);
// The nodes should all now be at their original locations
std::map<Node<2>*, c_vector<double, 2> > node_locations_after;
for (unsigned node_index=0; node_index<p_mesh->GetNumNodes(); node_index++)
{
node_locations_after[crypt.GetNode(node_index)] = crypt.GetNode(node_index)->rGetLocation();
}
for (unsigned node_index=0; node_index<p_mesh->GetNumNodes(); node_index++)
{
TS_ASSERT_DELTA(node_locations_before[crypt.GetNode(node_index)](0), node_locations_after[crypt.GetNode(node_index)](0), 1e-3);
TS_ASSERT_DELTA(node_locations_before[crypt.GetNode(node_index)](1), node_locations_after[crypt.GetNode(node_index)](1), 1e-3);
}
}
void TestImposeBoundaryConditionWithWnt1d() throw(Exception)
{
// Create 1D cell population
unsigned num_cells = 5;
MutableMesh<1,1> mesh;
mesh.ConstructLinearMesh(num_cells-1);
std::vector<CellPtr> cells;
CellsGenerator<FixedDurationGenerationBasedCellCycleModel, 2> cells_generator;
cells_generator.GenerateBasic(cells, mesh.GetNumNodes());
MeshBasedCellPopulation<1> crypt(mesh, cells);
// Set up a WntConcentration singleton object
WntConcentration<1>* p_wnt = WntConcentration<1>::Instance();
WntConcentration<1>::Instance()->SetType(LINEAR);
WntConcentration<1>::Instance()->SetCellPopulation(crypt);
WntConcentration<1>::Instance()->SetCryptLength(crypt.GetWidth(0));
TS_ASSERT_EQUALS(p_wnt->IsWntSetUp(), true);
// Store the node locations
std::map<Node<1>*, c_vector<double, 1> > node_locations_before;
for (unsigned node_index=0; node_index<mesh.GetNumNodes(); node_index++)
{
node_locations_before[crypt.GetNode(node_index)] = crypt.GetNode(node_index)->rGetLocation();
}
// Now move the first cell (which should be on x=0) to the left a bit
AbstractCellPopulation<1>::Iterator cell_iter = crypt.Begin();
// Check initially at x=0
TS_ASSERT_DELTA(crypt.GetLocationOfCellCentre(*cell_iter)[0], 0.0, 1e-6);
// Now move to the left a bit
crypt.GetNode(0)->rGetModifiableLocation()[0] = -0.1;
TS_ASSERT_DELTA(-0.1, crypt.GetLocationOfCellCentre(*cell_iter)[0], 1e-3);
// Pass this cell population to a boundary condition object
CryptSimulationBoundaryCondition<1> boundary_condition(&crypt);
// Impose the boundary condition with a Wnt stimulus
boundary_condition.ImposeBoundaryCondition(node_locations_before);
// This node will be moved back to 0.0
TS_ASSERT_DELTA(0.0, crypt.GetLocationOfCellCentre(*cell_iter)[0], 1e-3);
// Tidy up
WntConcentration<1>::Destroy();
}
void TestConstructorWithCellPopulation2d() throw (Exception)
{
// Create a 2d mesh-based cell population
CylindricalHoneycombMeshGenerator generator(4, 4, 0, 1.0);
Cylindrical2dMesh* p_mesh = generator.GetCylindricalMesh();
std::vector<unsigned> location_indices = generator.GetCellLocationIndices();
std::vector<CellPtr> cells;
CryptCellsGenerator<FixedDurationGenerationBasedCellCycleModel> cells_generator;
cells_generator.Generate(cells, p_mesh, std::vector<unsigned>(), true);
MeshBasedCellPopulationWithGhostNodes<2> crypt(*p_mesh, cells, location_indices);
// Pass this cell population to a boundary condition object
CryptSimulationBoundaryCondition<2> boundary_condition(&crypt);
// Test access to the cell population
const AbstractCellPopulation<2>* p_population = boundary_condition.GetCellPopulation();
TS_ASSERT(p_population != NULL);
}
void TestVerifyBoundaryCondition1d() throw(Exception)
{
// Create 1D cell population
unsigned num_cells = 5;
MutableMesh<1,1> mesh;
mesh.ConstructLinearMesh(num_cells-1);
std::vector<CellPtr> cells;
CellsGenerator<FixedDurationGenerationBasedCellCycleModel, 2> cells_generator;
cells_generator.GenerateBasic(cells, mesh.GetNumNodes());
MeshBasedCellPopulation<1> crypt(mesh, cells);
// Set up a WntConcentration singleton object
WntConcentration<1>* p_wnt = WntConcentration<1>::Instance();
WntConcentration<1>::Instance()->SetType(LINEAR);
WntConcentration<1>::Instance()->SetCellPopulation(crypt);
WntConcentration<1>::Instance()->SetCryptLength(crypt.GetWidth(0));
TS_ASSERT_EQUALS(p_wnt->IsWntSetUp(), true);
// Store the node locations
std::map<Node<1>*, c_vector<double, 1> > node_locations_before;
for (unsigned node_index=0; node_index<mesh.GetNumNodes(); node_index++)
{
node_locations_before[crypt.GetNode(node_index)] = crypt.GetNode(node_index)->rGetLocation();
}
crypt.GetNode(0)->rGetModifiableLocation()[0] = -0.1;
// Create a boundary condition object
CryptSimulationBoundaryCondition<1> boundary_condition(&crypt);
// Before imposing the boundary condition, it should not be satisfied
TS_ASSERT_EQUALS(boundary_condition.VerifyBoundaryCondition(), false);
boundary_condition.ImposeBoundaryCondition(node_locations_before);
// After imposing the boundary condition, it should be satisfied
TS_ASSERT_EQUALS(boundary_condition.VerifyBoundaryCondition(), true);
}
void TestOutputParameters2d() throw(Exception)
{
std::string output_directory = "TestOutputParameters2d";
OutputFileHandler output_file_handler(output_directory, false);
CryptSimulationBoundaryCondition<2> boundary_condition(NULL);
TS_ASSERT_EQUALS(boundary_condition.GetIdentifier(), "CryptSimulationBoundaryCondition-2");
out_stream boundary_condition_parameter_file = output_file_handler.OpenOutputFile("results2d.parameters");
boundary_condition.OutputCellPopulationBoundaryConditionParameters(boundary_condition_parameter_file);
boundary_condition_parameter_file->close();
std::string boundary_condition_results_dir = output_file_handler.GetOutputDirectoryFullPath();
FileComparison( boundary_condition_results_dir + "results2d.parameters", "crypt/test/data/TestCryptSimulationBoundaryCondition/results2d.parameters").CompareFiles();
// Test OutputCellPopulationBoundaryConditionInfo() method
out_stream boundary_condition_info_file = output_file_handler.OpenOutputFile("results2d.info");
boundary_condition.OutputCellPopulationBoundaryConditionInfo(boundary_condition_info_file);
boundary_condition_info_file->close();
FileComparison( boundary_condition_results_dir + "results2d.info", "crypt/test/data/TestCryptSimulationBoundaryCondition/results2d.info").CompareFiles();
}
void TestArchiving2d() throw (Exception)
{
// Set up singleton classes
OutputFileHandler handler("archive", false); // don't erase contents of folder
std::string archive_filename = handler.GetOutputDirectoryFullPath() + "CryptSimulationBoundaryCondition2.arch";
{
// Create an output archive
CryptSimulationBoundaryCondition<2> boundary_condition(NULL);
boundary_condition.SetUseJiggledBottomCells(true);
std::ofstream ofs(archive_filename.c_str());
boost::archive::text_oarchive output_arch(ofs);
// Serialize via pointer
AbstractCellPopulationBoundaryCondition<2>* const p_boundary_condition = &boundary_condition;
output_arch << p_boundary_condition;
}
{
// Create an input archive
std::ifstream ifs(archive_filename.c_str(), std::ios::binary);
boost::archive::text_iarchive input_arch(ifs);
AbstractCellPopulationBoundaryCondition<2>* p_boundary_condition;
// Restore from the archive
input_arch >> p_boundary_condition;
// Test we have restored the plane geometry correctly
TS_ASSERT_EQUALS(static_cast<CryptSimulationBoundaryCondition<2>*>(p_boundary_condition)->GetUseJiggledBottomCells(), true);
// Tidy up
delete p_boundary_condition;
}
}
void update ( int id, int p )
/******************************************************************************/
/*
Purpose:
UPDATE computes the solution of the heat equation.
Discussion:
If there is only one processor ( P == 1 ), then the program writes the
values of X and H to files.
Parameters:
Input, int ID, the id of this processor.
Input, int P, the number of processors.
*/
{
double cfl;
double *h;
FILE *h_file;
double *h_new;
int i;
int j;
int j_min = 0;
int j_max = 400;
double k = 0.002;
int n = 11;
MPI_Status status;
int tag;
double time;
double time_delta;
double time_max = 10.0;
double time_min = 0.0;
double time_new;
double *x;
double x_delta;
FILE *x_file;
double x_max = 1.0;
double x_min = 0.0;
/*
Have process 0 print out some information.
*/
if ( id == 0 )
{
printf ( "\n" );
printf ( " Compute an approximate solution to the time dependent\n" );
printf ( " one dimensional heat equation:\n" );
printf ( "\n" );
printf ( " dH/dt - K * d2H/dx2 = f(x,t)\n" );
printf ( "\n" );
printf ( " for %f = x_min < x < x_max = %f\n", x_min, x_max );
printf ( "\n" );
printf ( " and %f = time_min < t <= t_max = %f\n", time_min, time_max );
printf ( "\n" );
printf ( " Boundary conditions are specified at x_min and x_max.\n" );
printf ( " Initial conditions are specified at time_min.\n" );
printf ( "\n" );
printf ( " The finite difference method is used to discretize the\n" );
printf ( " differential equation.\n" );
printf ( "\n" );
printf ( " This uses %d equally spaced points in X\n", p * n );
printf ( " and %d equally spaced points in time.\n", j_max );
printf ( "\n" );
printf ( " Parallel execution is done using %d processors.\n", p );
printf ( " Domain decomposition is used.\n" );
printf ( " Each processor works on %d nodes, \n", n );
printf ( " and shares some information with its immediate neighbors.\n" );
}
/*
Set the X coordinates of the N nodes.
We don't actually need ghost values of X but we'll throw them in
as X[0] and X[N+1].
*/
x = ( double * ) malloc ( ( n + 2 ) * sizeof ( double ) );
for ( i = 0; i <= n + 1; i++ )
{
x[i] = ( ( double ) ( id * n + i - 1 ) * x_max
+ ( double ) ( p * n - id * n - i ) * x_min )
/ ( double ) ( p * n - 1 );
}
/*
In single processor mode, write out the X coordinates for display.
*/
if ( p == 1 )
{
x_file = fopen ( "x_data.txt", "w" );
for ( i = 1; i <= n; i++ )
{
fprintf ( x_file, " %f", x[i] );
}
fprintf ( x_file, "\n" );
fclose ( x_file );
}
/*
Set the values of H at the initial time.
*/
time = time_min;
h = ( double * ) malloc ( ( n + 2 ) * sizeof ( double ) );
h_new = ( double * ) malloc ( ( n + 2 ) * sizeof ( double ) );
h[0] = 0.0;
for ( i = 1; i <= n; i++ )
{
h[i] = initial_condition ( x[i], time );
}
h[n+1] = 0.0;
time_delta = ( time_max - time_min ) / ( double ) ( j_max - j_min );
x_delta = ( x_max - x_min ) / ( double ) ( p * n - 1 );
/*
Check the CFL condition, have processor 0 print out its value,
and quit if it is too large.
*/
cfl = k * time_delta / x_delta / x_delta;
if ( id == 0 )
{
printf ( "\n" );
printf ( "UPDATE\n" );
printf ( " CFL stability criterion value = %f\n", cfl );
}
if ( 0.5 <= cfl )
{
if ( id == 0 )
{
printf ( "\n" );
printf ( "UPDATE - Warning!\n" );
printf ( " Computation cancelled!\n" );
printf ( " CFL condition failed.\n" );
printf ( " 0.5 <= K * dT / dX / dX = %f\n", cfl );
}
return;
}
/*
In single processor mode, write out the values of H.
*/
if ( p == 1 )
{
h_file = fopen ( "h_data.txt", "w" );
for ( i = 1; i <= n; i++ )
{
fprintf ( h_file, " %f", h[i] );
}
fprintf ( h_file, "\n" );
}
/*
Compute the values of H at the next time, based on current data.
*/
for ( j = 1; j <= j_max; j++ )
{
time_new = ( ( double ) ( j - j_min ) * time_max
+ ( double ) ( j_max - j ) * time_min )
/ ( double ) ( j_max - j_min );
/*
Send H[1] to ID-1.
*/
if ( 0 < id )
{
tag = 1;
MPI_Send ( &h[1], 1, MPI_DOUBLE, id-1, tag, MPI_COMM_WORLD );
}
/*
Receive H[N+1] from ID+1.
*/
if ( id < p-1 )
{
tag = 1;
MPI_Recv ( &h[n+1], 1, MPI_DOUBLE, id+1, tag, MPI_COMM_WORLD, &status );
}
/*
Send H[N] to ID+1.
*/
if ( id < p-1 )
{
tag = 2;
MPI_Send ( &h[n], 1, MPI_DOUBLE, id+1, tag, MPI_COMM_WORLD );
}
/*
Receive H[0] from ID-1.
*/
if ( 0 < id )
{
tag = 2;
MPI_Recv ( &h[0], 1, MPI_DOUBLE, id-1, tag, MPI_COMM_WORLD, &status );
}
/*
Update the temperature based on the four point stencil.
*/
for ( i = 1; i <= n; i++ )
{
h_new[i] = h[i]
+ ( time_delta * k / x_delta / x_delta ) * ( h[i-1] - 2.0 * h[i] + h[i+1] )
+ time_delta * rhs ( x[i], time );
}
/*
H at the extreme left and right boundaries was incorrectly computed
using the differential equation. Replace that calculation by
the boundary conditions.
*/
if ( 0 == id )
{
h_new[1] = boundary_condition ( x[1], time_new );
}
if ( id == p - 1 )
{
h_new[n] = boundary_condition ( x[n], time_new );
}
/*
Update time and temperature.
*/
time = time_new;
for ( i = 1; i <= n; i++ )
{
h[i] = h_new[i];
}
/*
In single processor mode, add current solution data to output file.
*/
if ( p == 1 )
{
for ( i = 1; i <= n; i++ )
{
fprintf ( h_file, " %f", h[i] );
}
fprintf ( h_file, "\n" );
}
}
if ( p == 1 )
{
fclose ( h_file );
}
free ( h );
free ( h_new );
free ( x );
return;
}
//---------------------------------------------------------
int main(int argc, char **argv)
{
TPS<double> rbf;
Polinomio<double> pol;
Matrix<double> A,B;
Vector<double> x,y,f;
Vector<double> lambda,b;
Vector<double> xnew,ynew,fnew;
double c=0.01;
int n,ni,m;
//make the data in the square [0,1] x [0,1]
make_data(0,1,0,1, 21, 21, x, y, ni, n);
//stablish the exponent in: r^beta log(r)
rbf.set_beta(4);
//configure the associate polynomial
// pol.make( data_dimension, degree_pol)
pol.make(2 , rbf.get_degree_pol());
//show the rbf and pol info
cout<<rbf;
cout<<pol;
//show the number of nodes
cout<<endl;
cout<<"total nodes N = "<<n<<endl;
cout<<"interior nodes ni = "<<ni<<endl;
cout<<"boundary nodes nf = "<<n-ni<<endl;
cout<<endl;
//get the number of elements in the polynomial base
m = pol.get_M();
//resize the matrices to store the partial derivatives
A.Resize(n+m,n+m); A = 0.0;
B.Resize(n+m,n+m); B = 0.0;
//Recall that this problem has the general form
// (Uxx+Uyy) (Pxx+Pyy) = f interior nodes 0..ni
// U P_b = g boundary nodes ni..n
// P^transpose 0 = 0 momentun conditions in P
//
// P is the polynomial wit size n x m
// P_b is the polynomial working in the boundary nodes, size nf x m
// Pxx+Pyy has size ni x m
//make the matriz derivatives
fill_matrix( "dxx" , rbf , pol , c , x , y, 0 , ni , A);
fill_matrix( "dyy" , rbf , pol , c , x , y, 0 , ni , B);
A = A + B; // A <- Uxx + Uyy
//Add the submatriz for the boundary nodes: U , P_b boundary nodes ni..n
fill_matrix( "normal" , rbf , pol , c , x , y, ni, n , A);
//Add the submatriz P^transpose at the end: P^transpose
fill_matrix( "pol_trans" , rbf , pol , c , x , y, n , n+m, A);
//resize the vector to store the right_size of the PDE
b.Resize(n+m); b = 0.0;
//fill with f
for(int i=0;i<ni;i++)
b(i) = right_side(x(i), y(i));
//fill with the boundary condition
for(int i=ni;i<n;i++)
b(i) = boundary_condition(x(i),y(i));
//solve the linear system of equations
lambda = gauss(A,b);
//make the new data grid
int ni2,n2;
make_data(0,1,0,1, 41, 41, xnew, ynew, ni2, n2);
//interpolate on this new data grid (xnew,ynew)
fnew = interpolate(rbf,pol,c,lambda,x,y,xnew,ynew);
//determine the maximum error
double e=0.0;
for(int i=0;i<ni2;i++)
{
e = max(e, fabs(fnew(i) - sin(2*M_PI*xnew(i))*cos(2*M_PI*ynew(i))) );
}
//show the error
cout<<endl;
cout<<"The maximum error: e_max = "<<e<<endl<<endl;
//store the interpolated data
save_gnu_data("data",xnew,ynew,fnew);
return 0;
}