CellFilter CellFilter::operator-(const CellFilter& other) const
{
if (other.isNull())
{
return *this;
}
else if (isKnownDisjointWith(other) || other.isKnownDisjointWith(*this))
{
return *this;
}
else if (isKnownSubsetOf(other))
{
CellFilter rtn;
return rtn;
}
else if (*this == other)
{
CellFilter rtn;
return rtn;
}
else
{
CellFilter rtn
= new BinaryCellFilter(*this, other, BinaryCellFilter::Difference);
rtn.registerDisjoint(other);
this->registerSubset(rtn);
return rtn;
}
}
HomogeneousDOFMap::HomogeneousDOFMap(const Mesh& mesh,
const BasisFamily& basis,
int numFuncs,
int setupVerb)
: DOFMapBase(mesh, setupVerb),
dim_(mesh.spatialDim()),
dofs_(mesh.spatialDim()+1),
maximalDofs_(),
haveMaximalDofs_(false),
localNodePtrs_(mesh.spatialDim()+1),
nNodesPerCell_(mesh.spatialDim()+1),
totalNNodesPerCell_(mesh.spatialDim()+1, 0),
numFacets_(mesh.spatialDim()+1),
originalFacetOrientation_(2),
basisIsContinuous_(false)
{
verbosity() = DOFMapBase::classVerbosity();
CellFilter maximalCells = new MaximalCellFilter();
cellSets().append(maximalCells.getCells(mesh));
cellDimOnCellSets().append(mesh.spatialDim());
allocate(mesh, basis, numFuncs);
initMap();
}
CellFilter CellFilter::intersection(const CellFilter& other) const
{
if (isNull() || other.isNull())
{
CellFilter rtn;
return rtn;
}
else if (isKnownDisjointWith(other) || other.isKnownDisjointWith(*this))
{
CellFilter rtn;
return rtn;
}
else if (isKnownSubsetOf(other))
{
return *this;
}
else if (other.isKnownSubsetOf(*this))
{
return other;
}
else if (*this==other)
{
return *this;
}
else
{
CellFilter rtn
= new BinaryCellFilter(*this, other, BinaryCellFilter::Intersection);
other.registerSubset(rtn);
this->registerSubset(rtn);
return rtn;
}
}
void CellFilter::registerDisjoint(const CellFilter& sub) const
{
SubsetManager::registerDisjoint(*this, sub);
for (Set<CellFilter>::const_iterator
i=sub.knownDisjoints().begin(); i!=sub.knownDisjoints().end(); i++)
{
SubsetManager::registerDisjoint(*this, *i);
}
}
/* weak form of poisson with Nitsche-type weak BC's */
Expr poissonEquationNitsche( bool splitBC,
Expr u ,
Expr v ,
Expr alpha ,
QuadratureFamily quad )
{
CellFilter interior = new MaximalCellFilter();
CellFilter boundary = new BoundaryCellFilter();
CellFilter left = boundary.subset( new LeftPointTest() );
CellFilter right = boundary.subset( new RightPointTest() );
CellFilter top = boundary.subset( new TopPointTest() );
CellFilter bottom = boundary.subset( new BottomPointTest() );
CellFilter allBdry = left+right+top+bottom;
Expr dx = new Derivative(0);
Expr dy = new Derivative(1);
Expr x = new CoordExpr(0);
Expr y = new CoordExpr(1);
Expr grad = List( dx , dy );
Expr uvTerm;
if (splitBC)
{
Out::os() << "BC expressions split over domains" << std::endl;
uvTerm = Integral( left , alpha*u * v , quad )
+ Integral( right , alpha*u * v , quad )
+ Integral( top , alpha*u * v , quad )
+ Integral( bottom , alpha*u * v , quad );
}
else
{
Out::os() << "BC expressions not split over domains" << std::endl;
uvTerm = Integral( allBdry , alpha*u * v , quad );
}
const double pi = 4.0*atan(1.0);
Expr force = 2.0*pi*pi*sin(pi*x)*sin(pi*y);
return Integral( interior , (grad*v) * (grad*u) - force * v , quad )
/* du/dn term */
- Integral( left , -(dx*u)*v , quad )
- Integral( top , (dy*u)*v , quad )
- Integral( right , (dx*u)*v , quad )
- Integral( bottom , -(dy*u)*v , quad )
/* dv/dn term */
- Integral( left , -(dx*v)*u , quad )
- Integral( top , (dy*v)*u , quad )
- Integral( right , (dx*v)*u , quad )
- Integral( bottom , -(dy*v)*u , quad )
/* u,v term -- alpha = C / h */
+ uvTerm;
}
DiscreteSpace::DiscreteSpace(const Mesh& mesh, const BasisArray& basis,
const RCP<FunctionSupportResolver>& fsr,
const VectorType<double>& vecType,
int setupVerb)
: setupVerb_(setupVerb),
map_(),
mesh_(mesh),
subdomains_(),
basis_(basis),
vecSpace_(),
vecType_(vecType),
ghostImporter_()
,transformationBuilder_(new DiscreteSpaceTransfBuilder())
{
bool partitionBCs = false;
DOFMapBuilder builder(mesh, fsr, partitionBCs, setupVerb);
map_ = builder.colMap()[0];
Array<Set<CellFilter> > cf = builder.unkCellFilters()[0];
for (int i=0; i<cf.size(); i++)
{
Array<Array<CellFilter> > dimCF(mesh.spatialDim()+1);
for (Set<CellFilter>::const_iterator
iter=cf[i].begin(); iter != cf[i].end(); iter++)
{
CellFilter f = *iter;
int dim = f.dimension(mesh);
dimCF[dim].append(f);
}
for (int d=mesh.spatialDim(); d>=0; d--)
{
if (dimCF[d].size() == 0) continue;
CellFilter f = dimCF[d][0];
for (int j=1; j<dimCF[d].size(); j++)
{
f = f + dimCF[d][j];
}
subdomains_.append(f);
break;
}
}
RCP<Array<int> > dummyBCIndices;
// set up the transformation
transformationBuilder_ = rcp(new DiscreteSpaceTransfBuilder( mesh , basis , map_ ));
initVectorSpace(dummyBCIndices, partitionBCs);
initImporter();
}
bool CellFilter::isKnownDisjointWith(const CellFilter& other) const
{
if (other.knownDisjoints().contains(*this)) return true;
if (this->knownDisjoints().contains(other)) return true;
return false;
}
CellSet connectedNodeSet(const CellFilter& f, const Mesh& mesh)
{
CellSet cells = f.getCells(mesh);
int dim = cells.dimension();
if (dim==0) return cells;
Array<int> cellLID;
for (CellIterator i=cells.begin(); i!=cells.end(); i++)
{
cellLID.append(*i);
}
Array<int> nodes;
Array<int> fo;
mesh.getFacetLIDs(dim, cellLID, 0, nodes, fo);
Set<int> nodeSet;
for (int i=0; i<nodes.size(); i++)
{
nodeSet.put(nodes[i]);
}
return CellSet(mesh, 0, PointCell, nodeSet);
}
CellFilter CellFilter::operator+(const CellFilter& other) const
{
if (isNull())
{
return other;
}
else if (other.isNull())
{
return *this;
}
else
{
CellFilter rtn
= new BinaryCellFilter(*this, other, BinaryCellFilter::Union);
rtn.registerSubset(*this);
rtn.registerSubset(other);
return rtn;
}
}
bool CellFilter::isSubsetOf(const CellFilter& other,
const Mesh& mesh) const
{
if (isKnownSubsetOf(other))
{
return true;
}
else
{
CellSet myCells = getCells(mesh);
CellSet yourCells = other.getCells(mesh);
CellSet inter = myCells.setIntersection(yourCells);
if (inter.begin() == inter.end()) return false;
CellSet diff = myCells.setDifference(inter);
return (diff.begin() == diff.end());
}
}
/**
* This example program sets up and solves the Laplace
* equation \f$-\nabla^2 u=0\f$. See the
* document GettingStarted.pdf for more information.
*/
int main(int argc, char** argv)
{
try
{
/* command-line options */
std::string meshFile="plateWithHole3D-1";
std::string solverFile = "aztec-ml.xml";
Sundance::setOption("meshFile", meshFile, "mesh file");
Sundance::setOption("solver", solverFile,
"name of XML file for solver");
/* Initialize */
Sundance::init(&argc, &argv);
/* --- Specify vector representation to be used --- */
VectorType<double> vecType = new EpetraVectorType();
/* --- Read mesh --- */
MeshType meshType = new BasicSimplicialMeshType();
MeshSource meshSrc
= new ExodusMeshReader(meshFile, meshType);
Mesh mesh = meshSrc.getMesh();
/* --- Specification of geometric regions --- */
/* Region "interior" consists of all maximal-dimension cells */
CellFilter interior = new MaximalCellFilter();
/* Identify boundary regions via labels in mesh */
CellFilter edges = new DimensionalCellFilter(2);
CellFilter south = edges.labeledSubset(1);
CellFilter east = edges.labeledSubset(2);
CellFilter north = edges.labeledSubset(3);
CellFilter west = edges.labeledSubset(4);
CellFilter hole = edges.labeledSubset(5);
CellFilter down = edges.labeledSubset(6);
CellFilter up = edges.labeledSubset(7);
/* --- Symbolic equation definition --- */
/* Test and unknown function */
BasisFamily basis = new Lagrange(1);
Expr u = new UnknownFunction(basis, "u");
Expr v = new TestFunction(basis, "v");
/* Gradient operator */
Expr dx = new Derivative(0);
Expr dy = new Derivative(1);
Expr dz = new Derivative(2);
Expr grad = List(dx, dy, dz);
/* We need a quadrature rule for doing the integrations */
QuadratureFamily quad1 = new GaussianQuadrature(1);
QuadratureFamily quad2 = new GaussianQuadrature(2);
/** Write the weak form */
Expr eqn
= Integral(interior, (grad*u)*(grad*v), quad1)
+ Integral(east, v, quad1);
/* Write the essential boundary conditions */
Expr h = new CellDiameterExpr();
Expr bc = EssentialBC(west, v*u/h, quad2);
/* Set up linear problem */
LinearProblem prob(mesh, eqn, bc, v, u, vecType);
/* --- solve the problem --- */
/* Create the solver as specified by parameters in
* an XML file */
LinearSolver<double> solver
= LinearSolverBuilder::createSolver(solverFile);
/* Solve! The solution is returned as an Expr containing a
* DiscreteFunction */
Expr soln = prob.solve(solver);
/* --- Postprocessing --- */
/* Project the derivative onto the P1 basis */
DiscreteSpace discSpace(mesh, List(basis, basis, basis), vecType);
L2Projector proj(discSpace, grad*soln);
Expr gradU = proj.project();
/* Write the solution and its projected gradient to a VTK file */
FieldWriter w = new VTKWriter("LaplaceDemo3D");
w.addMesh(mesh);
w.addField("soln", new ExprFieldWrapper(soln[0]));
w.addField("du_dx", new ExprFieldWrapper(gradU[0]));
w.addField("du_dy", new ExprFieldWrapper(gradU[1]));
w.addField("du_dz", new ExprFieldWrapper(gradU[2]));
w.write();
/* Check flux balance */
Expr n = CellNormalExpr(3, "n");
CellFilter wholeBdry = east+west+north+south+up+down+hole;
Expr fluxExpr
= Integral(wholeBdry, (n*grad)*soln, quad1);
double flux = evaluateIntegral(mesh, fluxExpr);
Out::root() << "numerical flux = " << flux << std::endl;
/* --- Let's compute a few other quantities, such as the centroid of
* the mesh:*/
/* Coordinate functions let us build up functions of position */
Expr x = new CoordExpr(0);
Expr y = new CoordExpr(1);
Expr z = new CoordExpr(2);
Expr xCMExpr = Integral(interior, x, quad1);
Expr yCMExpr = Integral(interior, y, quad1);
Expr zCMExpr = Integral(interior, z, quad1);
Expr volExpr = Integral(interior, 1.0, quad1);
double vol = evaluateIntegral(mesh, volExpr);
double xCM = evaluateIntegral(mesh, xCMExpr)/vol;
double yCM = evaluateIntegral(mesh, yCMExpr)/vol;
double zCM = evaluateIntegral(mesh, zCMExpr)/vol;
Out::root() << "centroid = (" << xCM << ", " << yCM
<< ", " << zCM << ")" << std::endl;
/* Next, compute the first Fourier sine coefficient of the solution on the
* surface of the hole.*/
Expr r = sqrt(x*x + y*y);
Expr sinPhi = y/r;
/* Use a higher-order quadrature rule for these integrals */
QuadratureFamily quad4 = new GaussianQuadrature(4);
Expr fourierSin1Expr = Integral(hole, sinPhi*soln, quad4);
Expr fourierDenomExpr = Integral(hole, sinPhi*sinPhi, quad2);
double fourierSin1 = evaluateIntegral(mesh, fourierSin1Expr);
double fourierDenom = evaluateIntegral(mesh, fourierDenomExpr);
Out::root() << "fourier sin m=1 = " << fourierSin1/fourierDenom << std::endl;
/* Compute the L2 norm of the solution */
Expr L2NormExpr = Integral(interior, soln*soln, quad2);
double l2Norm_method1 = sqrt(evaluateIntegral(mesh, L2NormExpr));
Out::os() << "method #1: ||soln|| = " << l2Norm_method1 << endl;
/* Use the L2Norm() function to do the same calculation */
double l2Norm_method2 = L2Norm(mesh, interior, soln, quad2);
Out::os() << "method #2: ||soln|| = " << l2Norm_method2 << endl;
/*
* Check that the flux is acceptably close to zero. The flux calculation
* is only O(h) so keep the tolerance loose. This
* is just a sanity check to ensure the code doesn't get completely
* broken after a change to the library.
*/
Sundance::passFailTest(fabs(flux), 1.0e-2);
}
catch(std::exception& e)
{
Sundance::handleException(e);
}
Sundance::finalize();
return Sundance::testStatus();
}
int main(int argc, char** argv)
{
try
{
const double pi = 4.0*atan(1.0);
double lambda = 1.25*pi*pi;
int nx = 32;
int nt = 10;
double tFinal = 1.0/lambda;
Sundance::setOption("nx", nx, "Number of elements");
Sundance::setOption("nt", nt, "Number of timesteps");
Sundance::setOption("tFinal", tFinal, "Final time");
Sundance::init(&argc, &argv);
/* Creation of vector type */
VectorType<double> vecType = new EpetraVectorType();
/* Set up mesh */
MeshType meshType = new BasicSimplicialMeshType();
MeshSource meshSrc = new PartitionedRectangleMesher(
0.0, 1.0, nx,
0.0, 1.0, nx,
meshType);
Mesh mesh = meshSrc.getMesh();
/*
* Specification of cell filters
*/
CellFilter interior = new MaximalCellFilter();
CellFilter edges = new DimensionalCellFilter(1);
CellFilter west = edges.coordSubset(0, 0.0);
CellFilter east = edges.coordSubset(0, 1.0);
CellFilter south = edges.coordSubset(1, 0.0);
CellFilter north = edges.coordSubset(1, 1.0);
/* set up test and unknown functions */
BasisFamily basis = new Lagrange(1);
Expr u = new UnknownFunction(basis, "u");
Expr v = new TestFunction(basis, "v");
/* set up differential operators */
Expr grad = gradient(2);
Expr x = new CoordExpr(0);
Expr y = new CoordExpr(1);
Expr t = new Sundance::Parameter(0.0);
Expr tPrev = new Sundance::Parameter(0.0);
DiscreteSpace discSpace(mesh, basis, vecType);
Expr uExact = cos(0.5*pi*y)*sin(pi*x)*exp(-lambda*t);
L2Projector proj(discSpace, uExact);
Expr uPrev = proj.project();
/*
* We need a quadrature rule for doing the integrations
*/
QuadratureFamily quad = new GaussianQuadrature(2);
double deltaT = tFinal/nt;
Expr gWest = -pi*exp(-lambda*t)*cos(0.5*pi*y);
Expr gWestPrev = -pi*exp(-lambda*tPrev)*cos(0.5*pi*y);
/* Create the weak form */
Expr eqn = Integral(interior, v*(u-uPrev)/deltaT
+ 0.5*(grad*v)*(grad*u + grad*uPrev), quad)
+ Integral(west, -0.5*v*(gWest+gWestPrev), quad);
Expr bc = EssentialBC(east + north, v*u, quad);
LinearProblem prob(mesh, eqn, bc, v, u, vecType);
LinearSolver<double> solver
= LinearSolverBuilder::createSolver("amesos.xml");
FieldWriter w0 = new VTKWriter("TransientHeat2D-0");
w0.addMesh(mesh);
w0.addField("T", new ExprFieldWrapper(uPrev[0]));
w0.write();
for (int i=0; i<nt; i++)
{
t.setParameterValue((i+1)*deltaT);
tPrev.setParameterValue(i*deltaT);
Out::root() << "t=" << (i+1)*deltaT << endl;
Expr uNext = prob.solve(solver);
ostringstream oss;
oss << "TransientHeat2D-" << i+1;
FieldWriter w = new VTKWriter(oss.str());
w.addMesh(mesh);
w.addField("T", new ExprFieldWrapper(uNext[0]));
w.write();
updateDiscreteFunction(uNext, uPrev);
}
double err = L2Norm(mesh, interior, uExact-uPrev, quad);
Out::root() << "error norm=" << err << endl;
double h = 1.0/(nx-1.0);
double tol = 0.1*(pow(h,2.0) + pow(lambda*deltaT, 2.0));
Out::root() << "tol=" << tol << endl;
Sundance::passFailTest(err, tol);
}
catch(std::exception& e)
{
Sundance::handleException(e);
}
Sundance::finalize();
return Sundance::testStatus();
}
bool BlockStochPoissonTest1D()
{
/* We will do our linear algebra using Epetra */
VectorType<double> vecType = new EpetraVectorType();
/* Read a mesh */
MeshType meshType = new BasicSimplicialMeshType();
int nx = 32;
MeshSource mesher = new PartitionedLineMesher(0.0, 1.0, nx,
meshType);
Mesh mesh = mesher.getMesh();
/* Create a cell filter that will identify the maximal cells
* in the interior of the domain */
CellFilter interior = new MaximalCellFilter();
CellFilter pts = new DimensionalCellFilter(0);
CellFilter left = pts.subset(new CoordinateValueCellPredicate(0,0.0));
CellFilter right = pts.subset(new CoordinateValueCellPredicate(0,1.0));
Expr x = new CoordExpr(0);
/* Create the stochastic coefficients */
int nDim = 1;
int order = 6;
#ifdef HAVE_SUNDANCE_STOKHOS
Out::root() << "using Stokhos hermite basis" << std::endl;
SpectralBasis pcBasis = new Stokhos::HermiteBasis<int,double>(order);
#else
Out::root() << "using George's hermite basis" << std::endl;
SpectralBasis pcBasis = new HermiteSpectralBasis(nDim, order);
#endif
Array<Expr> q(pcBasis.nterms());
Array<Expr> kappa(pcBasis.nterms());
Array<Expr> uEx(pcBasis.nterms());
double a = 0.1;
q[0] = -2 + pow(a,2)*(4 - 9*x)*x - 2*pow(a,3)*(-1 + x)*(1 + 3*x*(-3 + 4*x));
q[1] = -(a*(-3 + 10*x + 2*a*(-1 + x*(8 - 9*x +
a*(-4 + 3*(5 - 4*x)*x + 12*a*(-1 + x)*(1 + 5*(-1 + x)*x))))));
q[2] = a*(-4 + 6*x + a*(1 - x*(2 + 3*x) + a*(4 - 28*x + 30*pow(x,2))));
q[3] = -(pow(a,2)*(-3 + x*(20 - 21*x +
a*(-4 + 3*(5 - 4*x)*x + 24*a*(-1 + x)*(1 + 5*(-1 + x)*x)))));
q[4] = pow(a,3)*(1 + x*(-6 + x*(3 + 4*x)));
q[5] = -4*pow(a,4)*(-1 + x)*x*(1 + 5*(-1 + x)*x);
q[6] = 0.0;
uEx[0] = -((-1 + x)*x);
uEx[1] = -(a*(-1 + x)*pow(x,2));
uEx[2] = a*pow(-1 + x,2)*x;
uEx[3] = pow(a,2)*pow(-1 + x,2)*pow(x,2);
uEx[4] = 0.0;
uEx[5] = 0.0;
uEx[6] = 0.0;
kappa[0] = 1.0;
kappa[1] = a*x;
kappa[2] = -(pow(a,2)*(-1 + x)*x);
kappa[3] = 1.0; // unused
kappa[4] = 1.0; // unused
kappa[5] = 1.0; // unused
kappa[6] = 1.0; // unused
Array<Expr> uBC(pcBasis.nterms());
for (int i=0; i<pcBasis.nterms(); i++) uBC[i] = 0.0;
int L = nDim+2;
int P = pcBasis.nterms();
Out::os() << "L = " << L << std::endl;
Out::os() << "P = " << P << std::endl;
/* Create the unknown and test functions. Do NOT use the spectral
* basis here */
Expr u = new UnknownFunction(new Lagrange(4), "u");
Expr v = new TestFunction(new Lagrange(4), "v");
/* Create differential operator and coordinate function */
Expr dx = new Derivative(0);
Expr grad = dx;
/* We need a quadrature rule for doing the integrations */
QuadratureFamily quad = new GaussianQuadrature(12);
/* Now we create problem objects to build each $K_j$ and $f_j$.
* There will be L matrix-vector pairs */
Array<Expr> eqn(P);
Array<Expr> bc(P);
Array<LinearProblem> prob(P);
Array<LinearOperator<double> > KBlock(L);
Array<Vector<double> > fBlock(P);
Array<Vector<double> > solnBlock;
for (int j=0; j<P; j++)
{
eqn[j] = Integral(interior, kappa[j]*(grad*v)*(grad*u) + v*q[j], quad);
bc[j] = EssentialBC(left+right, v*(u-uBC[j]), quad);
prob[j] = LinearProblem(mesh, eqn[j], bc[j], v, u, vecType);
if (j<L) KBlock[j] = prob[j].getOperator();
fBlock[j] = -1.0*prob[j].getSingleRHS();
}
/* Read the solver to be used on the diagonal blocks */
LinearSolver<double> diagSolver
= LinearSolverBuilder::createSolver("amesos.xml");
double convTol = 1.0e-12;
int maxIters = 30;
int verb = 1;
StochBlockJacobiSolver solver(diagSolver, pcBasis,
convTol, maxIters, verb);
solver.solve(KBlock, fBlock, solnBlock);
/* write the solution */
FieldWriter w = new MatlabWriter("Stoch1D");
w.addMesh(mesh);
DiscreteSpace discSpace(mesh, new Lagrange(4), vecType);
for (int i=0; i<P; i++)
{
L2Projector proj(discSpace, uEx[i]);
Expr ue_i = proj.project();
Expr df = new DiscreteFunction(discSpace, solnBlock[i]);
w.addField("u["+ Teuchos::toString(i)+"]",
new ExprFieldWrapper(df));
w.addField("uEx["+ Teuchos::toString(i)+"]",
new ExprFieldWrapper(ue_i));
}
w.write();
double totalErr2 = 0.0;
DiscreteSpace discSpace4(mesh, new Lagrange(4), vecType);
for (int i=0; i<P; i++)
{
Expr df = new DiscreteFunction(discSpace4, solnBlock[i]);
Expr errExpr = Integral(interior, pow(uEx[i]-df, 2.0), quad);
Expr scaleExpr = Integral(interior, pow(uEx[i], 2.0), quad);
double errSq = evaluateIntegral(mesh, errExpr);
double scale = evaluateIntegral(mesh, scaleExpr);
if (scale > 0.0)
Out::os() << "mode i=" << i << " error=" << sqrt(errSq/scale) << std::endl;
else
Out::os() << "mode i=" << i << " error=" << sqrt(errSq) << std::endl;
}
double tol = 1.0e-12;
return SundanceGlobal::checkTest(sqrt(totalErr2), tol);
}
int main(int argc, char** argv)
{
try
{
/*
* Initialization code
*/
std::string meshFile="plateWithHole2D-1";
std::string solverFile = "nox-aztec.xml";
Sundance::setOption("meshFile", meshFile, "mesh file");
Sundance::setOption("solver", solverFile,
"name of XML file for solver");
Sundance::init(&argc, &argv);
// This next line is just a hack to deal with some
// transitional code in the
// element integration logic.
Sundance::ElementIntegral::alwaysUseCofacets() = false;
/*
* Creation of vector type
*/
VectorType<double> vecType = new EpetraVectorType();
/*
* Creation of mesh
*/
MeshType meshType = new BasicSimplicialMeshType();
MeshSource meshSrc
= new ExodusMeshReader(meshFile, meshType);
Mesh mesh = meshSrc.getMesh();
/*
* Specification of cell filters
*/
CellFilter interior = new MaximalCellFilter();
CellFilter edges = new DimensionalCellFilter(1);
CellFilter south = edges.labeledSubset(1);
CellFilter east = edges.labeledSubset(2);
CellFilter north = edges.labeledSubset(3);
CellFilter west = edges.labeledSubset(4);
/*
* <Header level="subsubsection" name="symb_setup">
* Setup of symbolic problem description
* </Header>
*
* Create unknown and test functions discretized on the space
* first-order Lagrange polynomials.
*/
BasisFamily basis = new Lagrange(2);
Expr u = new UnknownFunction(basis, "u");
Expr v = new TestFunction(basis, "v");
/*
* Create differential operators and coordinate functions. Directions
* are indexed starting from zero. The \verb+List()+ function can
* collect expressions into a vector.
*/
Expr dx = new Derivative(0);
Expr dy = new Derivative(1);
Expr grad = List(dx, dy);
Expr x = new CoordExpr(0);
Expr y = new CoordExpr(1);
/*
* We need a quadrature rule for doing the integrations
*/
QuadratureFamily quad2 = new GaussianQuadrature(2);
QuadratureFamily quad4 = new GaussianQuadrature(4);
/*
* Create the weak form and the BCs
*/
Expr source=exp(u);
Expr eqn
= Integral(interior, (grad*u)*(grad*v)+v*source, quad4);
Expr h = new CellDiameterExpr();
Expr bc = EssentialBC(west+east, v*(u-1.0)/h, quad2);
/*
* <Header level="subsubsection" name="lin_prob">
* Creation of initial guess
* </Header>
*
* So far the setup has been almost identical to that for the linear
* problem, the only difference being the nonlinear term in the
* equation set.
*/
DiscreteSpace discSpace(mesh, basis, vecType);
L2Projector proj(discSpace, 1.0);
Expr u0 = proj.project();
/*
* <Header level="subsubsection" name="lin_prob">
* Creation of nonlinear problem
* </Header>
*
* Similar to the setup of a \verb+LinearProblem+, the equation, BCs,
* and mesh are put into a \verb+NonlinearProblem+ object which
* controls the construction of the \verb+Assembler+ and its use
* in building Jacobians and residuals during a nonlinear solve.
*/
NonlinearProblem prob(mesh, eqn, bc, v, u, u0, vecType);
/*
*
*/
ParameterXMLFileReader reader(solverFile);
ParameterList solverParams = reader.getParameters();
NOXSolver solver(solverParams);
prob.solve(solver);
/*
* Visualization output
*/
FieldWriter w = new VTKWriter("PoissonBoltzmannDemo2D");
w.addMesh(mesh);
w.addField("soln", new ExprFieldWrapper(u0));
w.write();
/*
* <Header level="subsubsection" name="postproc">
* Postprocessing
* </Header>
*
* Postprocessing can be done using the same symbolic language
* as was used for the problem specification. Here, we define
* an integral giving the flux, then evaluate it on the mesh.
*/
Expr n = CellNormalExpr(2, "n");
Expr fluxExpr
= Integral(east + west, (n*grad)*u0, quad2);
double flux = evaluateIntegral(mesh, fluxExpr);
Out::os() << "numerical flux = " << flux << std::endl;
Expr sourceExpr
= Integral(interior, exp(u0), quad4);
double src = evaluateIntegral(mesh, sourceExpr);
Out::os() << "numerical integrated source = " << src << std::endl;
/*
* Check that the flux is acceptably close to zero. This
* is just a sanity check to ensure the code doesn't get completely
* broken after a change to the library.
*/
Sundance::passFailTest(fabs(flux-src), 1.0e-3);
/*
* <Header level="subsubsection" name="finalize">
* Finalization boilerplate
* </Header>
* Finally, we have boilerplate code for exception handling
* and finalization.
*/
}
catch(std::exception& e)
{
Sundance::handleException(e);
}
Sundance::finalize(); return Sundance::testStatus();
return Sundance::testStatus();
}
int main(int argc, char** argv)
{
try
{
int depth = 0;
bool useCCode = false;
Sundance::ElementIntegral::alwaysUseCofacets() = true;
Sundance::clp().setOption("depth", &depth, "expression depth");
Sundance::clp().setOption("C", "symb", &useCCode, "Code type (C or symbolic)");
Sundance::init(&argc, &argv);
/* We will do our linear algebra using Epetra */
VectorType<double> vecType = new EpetraVectorType();
/* Read the mesh */
MeshType meshType = new BasicSimplicialMeshType();
MeshSource mesher
= new ExodusMeshReader("cube-0.1", meshType);
Mesh mesh = mesher.getMesh();
/* Create a cell filter that will identify the maximal cells
* in the interior of the domain */
CellFilter interior = new MaximalCellFilter();
CellFilter faces = new DimensionalCellFilter(2);
CellFilter side1 = faces.labeledSubset(1);
CellFilter side2 = faces.labeledSubset(2);
CellFilter side3 = faces.labeledSubset(3);
CellFilter side4 = faces.labeledSubset(4);
CellFilter side5 = faces.labeledSubset(5);
CellFilter side6 = faces.labeledSubset(6);
/* Create unknown and test functions, discretized using second-order
* Lagrange interpolants */
Expr u = new UnknownFunction(new Lagrange(1), "u");
Expr v = new TestFunction(new Lagrange(1), "v");
/* Create differential operator and coordinate functions */
Expr dx = new Derivative(0);
Expr dy = new Derivative(1);
Expr dz = new Derivative(2);
Expr grad = List(dx, dy, dz);
Expr x = new CoordExpr(0);
Expr y = new CoordExpr(1);
Expr z = new CoordExpr(2);
/* We need a quadrature rule for doing the integrations */
QuadratureFamily quad2 = new GaussianQuadrature(2);
QuadratureFamily quad4 = new GaussianQuadrature(4);
/* Define the weak form */
//Expr eqn = Integral(interior, (grad*v)*(grad*u) + v, quad);
Expr coeff = 1.0;
#ifdef FOR_TIMING
if (useCCode)
{
coeff = Poly(depth, x);
}
else
{
for (int i=0; i<depth; i++)
{
Expr t = 1.0;
for (int j=0; j<depth; j++) t = t*x;
coeff = coeff + 2.0*t - t - t;
}
}
#endif
Expr eqn = Integral(interior, coeff*(grad*v)*(grad*u) /*+ 2.0*v*/, quad2);
/* Define the Dirichlet BC */
Expr exactSoln = x;//(x + 1.0)*x - 1.0/4.0;
Expr h = new CellDiameterExpr();
WatchFlag watchBC("watch BCs");
watchBC.setParam("integration setup", 6);
watchBC.setParam("integration", 6);
watchBC.setParam("fill", 6);
watchBC.setParam("evaluation", 6);
watchBC.deactivate();
Expr bc = EssentialBC(side4, v*(u-exactSoln), quad4)
+ EssentialBC(side6, v*(u-exactSoln), quad4, watchBC);
/* We can now set up the linear problem! */
LinearProblem prob(mesh, eqn, bc, v, u, vecType);
#ifdef HAVE_CONFIG_H
ParameterXMLFileReader reader(searchForFile("SolverParameters/aztec-ml.xml"));
#else
ParameterXMLFileReader reader("aztec-ml.xml");
#endif
ParameterList solverParams = reader.getParameters();
std::cerr << "params = " << solverParams << std::endl;
LinearSolver<double> solver
= LinearSolverBuilder::createSolver(solverParams);
Expr soln = prob.solve(solver);
#ifndef FOR_TIMING
DiscreteSpace discSpace(mesh, new Lagrange(1), vecType);
L2Projector proj1(discSpace, exactSoln);
L2Projector proj2(discSpace, soln-exactSoln);
L2Projector proj3(discSpace, pow(soln-exactSoln, 2.0));
Expr exactDisc = proj1.project();
Expr errorDisc = proj2.project();
// Expr errorSqDisc = proj3.project();
std::cerr << "writing fields" << std::endl;
/* Write the field in VTK format */
FieldWriter w = new VTKWriter("Poisson3d");
w.addMesh(mesh);
w.addField("soln", new ExprFieldWrapper(soln[0]));
w.addField("exact soln", new ExprFieldWrapper(exactDisc));
w.addField("error", new ExprFieldWrapper(errorDisc));
// w.addField("errorSq", new ExprFieldWrapper(errorSqDisc));
w.write();
std::cerr << "computing error" << std::endl;
Expr errExpr = Integral(interior,
pow(soln-exactSoln, 2.0),
new GaussianQuadrature(4));
double errorSq = evaluateIntegral(mesh, errExpr);
std::cerr << "error norm = " << sqrt(errorSq) << std::endl << std::endl;
#else
double errorSq = 1.0;
#endif
double tol = 1.0e-10;
Sundance::passFailTest(sqrt(errorSq), tol);
}
catch(std::exception& e)
{
Sundance::handleException(e);
}
Sundance::finalize(); return Sundance::testStatus();
}
SubmaximalNodalDOFMap
::SubmaximalNodalDOFMap(const Mesh& mesh,
const CellFilter& cf,
int nFuncs,
int setupVerb)
: DOFMapBase(mesh, setupVerb),
dim_(0),
nTotalFuncs_(nFuncs),
domain_(cf),
domains_(tuple(cf)),
nodeLIDs_(),
nodeDOFs_(),
lidToPtrMap_(),
mapStructure_()
{
Tabs tab0(0);
SUNDANCE_MSG1(setupVerb, tab0 << "in SubmaximalNodalDOFMap ctor");
Tabs tab1;
SUNDANCE_MSG2(setupVerb, tab1 << "domain " << domain_);
SUNDANCE_MSG2(setupVerb, tab1 << "N funcs " << nFuncs);
const MPIComm& comm = mesh.comm();
int rank = comm.getRank();
int nProc = comm.getNProc();
dim_ = cf.dimension(mesh);
TEUCHOS_TEST_FOR_EXCEPT(dim_ != 0);
CellSet nodes = cf.getCells(mesh);
int nc = nodes.numCells();
nodeLIDs_.reserve(nc);
nodeDOFs_.reserve(nc);
Array<Array<int> > remoteNodes(nProc);
int nextDOF = 0;
int k=0;
for (CellIterator c=nodes.begin(); c!=nodes.end(); c++, k++)
{
int nodeLID = *c;
lidToPtrMap_.put(nodeLID, k);
nodeLIDs_.append(nodeLID);
int remoteOwner = rank;
if (isRemote(0, nodeLID, remoteOwner))
{
int GID = mesh.mapLIDToGID(0, nodeLID);
remoteNodes[remoteOwner].append(GID);
for (int f=0; f<nFuncs; f++) nodeDOFs_.append(-1);
}
else
{
for (int f=0; f<nFuncs; f++) nodeDOFs_.append(nextDOF++);
}
}
/* Compute offsets for each processor */
int localCount = nextDOF;
computeOffsets(localCount);
/* Resolve remote DOF numbers */
shareRemoteDOFs(remoteNodes);
BasisFamily basis = new Lagrange(1);
mapStructure_ = rcp(new MapStructure(nTotalFuncs_, basis.ptr()));
}
int main(int argc, char** argv)
{
try
{
int nx = 32;
double convTol = 1.0e-8;
double lambda = 0.5;
Sundance::setOption("nx", nx, "Number of elements");
Sundance::setOption("tol", convTol, "Convergence tolerance");
Sundance::setOption("lambda", lambda, "Lambda (parameter in Bratu's equation)");
Sundance::init(&argc, &argv);
Out::root() << "Bratu problem (lambda=" << lambda << ")" << endl;
Out::root() << "Newton's method, linearized by hand" << endl << endl;
VectorType<double> vecType = new EpetraVectorType();
MeshType meshType = new BasicSimplicialMeshType();
MeshSource mesher = new PartitionedLineMesher(0.0, 1.0, nx, meshType);
Mesh mesh = mesher.getMesh();
CellFilter interior = new MaximalCellFilter();
CellFilter sides = new DimensionalCellFilter(mesh.spatialDim()-1);
CellFilter left = sides.subset(new CoordinateValueCellPredicate(0, 0.0));
CellFilter right = sides.subset(new CoordinateValueCellPredicate(0, 1.0));
BasisFamily basis = new Lagrange(1);
Expr w = new UnknownFunction(basis, "w");
Expr v = new TestFunction(basis, "v");
Expr grad = gradient(1);
Expr x = new CoordExpr(0);
const double pi = 4.0*atan(1.0);
Expr uExact = sin(pi*x);
Expr R = pi*pi*uExact - lambda*exp(uExact);
QuadratureFamily quad4 = new GaussianQuadrature(4);
QuadratureFamily quad2 = new GaussianQuadrature(2);
DiscreteSpace discSpace(mesh, basis, vecType);
Expr uPrev = new DiscreteFunction(discSpace, 0.5);
Expr stepVal = copyDiscreteFunction(uPrev);
Expr eqn
= Integral(interior, (grad*v)*(grad*w) + (grad*v)*(grad*uPrev)
- v*lambda*exp(uPrev)*(1.0+w) - v*R, quad4);
Expr h = new CellDiameterExpr();
Expr bc = EssentialBC(left+right, v*(uPrev+w)/h, quad2);
LinearProblem prob(mesh, eqn, bc, v, w, vecType);
LinearSolver<double> linSolver
= LinearSolverBuilder::createSolver("amesos.xml");
Out::root() << "Newton iteration" << endl;
int maxIters = 20;
Expr soln ;
bool converged = false;
for (int i=0; i<maxIters; i++)
{
/* solve for the next u */
prob.solve(linSolver, stepVal);
Vector<double> stepVec = getDiscreteFunctionVector(stepVal);
double deltaU = stepVec.norm2();
Out::root() << "Iter=" << setw(3) << i << " ||Delta u||=" << setw(20)
<< deltaU << endl;
addVecToDiscreteFunction(uPrev, stepVec);
if (deltaU < convTol)
{
soln = uPrev;
converged = true;
break;
}
}
TEUCHOS_TEST_FOR_EXCEPTION(!converged, std::runtime_error,
"Newton iteration did not converge after "
<< maxIters << " iterations");
FieldWriter writer = new DSVWriter("HandCodedBratu.dat");
writer.addMesh(mesh);
writer.addField("soln", new ExprFieldWrapper(soln[0]));
writer.write();
Out::root() << "Converged!" << endl << endl;
double L2Err = L2Norm(mesh, interior, soln-uExact, quad4);
Out::root() << "L2 Norm of error: " << L2Err << endl;
Sundance::passFailTest(L2Err, 1.5/((double) nx*nx));
}
catch(std::exception& e)
{
Sundance::handleException(e);
}
Sundance::finalize();
}
int main(int argc, char** argv)
{
try
{
int nx = 32;
double convTol = 1.0e-8;
double lambda = 0.5;
Sundance::setOption("nx", nx, "Number of elements");
Sundance::setOption("tol", convTol, "Convergence tolerance");
Sundance::setOption("lambda", lambda, "Lambda (parameter in Bratu's equation)");
Sundance::init(&argc, &argv);
Out::root() << "Bratu problem (lambda=" << lambda << ")" << endl;
Out::root() << "Newton's method with automated linearization"
<< endl << endl;
VectorType<double> vecType = new EpetraVectorType();
MeshType meshType = new BasicSimplicialMeshType();
MeshSource mesher = new PartitionedLineMesher(0.0, 1.0, nx, meshType);
Mesh mesh = mesher.getMesh();
CellFilter interior = new MaximalCellFilter();
CellFilter sides = new DimensionalCellFilter(mesh.spatialDim()-1);
CellFilter left = sides.subset(new CoordinateValueCellPredicate(0, 0.0));
CellFilter right = sides.subset(new CoordinateValueCellPredicate(0, 1.0));
BasisFamily basis = new Lagrange(1);
Expr u = new UnknownFunction(basis, "w");
Expr v = new TestFunction(basis, "v");
Expr grad = gradient(1);
Expr x = new CoordExpr(0);
const double pi = 4.0*atan(1.0);
Expr uExact = sin(pi*x);
Expr R = pi*pi*uExact - lambda*exp(uExact);
QuadratureFamily quad4 = new GaussianQuadrature(4);
QuadratureFamily quad2 = new GaussianQuadrature(2);
DiscreteSpace discSpace(mesh, basis, vecType);
Expr uPrev = new DiscreteFunction(discSpace, 0.5);
Expr eqn
= Integral(interior, (grad*v)*(grad*u) - v*lambda*exp(u) - v*R, quad4);
Expr h = new CellDiameterExpr();
Expr bc = EssentialBC(left+right, v*u/h, quad2);
NonlinearProblem prob(mesh, eqn, bc, v, u, uPrev, vecType);
NonlinearSolver<double> solver
= NonlinearSolverBuilder::createSolver("playa-newton-amesos.xml");
Out::root() << "Newton solve" << endl;
SolverState<double> state = prob.solve(solver);
TEUCHOS_TEST_FOR_EXCEPTION(state.finalState() != SolveConverged,
std::runtime_error,
"Nonlinear solve failed to converge: message=" << state.finalMsg());
Expr soln = uPrev;
FieldWriter writer = new DSVWriter("AutoLinearizedBratu.dat");
writer.addMesh(mesh);
writer.addField("soln", new ExprFieldWrapper(soln[0]));
writer.write();
Out::root() << "Converged!" << endl << endl;
double L2Err = L2Norm(mesh, interior, soln-uExact, quad4);
Out::root() << "L2 Norm of error: " << L2Err << endl;
Sundance::passFailTest(L2Err, 1.5/((double) nx*nx));
}
catch(std::exception& e)
{
Sundance::handleException(e);
}
Sundance::finalize();
return Sundance::testStatus();
}
int main(int argc, char** argv)
{
try
{
int nx = 32;
double convTol = 1.0e-8;
double lambda = 0.5;
Sundance::setOption("nx", nx, "Number of elements");
Sundance::setOption("tol", convTol, "Convergence tolerance");
Sundance::setOption("lambda", lambda, "Lambda (parameter in Bratu's equation)");
Sundance::init(&argc, &argv);
Out::root() << "Bratu problem (lambda=" << lambda << ")" << endl;
Out::root() << "Fixed-point iteration" << endl << endl;
VectorType<double> vecType = new EpetraVectorType();
MeshType meshType = new BasicSimplicialMeshType();
MeshSource mesher = new PartitionedLineMesher(0.0, 1.0, nx, meshType);
Mesh mesh = mesher.getMesh();
CellFilter interior = new MaximalCellFilter();
CellFilter sides = new DimensionalCellFilter(mesh.spatialDim()-1);
CellFilter left = sides.subset(new CoordinateValueCellPredicate(0, 0.0));
CellFilter right = sides.subset(new CoordinateValueCellPredicate(0, 1.0));
BasisFamily basis = new Lagrange(1);
Expr u = new UnknownFunction(basis, "u");
Expr v = new TestFunction(basis, "v");
Expr grad = gradient(1);
Expr x = new CoordExpr(0);
const double pi = 4.0*atan(1.0);
Expr uExact = sin(pi*x);
Expr R = pi*pi*uExact - lambda*exp(uExact);
QuadratureFamily quad4 = new GaussianQuadrature(4);
QuadratureFamily quad2 = new GaussianQuadrature(2);
DiscreteSpace discSpace(mesh, basis, vecType);
Expr uPrev = new DiscreteFunction(discSpace, 0.5);
Expr uCur = copyDiscreteFunction(uPrev);
Expr eqn
= Integral(interior, (grad*u)*(grad*v) - v*lambda*exp(uPrev) - v*R, quad4);
Expr h = new CellDiameterExpr();
Expr bc = EssentialBC(left+right, v*u/h, quad4);
LinearProblem prob(mesh, eqn, bc, v, u, vecType);
Expr normSqExpr = Integral(interior, pow(u-uPrev, 2.0), quad2);
Functional normSqFunc(mesh, normSqExpr, vecType);
FunctionalEvaluator normSqEval = normSqFunc.evaluator(u, uCur);
LinearSolver<double> linSolver
= LinearSolverBuilder::createSolver("amesos.xml");
Out::root() << "Fixed-point iteration" << endl;
int maxIters = 20;
Expr soln ;
bool converged = false;
for (int i=0; i<maxIters; i++)
{
/* solve for the next u */
prob.solve(linSolver, uCur);
/* evaluate the norm of (uCur-uPrev) using
* the FunctionalEvaluator defined above */
double deltaU = sqrt(normSqEval.evaluate());
Out::root() << "Iter=" << setw(3) << i << " ||Delta u||=" << setw(20)
<< deltaU << endl;
/* check for convergence */
if (deltaU < convTol)
{
soln = uCur;
converged = true;
break;
}
/* get the vector from the current discrete function */
Vector<double> uVec = getDiscreteFunctionVector(uCur);
/* copy the vector into the previous discrete function */
setDiscreteFunctionVector(uPrev, uVec);
}
TEUCHOS_TEST_FOR_EXCEPTION(!converged, std::runtime_error,
"Fixed point iteration did not converge after "
<< maxIters << " iterations");
FieldWriter writer = new DSVWriter("FixedPointBratu.dat");
writer.addMesh(mesh);
writer.addField("soln", new ExprFieldWrapper(soln[0]));
writer.write();
Out::root() << "Converged!" << endl << endl;
double L2Err = L2Norm(mesh, interior, soln-uExact, quad4);
Out::root() << "L2 Norm of error: " << L2Err << endl;
Sundance::passFailTest(L2Err, 1.5/((double) nx*nx));
}
catch(exception& e)
{
Sundance::handleException(e);
}
Sundance::finalize();
}
int main(int argc, char** argv)
{
try
{
Sundance::init(&argc, &argv);
/* We will do our linear algebra using Epetra */
VectorType<double> vecType = new EpetraVectorType();
/* Create a mesh. It will be of type BasisSimplicialMesh, and will
* be built using a PartitionedLineMesher. */
MeshType meshType = new BasicSimplicialMeshType();
int nx = 32;
MeshSource mesher = new PartitionedRectangleMesher(
0.0, 1.0, nx,
0.0, 1.0, nx,
meshType);
Mesh mesh = mesher.getMesh();
/* Create a cell filter that will identify the maximal cells
* in the interior of the domain */
CellFilter interior = new MaximalCellFilter();
/* Make cell filters for the east and west boundaries */
CellFilter edges = new DimensionalCellFilter(1);
CellFilter west = edges.coordSubset(0, 0.0);
CellFilter east = edges.coordSubset(0, 1.0);
/* Create unknown and test functions */
Expr u = new UnknownFunction(new Lagrange(1), "u");
Expr v = new TestFunction(new Lagrange(1), "v");
/* Create differential operator and coordinate function */
Expr x = new CoordExpr(0);
Expr grad = gradient(1);
/* We need a quadrature rule for doing the integrations */
QuadratureFamily quad = new GaussianQuadrature(4);
/* Define the parameter */
Expr xi = new Sundance::Parameter(0.0);
/* Construct a forcing term to provide an exact solution for
* validation purposes. This will involve the parameter. */
Expr uEx = x*(1.0-x)*(1.0+xi*exp(x));
Expr f = -(-20 - exp(x)*xi*(1 + 32*x + 10*x*x +
exp(x)*(-1 + 2*x*(2 + x))*xi))/10.0;
/* Define the weak form, using the parameter expression. This weak form
* can be used for all parameter values. */
Expr eqn = Integral(interior,
(1.0 + 0.1*xi*exp(x))*(grad*v)*(grad*u) - f*v, quad);
/* Define the Dirichlet BC */
Expr h = new CellDiameterExpr();
Expr bc = EssentialBC(east + west, v*u/h, quad);
/* We can now set up the linear problem. This can be reused
* for different parameter values. */
LinearProblem prob(mesh, eqn, bc, v, u, vecType);
/* make a projector for the exact solution. Just like the
* problem, this can be reused for different parameter values. */
DiscreteSpace ds(mesh, new Lagrange(1), vecType);
L2Projector proj(ds, uEx);
/* Get the solver and declare variables for the results */
LinearSolver<double> solver = LinearSolverBuilder::createSolver("aztec-ml.xml");
Expr soln;
SolverState<double> state;
/* Set up the sweep from xi=0 to xi=xiMax in nSteps steps. */
int nSteps = 10;
double xiMax = 2.0;
/* Make an array in which to keep the observed errors */
Array<double> err(nSteps);
/* Do the sweep */
for (int n=0; n<nSteps; n++)
{
/* Update the parameter value */
double xiVal = xiMax*n/(nSteps - 1.0);
xi.setParameterValue(xiVal);
Out::root() << "step n=" << n << " of " << nSteps << " xi=" << xiVal;
/* Solve the problem. The updated parameter value is automatically used. */
state = prob.solve(solver, soln);
TEUCHOS_TEST_FOR_EXCEPTION(state.finalState() != SolveConverged,
std::runtime_error,
"solve failed!");
/* Project the exact solution onto a discrrete space for viz. The updated
* parameter value is automatically used. */
Expr uEx0 = proj.project();
/* Write the approximate and exact solutions for viz */
FieldWriter w = new VTKWriter("ParameterSweep-" + Teuchos::toString(n));
w.addMesh(mesh);
w.addField("u", new ExprFieldWrapper(soln[0]));
w.addField("uEx", new ExprFieldWrapper(uEx0[0]));
w.write();
/* Compute the L2 norm of the error */
err[n] = L2Norm(mesh, interior, soln-uEx, quad);
Out::root() << " L2 error = " << err[n] << endl;
}
/* The errors are O(h^2), so use that to set a tolerance */
double hVal = 1.0/(nx-1.0);
double fudge = 2.0;
double tol = fudge*hVal*hVal;
/* Find the max error over all parameter values */
double maxErr = *std::max_element(err.begin(), err.end());
/* Check the error */
Sundance::passFailTest(maxErr, tol);
}
catch(std::exception& e)
{
Sundance::handleException(e);
}
Sundance::finalize();
return Sundance::testStatus();
}
bool DuffingFloquet()
{
int np = MPIComm::world().getNProc();
TEUCHOS_TEST_FOR_EXCEPT(np != 1);
const double pi = 4.0*atan(1.0);
/* We will do our linear algebra using Epetra */
VectorType<double> vecType = new EpetraVectorType();
/* Create a periodic mesh */
int nx = 128;
MeshType meshType = new PeriodicMeshType1D();
MeshSource mesher = new PeriodicLineMesher(0.0, 2.0*pi, nx, meshType);
Mesh mesh = mesher.getMesh();
/* Create a cell filter that will identify the maximal cells
* in the interior of the domain */
CellFilter interior = new MaximalCellFilter();
CellFilter pts = new DimensionalCellFilter(0);
CellFilter left = pts.subset(new CoordinateValueCellPredicate(0,0.0));
CellFilter right = pts.subset(new CoordinateValueCellPredicate(0,2.0*pi));
/* Create unknown and test functions, discretized using first-order
* Lagrange interpolants */
Expr u1 = new UnknownFunction(new Lagrange(1), "u1");
Expr u2 = new UnknownFunction(new Lagrange(1), "u2");
Expr v1 = new TestFunction(new Lagrange(1), "v1");
Expr v2 = new TestFunction(new Lagrange(1), "v2");
/* Create differential operator and coordinate function */
Expr dx = new Derivative(0);
Expr x = new CoordExpr(0);
/* We need a quadrature rule for doing the integrations */
QuadratureFamily quad = new GaussianQuadrature(4);
double F0 = 0.5;
double gamma = 2.0/3.0;
double a0 = 1.0;
double w0 = 1.0;
double eps = 0.5;
Expr u1Guess = -0.75*cos(x) + 0.237*sin(x);
Expr u2Guess = 0.237*cos(x) + 0.75*sin(x);
DiscreteSpace discSpace(mesh,
List(new Lagrange(1), new Lagrange(1)),
vecType);
L2Projector proj(discSpace, List(u1Guess, u2Guess));
Expr u0 = proj.project();
Expr rhs1 = u2;
Expr rhs2 = -w0*w0*u1 - gamma*u2 - eps*w0*w0*pow(u1,3.0)/a0/a0
+ F0*w0*w0*sin(x);
/* Define the weak form */
Expr eqn = Integral(interior,
v1*(dx*u1 - rhs1) + v2*(dx*u2 - rhs2),
quad);
Expr dummyBC ;
NonlinearProblem prob(mesh, eqn, dummyBC, List(v1,v2), List(u1,u2),
u0, vecType);
ParameterXMLFileReader reader("nox.xml");
ParameterList solverParams = reader.getParameters();
Out::root() << "finding periodic solution" << endl;
NOXSolver solver(solverParams);
prob.solve(solver);
/* unfold the solution onto a non-periodic mesh */
Expr uP = unfoldPeriodicDiscreteFunction(u0, "u_p");
Out::root() << "uP=" << uP << endl;
Mesh unfoldedMesh = DiscreteFunction::discFunc(uP)->mesh();
DiscreteSpace unfDiscSpace = DiscreteFunction::discFunc(uP)->discreteSpace();
FieldWriter writer = new MatlabWriter("Floquet.dat");
writer.addMesh(unfoldedMesh);
writer.addField("u_p[0]", new ExprFieldWrapper(uP[0]));
writer.addField("u_p[1]", new ExprFieldWrapper(uP[1]));
Array<Expr> a(2);
a[0] = new Sundance::Parameter(0.0, "a1");
a[1] = new Sundance::Parameter(0.0, "a2");
Expr bc = EssentialBC(left, v1*(u1-uP[0]-a[0]) + v2*(u2-uP[1]-a[1]), quad);
NonlinearProblem unfProb(unfoldedMesh, eqn, bc,
List(v1,v2), List(u1,u2), uP, vecType);
unfProb.setEvalPoint(uP);
LinearOperator<double> J = unfProb.allocateJacobian();
Vector<double> b = J.domain().createMember();
LinearSolver<double> linSolver
= LinearSolverBuilder::createSolver("amesos.xml");
SerialDenseMatrix<int, double> F(a.size(), a.size());
for (int i=0; i<a.size(); i++)
{
Out::root() << "doing perturbed orbit #" << i << endl;
for (int j=0; j<a.size(); j++)
{
if (i==j) a[j].setParameterValue(1.0);
else a[j].setParameterValue(0.0);
}
unfProb.computeJacobianAndFunction(J, b);
Vector<double> w = b.copy();
linSolver.solve(J, b, w);
Expr w_i = new DiscreteFunction(unfDiscSpace, w);
for (int j=0; j<a.size(); j++)
{
Out::root() << "postprocessing" << i << endl;
writer.addField("w[" + Teuchos::toString(i)
+ ", " + Teuchos::toString(j) + "]", new ExprFieldWrapper(w_i[j]));
Expr g = Integral(right, w_i[j], quad);
F(j,i) = evaluateIntegral(unfoldedMesh, g);
}
}
writer.write();
Out::root() << "Floquet matrix = " << endl
<< F << endl;
Out::root() << "doing eigenvalue analysis" << endl;
Array<double> ew_r(a.size());
Array<double> ew_i(a.size());
int lWork = 6*a.size();
Array<double> work(lWork);
int info = 0;
LAPACK<int, double> lapack;
lapack.GEEV('N','N', a.size(), F.values(),
a.size(), &(ew_r[0]), &(ew_i[0]), 0, 1, 0, 1, &(work[0]), lWork,
&info);
TEUCHOS_TEST_FOR_EXCEPTION(info != 0,
std::runtime_error,
"LAPACK GEEV returned error code =" << info);
Array<double> ew(a.size());
for (int i=0; i<a.size(); i++)
{
ew[i] = sqrt(ew_r[i]*ew_r[i]+ew_i[i]*ew_i[i]);
Out::root() << setw(5) << i
<< setw(16) << ew_r[i]
<< setw(16) << ew_i[i]
<< setw(16) << ew[i]
<< endl;
}
double err = ::fabs(ew[0] - 0.123);
return SundanceGlobal::checkTest(err, 0.001);
}
AToCPointLocator::AToCPointLocator(const Mesh& mesh,
const CellFilter& subdomain,
const std::vector<int>& nx)
: dim_(mesh.spatialDim()),
mesh_(mesh),
nFacets_(mesh.numFacets(dim_, 0, 0)),
nx_(nx),
low_(nx.size(), 1.0/ScalarTraits<double>::sfmin()),
high_(nx.size(), -1.0/ScalarTraits<double>::sfmin()),
dx_(nx.size()),
table_(),
subdomain_(subdomain),
neighborSet_()
{
TimeMonitor timer(pointLocatorCtorTimer());
/* allocate the neighbor set table */
neighborSet_.resize(mesh.numCells(dim_));
/* first pass to find bounding box */
CellSet cells = subdomain.getCells(mesh);
for (CellIterator i = cells.begin(); i!= cells.end(); i++)
{
int cellLID = *i;
Array<int> facetLIDs;
Array<int> facetOri;
mesh.getFacetArray(dim_, cellLID, 0, facetLIDs, facetOri);
for (int f=0; f<facetLIDs.size(); f++)
{
Point x = mesh.nodePosition(facetLIDs[f]);
for (int d=0; d<dim_; d++)
{
if (x[d] < low_[d]) low_[d] = x[d];
if (x[d] > high_[d]) high_[d] = x[d];
}
}
}
/* fudge the bounding box */
for (int d=0; d<dim_; d++)
{
low_[d] -= 0.01 * (high_[d] - low_[d]);
high_[d] += 0.01 * (high_[d] - low_[d]);
}
/* second pass to put cells in lookup table */
int s = 1;
for (int d=0; d<dim_; d++)
{
dx_[d] = (high_[d] - low_[d])/nx_[d];
s *= nx_[d];
}
table_ = rcp(new Array<int>(s, -1));
Array<int> lowIndex;
Array<int> highIndex;
for (CellIterator i = cells.begin(); i!= cells.end(); i++)
{
int cellLID = *i;
getGridRange(mesh, dim_, cellLID, lowIndex, highIndex);
if (dim_==2)
{
for (int ix=lowIndex[0]; ix<=highIndex[0]; ix++)
{
for (int iy=lowIndex[1]; iy<=highIndex[1]; iy++)
{
int index = nx_[1]*ix + iy;
(*table_)[index] = cellLID;
}
}
}
else
{
TEST_FOR_EXCEPT(true);
}
}
}
bool CellFilter::isKnownSubsetOf(const CellFilter& other) const
{
if (other.knownSubsets().contains(*this)) return true;
return false;
}
int main(int argc, char** argv)
{
try
{
Sundance::init(&argc, &argv);
int np = MPIComm::world().getNProc();
// DOFMapBase::classVerbosity() = VerbExtreme;
const double density = 1000.0; // kg/m^3
const double porosity = 0.442; // dimensionless %
const double A = 175.5; // dimensionless fit parameter
const double B = 1.83; // dimensionless fit parameter
const double criticalRe = 36.73; // dimensionless fit parameter
const double dynvisc = 1.31; // kg/(m-s)
const double graindia = 1.9996e-4; // m
const double charvel = 1.0; // m/s
double Reynolds = density*graindia*charvel/(dynvisc*porosity);
Expr Re = new Parameter(Reynolds);
/* We will do our linear algebra using Epetra */
VectorType<double> vecType = new EpetraVectorType();
/* Create a mesh. It will be of type BasisSimplicialMesh, and will
* be built using a PartitionedLineMesher. */
MeshType meshType = new BasicSimplicialMeshType();
MeshSource mesher = new PartitionedLineMesher(0.0, 1000.0, 100*np, meshType);
Mesh mesh = mesher.getMesh();
/* Create a cell filter that will identify the maximal cells
* in the interior of the domain */
CellFilter interior = new MaximalCellFilter();
CellFilter points = new DimensionalCellFilter(0);
CellPredicate leftPointFunc = new PositionalCellPredicate(leftPointTest);
CellPredicate rightPointFunc = new PositionalCellPredicate(rightPointTest);
CellFilter leftPoint = points.subset(leftPointFunc);
CellFilter rightPoint = points.subset(rightPointFunc);
/* Create unknown and test functions, discretized using first-order
* Lagrange interpolants */
Expr p = new UnknownFunction(new Lagrange(2), "p");
Expr q = new UnknownFunction(new Lagrange(2), "q");
Expr u = new TestFunction(new Lagrange(2), "u");
Expr v = new TestFunction(new Lagrange(2), "v");
/* Create differential operator and coordinate function */
Expr dx = new Derivative(0);
Expr x = new CoordExpr(0);
/* We need a quadrature rule for doing the integrations */
QuadratureFamily quad = new GaussianQuadrature(4);
/* Define the weak form */
Expr MassEqn = Integral(interior, q*(dx*u), quad)
+ Integral(leftPoint, - q*u,quad)
+ Integral(rightPoint, - q*u,quad);
Expr MomEqn = Integral(interior, (density/porosity)*q*q*(dx*v) + porosity*p*(dx*v) - porosity*q*v*A - (porosity*q*v*B*Re*Re)/((Re+criticalRe)*(1-porosity)), quad)
+ Integral(leftPoint, - density*q*q*v/porosity - porosity*p*v,quad)
+ Integral(rightPoint,- density*q*q*v/porosity - porosity*p*v,quad);
/* Define the Dirichlet BC */
Expr leftbc = EssentialBC(leftPoint, v*(q-charvel), quad);
Expr rightbc = EssentialBC(rightPoint, v*(q-charvel), quad);
/* Create a discrete space, and discretize the function 1.0 on it */
BasisFamily L2 = new Lagrange(2);
Array<BasisFamily> basis = tuple(L2, L2);
DiscreteSpace discSpace(mesh, basis, vecType);
Expr u0 = new DiscreteFunction(discSpace, 1.0, "u0");
Expr p0 = u0[0];
Expr q0 = u0[1];
/* Create a TSF NonlinearOperator object */
std::cerr << "about to make nonlinear object" << std::endl;
std::cerr.flush();
NonlinearOperator<double> F
= new NonlinearProblem(mesh, MassEqn+MomEqn, leftbc+rightbc, Sundance::List(u,v),Sundance::List(p,q) , u0, vecType);
// F.verbosity() = VerbExtreme;
/* Get the initial guess */
Vector<double> x0 = F.getInitialGuess();
/* Create an Aztec solver for solving the linear subproblems */
std::map<int,int> azOptions;
std::map<int,double> azParams;
azOptions[AZ_solver] = AZ_gmres;
azOptions[AZ_precond] = AZ_dom_decomp;
azOptions[AZ_subdomain_solve] = AZ_ilu;
azOptions[AZ_graph_fill] = 1;
azOptions[AZ_max_iter] = 1000;
azParams[AZ_tol] = 1.0e-13;
LinearSolver<double> linSolver = new AztecSolver(azOptions,azParams);
/* Now let's create a NOX solver */
NOX::TSF::Group grp(x0, F, linSolver);
grp.verbosity() = VerbExtreme;
// Set up the status tests
NOX::StatusTest::NormF statusTestA(grp, 1.0e-10);
NOX::StatusTest::MaxIters statusTestB(20);
NOX::StatusTest::Combo statusTestsCombo(NOX::StatusTest::Combo::OR, statusTestA, statusTestB);
// Create the list of solver parameters
NOX::Parameter::List solverParameters;
// Set the solver (this is the default)
solverParameters.setParameter("Nonlinear Solver", "Line Search Based");
// Create the line search parameters sublist
NOX::Parameter::List& lineSearchParameters = solverParameters.sublist("Line Search");
// Set the line search method
lineSearchParameters.setParameter("Method","More'-Thuente");
// Create the solver
NOX::Solver::Manager solver(grp, statusTestsCombo, solverParameters);
// Solve the nonlinear system
NOX::StatusTest::StatusType status = solver.solve();
// Print the answer
cout << "\n" << "-- Parameter List From Solver --" << "\n";
solver.getParameterList().print(cout);
// Get the answer
grp = solver.getSolutionGroup();
// Print the answer
cout << "\n" << "-- Final Solution From Solver --" << "\n";
grp.print();
double tol = 1.0e-12;
Sundance::passFailTest(0, tol);
}
catch(std::exception& e)
{
Sundance::handleException(e);
}
Sundance::finalize(); return Sundance::testStatus();
}
bool NonlinReducedIntegration()
{
int np = MPIComm::world().getNProc();
int n = 4;
bool increaseProbSize = true;
if ( (np % 4)==0 ) increaseProbSize = false;
Array<double> h;
Array<double> errQuad;
Array<double> errReduced;
for (int i=0; i<4; i++)
{
n *= 2;
int nx = n;
int ny = n;
VectorType<double> vecType = new EpetraVectorType();
MeshType meshType = new BasicSimplicialMeshType();
int npx = -1;
int npy = -1;
PartitionedRectangleMesher::balanceXY(np, &npx, &npy);
TEUCHOS_TEST_FOR_EXCEPT(npx < 1);
TEUCHOS_TEST_FOR_EXCEPT(npy < 1);
TEUCHOS_TEST_FOR_EXCEPT(npx * npy != np);
if (increaseProbSize)
{
nx = nx*npx;
ny = ny*npy;
}
MeshSource mesher = new PartitionedRectangleMesher(0.0, 1.0, nx, npx,
0.0, 1.0, ny, npy, meshType);
Mesh mesh = mesher.getMesh();
WatchFlag watchMe("watch eqn");
watchMe.setParam("integration setup", 0);
watchMe.setParam("integration", 0);
watchMe.setParam("fill", 0);
watchMe.setParam("evaluation", 0);
watchMe.deactivate();
WatchFlag watchBC("watch BCs");
watchBC.setParam("integration setup", 0);
watchBC.setParam("integration", 0);
watchBC.setParam("fill", 0);
watchBC.setParam("evaluation", 0);
watchBC.deactivate();
CellFilter interior = new MaximalCellFilter();
CellFilter edges = new DimensionalCellFilter(1);
CellFilter left = edges.subset(new CoordinateValueCellPredicate(0,0.0));
CellFilter right = edges.subset(new CoordinateValueCellPredicate(0,1.0));
CellFilter top = edges.subset(new CoordinateValueCellPredicate(1,1.0));
CellFilter bottom = edges.subset(new CoordinateValueCellPredicate(1,0.0));
BasisFamily basis = new Lagrange(1);
Expr u = new UnknownFunction(basis, "u");
Expr v = new TestFunction(basis, "v");
Expr dx = new Derivative(0);
Expr dy = new Derivative(1);
Expr grad = List(dx, dy);
Expr x = new CoordExpr(0);
Expr y = new CoordExpr(1);
QuadratureFamily quad = new ReducedQuadrature();
QuadratureFamily quad2 = new GaussianQuadrature(2);
/* Define the weak form */
const double pi = 4.0*atan(1.0);
Expr c = cos(pi*x);
Expr s = sin(pi*x);
Expr ch = cosh(y);
Expr sh = sinh(y);
Expr s2 = s*s;
Expr c2 = c*c;
Expr sh2 = sh*sh;
Expr ch2 = ch*ch;
Expr pi2 = pi*pi;
Expr uEx = s*ch;
Expr eu = exp(uEx);
Expr f = -(ch*eu*(-1 + pi2)*s) + ch2*(c2*eu*pi2 - s2) + eu*s2*sh2;
Expr eqn = Integral(interior, exp(u)*(grad*u)*(grad*v)
+ v*f + v*u*u, quad, watchMe)
+ Integral(right, v*exp(u)*pi*cosh(y), quad,watchBC);
/* Define the Dirichlet BC */
Expr bc = EssentialBC(left+top, v*(u-uEx), quad, watchBC);
Expr eqn2 = Integral(interior, exp(u)*(grad*u)*(grad*v)
+ v*f + v*u*u, quad2, watchMe)
+ Integral(right, v*exp(u)*pi*cosh(y), quad2,watchBC);
/* Define the Dirichlet BC */
Expr bc2 = EssentialBC(left+top, v*(u-uEx), quad2, watchBC);
DiscreteSpace discSpace(mesh, new Lagrange(1), vecType);
Expr soln1 = new DiscreteFunction(discSpace, 0.0, "u0");
Expr soln2 = new DiscreteFunction(discSpace, 0.0, "u0");
L2Projector proj(discSpace, uEx);
Expr uEx0 = proj.project();
NonlinearProblem nlp(mesh, eqn, bc, v, u, soln1, vecType);
NonlinearProblem nlp2(mesh, eqn2, bc2, v, u, soln2, vecType);
ParameterXMLFileReader reader("nox-aztec.xml");
ParameterList noxParams = reader.getParameters();
NOXSolver solver(noxParams);
nlp.solve(solver);
nlp2.solve(solver);
FieldWriter w = new VTKWriter("NonlinReduced-n" + Teuchos::toString(n));
w.addMesh(mesh);
w.addField("soln1", new ExprFieldWrapper(soln1[0]));
w.addField("soln2", new ExprFieldWrapper(soln2[0]));
w.addField("exact", new ExprFieldWrapper(uEx0[0]));
w.write();
Expr err1 = uEx - soln1;
Expr errExpr1 = Integral(interior,
err1*err1,
new GaussianQuadrature(4));
Expr err2 = uEx - soln2;
Expr errExpr2 = Integral(interior,
err2*err2,
new GaussianQuadrature(4));
Expr err12 = soln2 - soln1;
Expr errExpr12 = Integral(interior,
err12*err12,
new GaussianQuadrature(4));
double error1 = ::sqrt(evaluateIntegral(mesh, errExpr1));
double error2 = ::sqrt(evaluateIntegral(mesh, errExpr2));
double error12 = ::sqrt(evaluateIntegral(mesh, errExpr12));
Out::root() << "final result: " << n << " " << error1 << " " << error2 << " " << error12
<< endl;
h.append(1.0/((double) n));
errQuad.append(error2);
errReduced.append(error1);
}
double pQuad = fitPower(h, errQuad);
double pRed = fitPower(h, errReduced);
Out::root() << "exponent (reduced integration) " << pRed << endl;
Out::root() << "exponent (full integration) " << pQuad << endl;
return SundanceGlobal::checkTest(::fabs(pRed-2.0), 0.1);
}
