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() << "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();
}
