00001 #include "Sundance.hpp"
00002 #include "PlayaNonlinearSolverBuilder.hpp"
00003
00004
00005
00006
00007
00008 int main(int argc, char** argv)
00009 {
00010 try
00011 {
00012 int nx = 32;
00013 double convTol = 1.0e-8;
00014 double lambda = 0.5;
00015 Sundance::setOption("nx", nx, "Number of elements");
00016 Sundance::setOption("tol", convTol, "Convergence tolerance");
00017 Sundance::setOption("lambda", lambda, "Lambda (parameter in Bratu's equation)");
00018
00019 Sundance::init(&argc, &argv);
00020
00021 Out::root() << "Bratu problem (lambda=" << lambda << ")" << endl;
00022 Out::root() << "Newton's method with automated linearization"
00023 << endl << endl;
00024
00025 VectorType<double> vecType = new EpetraVectorType();
00026
00027 MeshType meshType = new BasicSimplicialMeshType();
00028 MeshSource mesher = new PartitionedLineMesher(0.0, 1.0, nx, meshType);
00029 Mesh mesh = mesher.getMesh();
00030
00031 CellFilter interior = new MaximalCellFilter();
00032 CellFilter sides = new DimensionalCellFilter(mesh.spatialDim()-1);
00033 CellFilter left = sides.subset(new CoordinateValueCellPredicate(0, 0.0));
00034 CellFilter right = sides.subset(new CoordinateValueCellPredicate(0, 1.0));
00035
00036 BasisFamily basis = new Lagrange(1);
00037 Expr u = new UnknownFunction(basis, "w");
00038 Expr v = new TestFunction(basis, "v");
00039
00040 Expr grad = gradient(1);
00041
00042 Expr x = new CoordExpr(0);
00043
00044 const double pi = 4.0*atan(1.0);
00045 Expr uExact = sin(pi*x);
00046 Expr R = pi*pi*uExact - lambda*exp(uExact);
00047
00048 QuadratureFamily quad4 = new GaussianQuadrature(4);
00049 QuadratureFamily quad2 = new GaussianQuadrature(2);
00050
00051 DiscreteSpace discSpace(mesh, basis, vecType);
00052 Expr uPrev = new DiscreteFunction(discSpace, 0.5);
00053
00054 Expr eqn
00055 = Integral(interior, (grad*v)*(grad*u) - v*lambda*exp(u) - v*R, quad4);
00056
00057 Expr h = new CellDiameterExpr();
00058 Expr bc = EssentialBC(left+right, v*u/h, quad2);
00059
00060 NonlinearProblem prob(mesh, eqn, bc, v, u, uPrev, vecType);
00061
00062 NonlinearSolver<double> solver
00063 = NonlinearSolverBuilder::createSolver("playa-newton-amesos.xml");
00064
00065 Out::root() << "Newton solve" << endl;
00066
00067 SolverState<double> state = prob.solve(solver);
00068
00069 TEUCHOS_TEST_FOR_EXCEPTION(state.finalState() != SolveConverged,
00070 std::runtime_error,
00071 "Nonlinear solve failed to converge: message=" << state.finalMsg());
00072
00073 Expr soln = uPrev;
00074 FieldWriter writer = new DSVWriter("AutoLinearizedBratu.dat");
00075 writer.addMesh(mesh);
00076 writer.addField("soln", new ExprFieldWrapper(soln[0]));
00077 writer.write();
00078
00079 Out::root() << "Converged!" << endl << endl;
00080
00081 double L2Err = L2Norm(mesh, interior, soln-uExact, quad4);
00082 Out::root() << "L2 Norm of error: " << L2Err << endl;
00083
00084 Sundance::passFailTest(L2Err, 1.5/((double) nx*nx));
00085 }
00086 catch(std::exception& e)
00087 {
00088 Sundance::handleException(e);
00089 }
00090 Sundance::finalize();
00091 return Sundance::testStatus();
00092 }
00093