int main(int argc, char** argv) { try { Sundance::init(&argc, &argv); int np = MPIComm::world().getNProc(); int nx = 48; int ny = 48; 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); MeshType meshType = new BasicSimplicialMeshType(); MeshSource mesher = new PartitionedRectangleMesher(0.0, 1.0, nx, npx, 0.0, 1.0, ny, npy, meshType); Mesh mesh = mesher.getMesh(); CellFilter interior = new MaximalCellFilter(); CellFilter bdry = new BoundaryCellFilter(); /* Create a vector space factory, used to * specify the low-level linear algebra representation */ VectorType<double> vecType = new EpetraVectorType(); /* create a discrete space on the mesh */ DiscreteSpace discreteSpace(mesh, new Lagrange(1), vecType); /* initialize the design, state, and multiplier vectors */ Expr alpha0 = new DiscreteFunction(discreteSpace, 1.0, "alpha0"); Expr u0 = new DiscreteFunction(discreteSpace, 1.0, "u0"); Expr lambda0 = new DiscreteFunction(discreteSpace, 1.0, "lambda0"); /* create symbolic objects for test and unknown functions */ Expr u = new UnknownFunction(new Lagrange(1), "u"); Expr lambda = new UnknownFunction(new Lagrange(1), "lambda"); Expr alpha = new UnknownFunction(new Lagrange(1), "alpha"); /* create symbolic differential operators */ Expr dx = new Derivative(0); Expr dy = new Derivative(1); Expr grad = List(dx, dy); /* create symbolic coordinate functions */ Expr x = new CoordExpr(0); Expr y = new CoordExpr(1); /* create target function */ const double pi = 4.0*atan(1.0); Expr uStar = sin(pi*x)*sin(pi*y); /* create quadrature rules of different orders */ QuadratureFamily q1 = new GaussianQuadrature(1); QuadratureFamily q2 = new GaussianQuadrature(2); QuadratureFamily q4 = new GaussianQuadrature(4); /* Regularization weight */ double R = 0.001; double U0 = 1.0/(1.0 + 4.0*pow(pi,4.0)*R); double A0 = -2.0*pi*pi*U0; /* Form objective function */ Expr reg = Integral(interior, 0.5 * R * alpha*alpha, q2); Expr fit = Integral(interior, 0.5 * pow(u-uStar, 2.0), q4); Expr constraintEqn = Integral(interior, (grad*lambda)*(grad*u) + lambda*alpha, q2); Expr L = reg + fit + constraintEqn; Expr constraintBC = EssentialBC(bdry, lambda*u, q2); Functional Lagrangian(mesh, L, constraintBC, vecType); LinearSolver<double> solver = LinearSolverBuilder::createSolver("amesos.xml"); RCP<ObjectiveBase> obj = rcp(new LinearPDEConstrainedObj( Lagrangian, u, u0, lambda, lambda0, alpha, alpha0, solver)); Vector<double> xInit = obj->getInit(); bool doFDCheck = false; if (doFDCheck) { Out::root() << "Doing FD check of gradient..." << endl; bool fdOK = obj->fdCheck(xInit, 1.0e-6, 2); if (fdOK) { Out::root() << "FD check OK" << endl; } else { Out::root() << "FD check FAILED" << endl; } } RCP<UnconstrainedOptimizerBase> opt = OptBuilder::createOptimizer("basicLMBFGS.xml"); opt->setVerb(2); OptState state = opt->run(obj, xInit); bool ok = true; if (state.status() != Opt_Converged) { Out::root()<< "optimization failed: " << state.status() << endl; TEUCHOS_TEST_FOR_EXCEPT(state.status() != Opt_Converged); } Out::root() << "opt converged: " << state.iter() << " iterations" << endl; Out::root() << "exact solution: U0=" << U0 << " A0=" << A0 << endl; FieldWriter w = new VTKWriter("PoissonSourceInversion"); w.addMesh(mesh); w.addField("u", new ExprFieldWrapper(u0)); w.addField("alpha", new ExprFieldWrapper(alpha0)); w.addField("lambda", new ExprFieldWrapper(lambda0)); w.write(); double uErr = L2Norm(mesh, interior, u0-U0*uStar, q4); double aErr = L2Norm(mesh, interior, alpha0-A0*uStar, q4); Out::root() << "error in u = " << uErr << endl; Out::root() << "error in alpha = " << aErr << endl; double tol = 0.01; Sundance::passFailTest(uErr + aErr, tol); } catch(std::exception& e) { cerr << "main() caught exception: " << e.what() << endl; } Sundance::finalize(); return Sundance::testStatus(); }
int main(int argc, char** argv) { try { Sundance::init(&argc, &argv); int np = MPIComm::world().getNProc(); int nx = 64; const double pi = 4.0*atan(1.0); MeshType meshType = new BasicSimplicialMeshType(); MeshSource mesher = new PartitionedLineMesher(0.0, pi, nx, meshType); Mesh mesh = mesher.getMesh(); CellFilter interior = new MaximalCellFilter(); CellFilter bdry = new BoundaryCellFilter(); /* Create a vector space factory, used to * specify the low-level linear algebra representation */ VectorType<double> vecType = new EpetraVectorType(); /* create symbolic coordinate functions */ Expr x = new CoordExpr(0); /* create target function */ double R = 0.01; Expr sx = sin(x); Expr cx = cos(x); Expr ssx = sin(sx); Expr sx2 = sx*sx; Expr cx2 = cx*cx; Expr f = sx2 - sx - ssx; Expr uStar = 2.0*R*(sx2-cx2) + R*sx2*ssx + sx; /* Form exact solution */ Expr uEx = sx; Expr lambdaEx = R*sx2; Expr alphaEx = -lambdaEx/R; /* create a discrete space on the mesh */ BasisFamily bas = new Lagrange(1); DiscreteSpace discreteSpace(mesh, bas, vecType); /* initialize the design, state, and multiplier vectors to constants */ Expr alpha0 = new DiscreteFunction(discreteSpace, 0.25, "alpha0"); Expr u0 = new DiscreteFunction(discreteSpace, 0.5, "u0"); Expr lambda0 = new DiscreteFunction(discreteSpace, 0.25, "lambda0"); /* create symbolic objects for test and unknown functions */ Expr u = new UnknownFunction(bas, "u"); Expr lambda = new UnknownFunction(bas, "lambda"); Expr alpha = new UnknownFunction(bas, "alpha"); /* create symbolic differential operators */ Expr dx = new Derivative(0); Expr grad = dx; /* create quadrature rules of different orders */ QuadratureFamily q1 = new GaussianQuadrature(1); QuadratureFamily q2 = new GaussianQuadrature(2); QuadratureFamily q4 = new GaussianQuadrature(4); /* Form objective function */ Expr reg = Integral(interior, 0.5 * R * alpha*alpha, q2); Expr fit = Integral(interior, 0.5 * pow(u-uStar, 2.0), q4); Expr constraintEqn = Integral(interior, (grad*lambda)*(grad*u) + lambda*(alpha + sin(u) + f), q4); Expr L = reg + fit + constraintEqn; Expr constraintBC = EssentialBC(bdry, lambda*u, q2); Functional Lagrangian(mesh, L, constraintBC, vecType); LinearSolver<double> adjSolver = LinearSolverBuilder::createSolver("amesos.xml"); ParameterXMLFileReader reader("nox-amesos.xml"); ParameterList noxParams = reader.getParameters(); NOXSolver nonlinSolver(noxParams); RCP<PDEConstrainedObjBase> obj = rcp(new NonlinearPDEConstrainedObj( Lagrangian, u, u0, lambda, lambda0, alpha, alpha0, nonlinSolver, adjSolver)); Vector<double> xInit = obj->getInit(); bool doFDCheck = true; if (doFDCheck) { Out::root() << "Doing FD check of gradient..." << endl; bool fdOK = obj->fdCheck(xInit, 1.0e-6, 0); if (fdOK) { Out::root() << "FD check OK" << endl; } else { Out::root() << "FD check FAILED" << endl; TEUCHOS_TEST_FOR_EXCEPT(!fdOK); } } RCP<UnconstrainedOptimizerBase> opt = OptBuilder::createOptimizer("basicLMBFGS.xml"); opt->setVerb(3); OptState state = opt->run(obj, xInit); if (state.status() != Opt_Converged) { Out::root()<< "optimization failed: " << state.status() << endl; TEUCHOS_TEST_FOR_EXCEPT(state.status() != Opt_Converged); } else { Out::root() << "opt converged: " << state.iter() << " iterations" << endl; } FieldWriter w = new MatlabWriter("NonlinControl1D"); w.addMesh(mesh); w.addField("u", new ExprFieldWrapper(u0)); w.addField("alpha", new ExprFieldWrapper(alpha0)); w.addField("lambda", new ExprFieldWrapper(lambda0)); w.write(); double uErr = L2Norm(mesh, interior, u0-uEx, q4); double lamErr = L2Norm(mesh, interior, lambda0-lambdaEx, q4); double aErr = L2Norm(mesh, interior, alpha0-alphaEx, q4); Out::root() << "error in u = " << uErr << endl; Out::root() << "error in lambda = " << lamErr << endl; Out::root() << "error in alpha = " << aErr << endl; double tol = 0.05; Sundance::passFailTest(uErr + lamErr + aErr, tol); } catch(exception& e) { cerr << "main() caught exception: " << e.what() << endl; } Sundance::finalize(); return Sundance::testStatus(); }