int main(int argc, char** argv) { try { Sundance::init(&argc, &argv); int np = MPIComm::world().getNProc(); TEST_FOR_EXCEPT(np != 1); /* We will do our linear algebra using Epetra */ VectorType<double> vecType = new EpetraVectorType(); /* Create a periodic mesh */ int nx = 1000; const double pi = 4.0*atan(1.0); 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(); /* Create unknown and test functions, discretized using first-order * Lagrange interpolants */ Expr u = new UnknownFunction(new Lagrange(1), "u"); Expr v = new TestFunction(new Lagrange(1), "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 eqn = Integral(interior, (dx*v)*(dx*u) - 2.0*v*(dx*u) - v*u + v*sin(2*x), quad); Expr bc ; // no explicit BC needed /* We can now set up the linear problem! */ LinearProblem prob(mesh, eqn, bc, v, u, vecType); ParameterXMLFileReader reader("amesos.xml"); ParameterList solverParams = reader.getParameters(); LinearSolver<double> solver = LinearSolverBuilder::createSolver(solverParams); Out::os() << "solving problem " << std::endl; Expr soln = prob.solve(solver); Expr uExact = -1.0/25.0 * (4.0*cos(2.0*x) + 3.0*sin(2.0*x)); Expr uErr = uExact - soln; Expr uErrExpr = Integral(interior, uErr*uErr, new GaussianQuadrature(6)); FunctionalEvaluator uErrInt(mesh, uErrExpr); double uErrorSq = uErrInt.evaluate(); std::cerr << "u error norm = " << sqrt(uErrorSq) << std::endl << std::endl; /* make sure the unfolded solution is also correct */ Out::os() << "unfolding " << std::endl; Expr unfoldedSoln = unfoldPeriodicDiscreteFunction(soln); Expr ufErr = uExact - unfoldedSoln; Expr ufErrExpr = Integral(interior, ufErr*ufErr, new GaussianQuadrature(6)); Mesh unfoldedMesh = DiscreteFunction::discFunc(unfoldedSoln)->mesh(); FunctionalEvaluator ufErrInt(unfoldedMesh, ufErrExpr); double ufErrorSq = ufErrInt.evaluate(); std::cerr << "unfolded error norm = " << sqrt(ufErrorSq) << std::endl << std::endl; double tol = 1.0e-3; Sundance::passFailTest(sqrt(uErrorSq + ufErrorSq), 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); }