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);
}