481 lines
15 KiB
C++
481 lines
15 KiB
C++
// MFEM Example 24
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//
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// Compile with: make ex24
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//
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// Sample runs: ex24 -m ../data/mobius-strip -r 1
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// ex24 -p 0 -r 1
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// ex24 -p 1 -r 1
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// ex24 -p 2 -r 1
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// ex24 -p 3 -r 1
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//
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// Device sample runs:
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// ex24 -p 0 -pa
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#include "mfem.hpp"
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#include <fstream>
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#include <iostream>
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using namespace std;
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using namespace mfem;
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// Constant variables
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const double pi = M_PI;
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const double eps = 1.e-12;
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static socketstream glvis;
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const int visport = 19916;
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const char vishost[] = "localhost";
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// Parametrizations: Scherk, Enneper, Catenoid, Helicoid
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void scherk(const Vector &x, Vector &p);
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void enneper1(const Vector &x, Vector &p);
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void enneper2(const Vector &x, Vector &p);
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void helicoid(const Vector &x, Vector &p);
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void catenoid(const Vector &x, Vector &p);
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void catenoid_postfix(const int, const int, Mesh*);
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void mollusc(const Vector &x, Vector &p);
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void hold(const Vector &x, Vector &p);
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void peach(const Vector &x, Vector &p);
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// Surface mesh class *********************************************************
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class SurfaceMesh: public Mesh
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{
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public:
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SurfaceMesh(const int order,
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void (*parametrization)(const Vector &x, Vector &p),
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void (*postfix)(const int nx, const int ny, Mesh*),
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const int nx = 4,
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const int ny = 4,
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const double sx = 1.0,
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const double sy = 1.0,
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const int space_dim = 3,
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const Element::Type type = Element::QUADRILATERAL,
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const bool generate_edges = true,
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const bool space_filling_curve = true,
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const bool discontinuous = false):
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Mesh(nx, ny, type, generate_edges, sx, sy, space_filling_curve)
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{
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SetCurvature(order, discontinuous, space_dim, Ordering::byNODES);
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if (parametrization) { Transform(parametrization); }
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if (postfix) { postfix(nx, ny, this); }
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RemoveUnusedVertices();
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RemoveInternalBoundaries();
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SetCurvature(order, discontinuous, space_dim, Ordering::byVDIM);
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GridFunction &nodes = *GetNodes();
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for (int i = 0; i < nodes.Size(); i++)
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{ if (std::abs(nodes(i)) < eps) { nodes(i) = 0.0; } }
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}
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};
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// Surface solver class *******************************************************
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class SurfaceSolver
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{
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protected:
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const bool pa, visualization, wait;
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const int niter;
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const int sdim;
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Mesh *mesh;
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Vector X, B;
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OperatorPtr A;
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FiniteElementSpace *fes;
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BilinearForm a;
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Array<int> bc;
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GridFunction x, b, *nodes, solution;
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ConstantCoefficient one;
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public:
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virtual ~SurfaceSolver() {}
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SurfaceSolver(const bool p, const bool v,
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const int n, const bool w,
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Mesh *m, FiniteElementSpace *f,
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Array<int> ess_tdof_list):
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pa(p), visualization(v), wait(w), niter(n),
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sdim(m->SpaceDimension()), mesh(m), fes(f),
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a(fes), bc(ess_tdof_list), x(fes), b(fes),
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nodes(mesh->GetNodes()), solution(*nodes), one(1.0) { }
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virtual void Solve() { MFEM_ABORT("Not implemented!"); }
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};
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// ****************************************************************************
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class ComponentSolver: public SurfaceSolver
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{
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public:
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ComponentSolver(const bool pa,
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const bool vis,
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const int niter,
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const bool wait,
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Mesh *mesh,
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FiniteElementSpace *fes,
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Array<int> bc):
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SurfaceSolver(pa, vis, niter, wait, mesh, fes, bc) { }
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void Solve()
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{
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if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
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a.AddDomainIntegrator(new DiffusionIntegrator(one));
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for (int iiter=0; iiter<niter; ++iiter)
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{
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a.Assemble();
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solution = *nodes;
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for (int i=0; i<sdim; ++i)
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{
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x = b = 0.0;
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GetComponent(solution, x, i);
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a.FormLinearSystem(bc, x, b, A, X, B);
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if (!pa)
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{
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// Use a simple symmetric Gauss-Seidel preconditioner with PCG.
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GSSmoother M(static_cast<SparseMatrix&>(*A));
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PCG(*A, M, B, X, 3, 2000, eps, 0.0);
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}
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else { CG(*A, B, X, 3, 2000, eps, 0.0); }
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// Recover the solution as a finite element grid function.
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a.RecoverFEMSolution(X, b, x);
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SetComponent(solution, x, i);
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}
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*nodes = solution;
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// Send the solution by socket to a GLVis server.
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if (visualization)
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{
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glvis << "mesh\n" << *mesh << flush;
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if (wait) { glvis << "pause\n" << flush; }
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}
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a.Update();
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}
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}
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private:
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void SetComponent(GridFunction &phi, const GridFunction &phi_i, const int d)
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{
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// ASSUME phi IS ORDERED byNODES!
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const int ndof = fes->GetNDofs();
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for (int i = 0; i < ndof; i++)
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{ phi[d*ndof + i] = phi_i[i]; }
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}
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void GetComponent(const GridFunction &phi, GridFunction &phi_i, const int d)
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{
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// ASSUME phi IS ORDERED byNODES!
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const int ndof = fes->GetNDofs();
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for (int i = 0; i < ndof; i++)
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{ phi_i[i] = phi[d*ndof + i]; }
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}
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};
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// ****************************************************************************
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class VectorSolver: public SurfaceSolver
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{
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public:
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VectorSolver(const bool pa,
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const bool vis,
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const int niter,
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const bool wait,
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Mesh *mesh,
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FiniteElementSpace *fes,
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Array<int> bc):
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SurfaceSolver(pa, vis, niter, wait, mesh, fes, bc) {}
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void Solve()
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{
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if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
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a.AddDomainIntegrator(new VectorDiffusionIntegrator(one));
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for (int iiter=0; iiter<niter; ++iiter)
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{
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a.Assemble();
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b = 0.0;
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x = *nodes; // should only copy the BC
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Vector B, X;
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OperatorPtr A;
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a.FormLinearSystem(bc, x, b, A, X, B);
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if (!pa)
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{
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// Use a simple symmetric Gauss-Seidel preconditioner with PCG.
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GSSmoother M(static_cast<SparseMatrix&>(*A));
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PCG(*A, M, B, X, 3, 2000, eps, 0.0);
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}
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else { CG(*A, B, X, 3, 2000, eps, 0.0); }
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// Recover the solution as a finite element grid function.
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a.RecoverFEMSolution(X, b, x);
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*nodes = x;
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// Send the solution by socket to a GLVis server.
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if (visualization)
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{
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glvis << "mesh\n" << *mesh << flush;
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if (wait) { glvis << "pause\n" << flush; }
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}
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a.Update();
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}
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}
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};
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// ****************************************************************************
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int main(int argc, char *argv[])
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{
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int nx = 4;
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int ny = 4;
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int order = 4;
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int niter = 4;
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bool pa = false;
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int ref_levels = 1;
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bool wait = false;
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bool components = true;
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int parametrization = 0;
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bool visualization = true;
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const char *keys = "gAaa";
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const char *device_config = "cpu";
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const char *mesh_file = "../data/mobius-strip.mesh";
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// 1. Parse command-line options.
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OptionsParser args(argc, argv);
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args.AddOption(&mesh_file, "-m", "--mesh", "Mesh file to use.");
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args.AddOption(¶metrization, "-p", "--parametrization",
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"Enable or disable parametrization .");
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args.AddOption(&wait, "-w", "--wait", "-no-w", "--no-wait",
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"Enable or disable a GLVis pause.");
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args.AddOption(&nx, "-nx", "--num-elements-x",
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"Number of elements in x-direction.");
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args.AddOption(&ny, "-ny", "--num-elements-y",
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"Number of elements in y-direction.");
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args.AddOption(&order, "-o", "--order", "Finite element order.");
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args.AddOption(&ref_levels, "-r", "--ref-levels", "Refinement");
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args.AddOption(&niter, "-n", "--niter", "Number of iterations");
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args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
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"--no-partial-assembly", "Enable Partial Assembly.");
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args.AddOption(&device_config, "-d", "--device",
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"Device configuration string, see Device::Configure().");
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args.AddOption(&keys, "-k", "--keys", "GLVis configuration keys.");
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args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
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"--no-visualization", "Enable or disable GLVis visualization.");
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args.AddOption(&components, "-c", "--components", "-no-c",
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"--no-components", "Enable or disable the 'by component' solver");
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args.Parse();
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if (!args.Good()) { args.PrintUsage(cout); return 1; }
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args.PrintOptions(cout);
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MFEM_VERIFY(components || !pa, "Vector solver does not support PA yet!");
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// 2. Enable hardware devices such as GPUs, and programming models such as
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// CUDA, OCCA, RAJA and OpenMP based on command line options.
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Device device(device_config);
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device.Print();
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if (visualization)
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{
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glvis.open(vishost, visport);
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glvis.precision(8);
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}
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// Initialize our surface mesh from command line option.
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Mesh *mesh = nullptr;
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if (parametrization<0)
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{
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const int refine = 1;
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const int generate_edges = 1;
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mesh = new Mesh(mesh_file, generate_edges, refine);
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}
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else if (parametrization==0)
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{ mesh = new SurfaceMesh(order, catenoid, catenoid_postfix, nx, ny); }
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else if (parametrization==1)
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{ mesh = new SurfaceMesh(order, helicoid, nullptr, nx, ny); }
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else if (parametrization==2)
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{ mesh = new SurfaceMesh(order, enneper2, nullptr, nx, ny); }
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else if (parametrization==3)
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{ mesh = new SurfaceMesh(order, scherk, nullptr, nx, ny); }
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else if (parametrization==4)
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{ mesh = new SurfaceMesh(order, mollusc, nullptr, nx, ny); }
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else if (parametrization==5)
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{ mesh = new SurfaceMesh(order, hold, nullptr, nx, ny); }
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else if (parametrization==6)
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{ mesh = new SurfaceMesh(order, peach, nullptr, nx, ny); }
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else { mfem_error("Not a valid parametrization, p should be in ]-infty, 6]"); }
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const bool discontinuous = false;
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const int mdim = mesh->Dimension();
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const int sdim = mesh->SpaceDimension();
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cout << "mesh dimension: " << mdim << " mesh space dimension: " << sdim << endl;
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mesh->SetCurvature(order, discontinuous, sdim, Ordering::byNODES);
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// Refine the mesh to increase the resolution.
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for (int l = 0; l < ref_levels; l++) { mesh->UniformRefinement(); }
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// Define a finite element space on the mesh.
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const H1_FECollection fec(order, mdim);
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FiniteElementSpace *sfes = new FiniteElementSpace(mesh, &fec);
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FiniteElementSpace *vfes = new FiniteElementSpace(mesh, &fec, sdim);
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cout << "Number of finite element unknowns: " << vfes->GetTrueVSize() << endl;
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// Determine the list of true (i.e. conforming) essential boundary dofs.
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Array<int> v_ess_tdof_list, s_ess_tdof_list;
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if (mesh->bdr_attributes.Size())
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{
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Array<int> ess_bdr(mesh->bdr_attributes.Max());
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ess_bdr = 1;
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sfes->GetEssentialTrueDofs(ess_bdr, s_ess_tdof_list);
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vfes->GetEssentialTrueDofs(ess_bdr, v_ess_tdof_list);
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}
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if (visualization)
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{
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//glvis << "solution\n" << *mesh << s <<flush;
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glvis << "mesh\n" << *mesh << flush;
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glvis << "keys " << keys << "\n";
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glvis << "window_size 800 800\n";
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if (wait) { glvis << "pause\n" << flush; }
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}
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SurfaceSolver *solver;
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if (components)
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{
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solver = new ComponentSolver(pa, visualization, niter, wait,
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mesh, sfes, s_ess_tdof_list);
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}
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else
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{
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solver = new VectorSolver(pa, visualization, niter, wait,
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mesh, vfes, v_ess_tdof_list);
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}
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solver->Solve();
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// Free the used memory.
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delete sfes;
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delete vfes;
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delete mesh;
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return 0;
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}
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// Parametrization of a Catenoid surface
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void catenoid(const Vector &x, Vector &p)
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{
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p.SetSize(3);
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// u in [0,2π] and v in [-2π/3,2π/3]
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const double u = 2.0*pi*x[0];
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const double v = 2.0*pi*(2.0*x[1]-1.0)/3.0;
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p[0] = cos(u)*cosh(v);
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p[1] = sin(u)*cosh(v);
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p[2] = v;
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}
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// Postfix of the Catenoid surface
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void catenoid_postfix(const int nx, const int ny, Mesh *mesh)
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{
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Array<int> v2v(mesh->GetNV());
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for (int i = 0; i < v2v.Size(); i++) { v2v[i] = i; }
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// identify vertices on vertical lines
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for (int j = 0; j <= ny; j++)
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{
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const int v_old = nx + j * (nx + 1);
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const int v_new = j * (nx + 1);
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v2v[v_old] = v_new;
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}
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// renumber elements
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for (int i = 0; i < mesh->GetNE(); i++)
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{
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Element *el = mesh->GetElement(i);
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int *v = el->GetVertices();
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const int nv = el->GetNVertices();
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for (int j = 0; j < nv; j++)
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{ v[j] = v2v[v[j]]; }
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}
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// renumber boundary elements
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for (int i = 0; i < mesh->GetNBE(); i++)
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{
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Element *el = mesh->GetBdrElement(i);
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int *v = el->GetVertices();
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const int nv = el->GetNVertices();
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for (int j = 0; j < nv; j++)
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{ v[j] = v2v[v[j]]; }
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}
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}
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// Parametrization of a Helicoid surface
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void helicoid(const Vector &x, Vector &p)
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{
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p.SetSize(3);
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const double a = 1.0;
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// u in [0,2π] and v in [-2π/3,2π/3]
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const double u = 2.0*pi*x[0];
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const double v = 2.0*pi*(2.0*x[1]-1.0)/3.0;
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p[0] = a*cos(u)*sinh(v);
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p[1] = a*sin(u)*sinh(v);
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p[2] = a*u;
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}
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// Parametrization of Enneper's surface
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void enneper1(const Vector &x, Vector &p)
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{
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p.SetSize(3);
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// r in [0,1] and t in [−π, π]
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const double r = x[0];
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const double t = pi*(2.0*x[1]-1.0);
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const double third = 1./3.;
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const double u = r*cos(t);
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const double v = r*sin(t);
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p[0] = u - third*u*u*u + u*v*v;
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p[1] = v - third*v*v*v + u*u*v;
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p[2] = u*u - v*v;
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}
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void enneper2(const Vector &x, Vector &p)
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{
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p.SetSize(3);
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// (u,v) in [-2, +2]
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const double u = 2.0*(2.0*x[0]-1.0);
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const double v = 2.0*(2.0*x[1]-1.0);
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p[0] = +u - u*u*u/3.0 + u*v*v;
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p[1] = -v - u*u*v + v*v*v/3.0;
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p[2] = u*u - v*v;
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}
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// Parametrization of Scherk's surface
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void scherk(const Vector &x, Vector &p)
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{
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p.SetSize(3);
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const double alpha = 0.49;
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// (u,v) in [-απ, +απ]
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const double u = alpha*pi*(2.0*x[0]-1.0);
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const double v = alpha*pi*(2.0*x[1]-1.0);
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p[0] = u;
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p[1] = v;
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p[2] = log(cos(u)/cos(v));
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}
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// Mollusc shell model
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void mollusc(const Vector &x, Vector &p)
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{
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p.SetSize(3);
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// u in [0,2π] and v in [-15, 6]
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const double u = 2.0*pi*x[0];
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const double v = 21.0*x[1]-15.0;
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p[0] = +1.0*pow(1.16,v)*cos(v)*(1.0+cos(u));
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p[1] = -1.0*pow(1.16,v)*sin(v)*(1.0+cos(u));
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p[2] = -2.0*pow(1.16,v)*(1.0+sin(u));
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}
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// **********************************
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void hold(const Vector &x, Vector &p)
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{
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p.SetSize(3);
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// u in [0,2π] and v in [0,1]
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const double u = 2.0*pi*x[0];
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const double v = x[1];
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p[0] = cos(u)*(1.0 + 0.3*sin(5.*u + pi*v));
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p[1] = sin(u)*(1.0 + 0.3*sin(5.*u + pi*v));
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p[2] = v;
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}
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// ***********************************
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void peach(const Vector &X, Vector &p)
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{
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p = X;
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const double x = 2.0*X[0]-1.0;
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const double y = X[1];
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const double h = 1.0;
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const double r = sqrt(x*x + y*y);
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const double t = (x==0.0) ? pi/2.0 :
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(y==0.0 && x>0.0) ? 0. :
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(y==0.0 && x<0.0) ? pi : acos(x/r);
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const double sqrtx = sqrt(1.0 + x*x);
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const double sqrty = sqrt(1.0 + y*y);
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const bool yaxis = pi/4.0<t && t < 3.0*pi/4.0;
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const double R = yaxis?sqrtx:sqrty;
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const double gamma = r/R;
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p[0] = gamma * cos(t);
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p[1] = gamma * sin(t);
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p[2] = h*(1.0 - gamma);
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}
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