Rodin::PETSc module

Submodules

• Math — PETSc vector, matrix, and linear system wrappers
• Solver — KSP, SNES, CG, and GMRES solver aliases
• Assembly — Assembly strategies for PETSc objects (sequential, MPI, OpenMP)
• Variational — Trial/test functions, forms, grid functions, and problems backed by PETSc

Typical Usage (Sequential)

#include <Rodin/PETSc.h>

PetscInitialize(&argc, &argv, PETSC_NULLPTR, PETSC_NULLPTR);

Mesh mesh;
mesh = mesh.UniformGrid(Polytope::Type::Triangle, {16, 16});
mesh.getConnectivity().compute(1, 2);

P1 Vh(mesh);
PETSc::Variational::TrialFunction u(Vh);
PETSc::Variational::TestFunction  v(Vh);

Problem poisson(u, v);
poisson = Integral(Grad(u), Grad(v))
        - Integral(f, v)
        + DirichletBC(u, Zero());

Solver::CG(poisson).solve();

PetscFinalize();

Typical Usage (MPI + PETSc)

#include <Rodin/MPI.h>
#include <Rodin/PETSc.h>

boost::mpi::environment env(argc, argv);
boost::mpi::communicator world;
Context::MPI mpi(env, world);
PetscInitialize(&argc, &argv, PETSC_NULLPTR, PETSC_NULLPTR);

// Partition and distribute mesh
MPI::Sharder sharder(mpi);
// ... (see MPI module documentation)
auto mesh = sharder.gather(0);
mesh.getConnectivity().compute(2, 3);
mesh.reconcile(2);

P1 Vh(mesh);
PETSc::Variational::TrialFunction u(Vh);
PETSc::Variational::TestFunction  v(Vh);

Problem poisson(u, v);
poisson = Integral(Grad(u), Grad(v))
        - Integral(f, v)
        + DirichletBC(u, Zero());

Solver::CG(poisson).solve();

PetscFinalize();

Multi-Field Problems (Stokes)

PETSc problems support an arbitrary number of coupled trial/test function pairs for saddle-point systems:

H1  uh(std::integral_constant<size_t, 2>{}, mesh, mesh.getSpaceDimension());
H1  ph(std::integral_constant<size_t, 1>{}, mesh);
P0g lh(mesh);

PETSc::Variational::TrialFunction u(uh);
PETSc::Variational::TrialFunction p(ph);
PETSc::Variational::TrialFunction l(lh);

PETSc::Variational::TestFunction v(uh);
PETSc::Variational::TestFunction q(ph);
PETSc::Variational::TestFunction m(lh);

Problem stokes(u, p, l, v, q, m);
stokes = Integral(Jacobian(u), Jacobian(v))
       - Integral(p, Div(v))
       + Integral(Div(u), q)
       + Integral(l, q)
       + Integral(p, m)
       - Integral(f, v)
       + DirichletBC(u, u_exact);

Solver::KSP(stokes).solve();

PETSc command-line options can be used to configure field-split preconditioning: ./Stokes -ksp_type gmres -pc_type fieldsplit -ksp_rtol 1e-8

Namespaces

namespace Assembly

PETSc-specific assembly strategies.

namespace Math

PETSc-backed linear algebra adapters.

namespace Solver

PETSc-backed linear and nonlinear solver adapters.

namespace Variational

PETSc-backed variational form adapters.

Classes

template<class Handle>

class Object

RAII base class for wrappers around PETSc opaque handles.

Typedefs

using Scalar = PetscScalar

Scalar type used by PETSc vectors and matrices.

using Integer = PetscInt

Integer index type used by PETSc row/column indices.

using Real = PetscReal

Real-valued floating-point type (tolerances, norms, etc.).

using Complex = PetscComplex

Complex scalar type (available when PETSc is built with complex support).

Typedef documentation