General concepts » I/O in Rodin » Grid Function I/O

Saving and loading grid functions in Rodin.

Introduction

Grid functions represent the discrete solution of a finite element problem. They associate numerical values (degrees of freedom) with a finite element space. Saving and loading grid functions is essential for:

Storing computed solutions
Post-processing and visualization
Checkpoint/restart of simulations
Transferring data between different analyses

Saving Grid Functions

MFEM Format

The MFEM format stores grid functions as text files:

#include <Rodin/Geometry.h>
#include <Rodin/Variational.h>

using namespace Rodin;
using namespace Rodin::Geometry;
using namespace Rodin::Variational;

int main()
{
  Mesh mesh;
  mesh = mesh.UniformGrid(Polytope::Type::Triangle, {16, 16});

  P1 Vh(mesh);
  GridFunction u(Vh);
  u = [](const Geometry::Point& p) { return p.x() * p.y(); };

  // Save grid function and mesh
  u.save("solution.gf", IO::FileFormat::MFEM);
  mesh.save("mesh.mesh", IO::FileFormat::MFEM);

  return 0;
}

XDMF Format (Recommended)

For visualization, the XDMF format is recommended. It stores both mesh and field data together and can be opened directly in ParaView:

#include <Rodin/IO/XDMF.h>

// After computing the solution...
IO::XDMF xdmf("Output");
xdmf.grid().setMesh(mesh).add("solution", u);
xdmf.write();

Loading Grid Functions

From MFEM Format

To load a grid function from MFEM format, you need the mesh and finite element space already set up:

// Load mesh
Mesh mesh;
mesh.load("mesh.mesh", IO::FileFormat::MFEM);

// Create FE space on loaded mesh
P1 Vh(mesh);

// Load grid function
GridFunction u(Vh);
u.load("solution.gf", IO::FileFormat::MFEM);

Format Coverage

Grid function I/O coverage depends on the role of the format:

Format	Tested grid function role
MFEM	P0, P1, and H1 finite element grid functions
MEDIT	Vertex-based solution files (`SolAtVertices`)
HDF5	Raw degree-of-freedom persistence
XDMF	Evaluated visualization attributes

MFEM H1 grid functions are tested against fixture files generated by MFEM for degrees K = 1, 2, 3, 4, 5, 6, for scalar and vector data, and for both MFEM vector orderings. P0 scalar grid functions are tested on Point, Segment, Triangle, Quadrilateral, Tetrahedron, Hexahedron, and Wedge meshes. P1 and H1 vector grid functions use the vector finite element spaces provided by Rodin; P0 currently exposes a scalar finite element space even though vector P0 elements exist internally.

Multiple Fields

When dealing with multiple fields, you can export them all in one XDMF file:

IO::XDMF xdmf("MultiField");
auto grid = xdmf.grid();
grid.setMesh(mesh);
grid.add("temperature", temperature);
grid.add("velocity", velocity);
grid.add("pressure", pressure);
xdmf.write();

All fields will be available for selection in ParaView.

Vector-Valued Fields

Vector-valued grid functions are defined on finite element spaces with multiple components:

// Create a vector P1 space (2 components)
P1 Vh(mesh, 2);
GridFunction velocity(Vh);
velocity = [](const Geometry::Point& p)
{
  return Math::Vector<Real>{{ -p.y(), p.x() }};
};

IO::XDMF xdmf("VectorField");
xdmf.grid().setMesh(mesh).add("velocity", velocity);
xdmf.write();