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);

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();