CHORAL library

Brief description

Choral is a Fortran library (2003 standard).

• Features
  • high order finite elements for diffusion and elasticity
  • hybrid meshes including curved geometrical elements
  • stabilised time stepping methods for reaction diffusion PDEs
    coupled with ODE systems
    \(~\)
• Dependencies (optional)
  • arpack for eigenvalue solvers
  • MMG for mesh adaptation
  • MUMPS

Applications

• scalar reaction diffusion PDE coupled with an ODE system
  • monodomain model in cardiac electrophysiology
  • Spiralling potential wave
  • P3-Lagrange finite elements / Order 3 Rush-Larsen time-stepping method
    \( ~ \)
    \( ~ \)
    \( ~ \)
• scalar reaction diffusion PDE coupled with an ODE system
  • monodomain model in cardiac electrophysiology
  • Curved (parabolic) geometry
  • P3-Lagrange finite elements / Order 3 Rush-Larsen time-stepping method
    \( ~ \)
    \( ~ \)
    \( ~ \)

Tutorial examples

• Basic

  mesh_visu.f90	\(~\)	mesh visualisation
  feSpace_visu.f90	\(~\)	finite element space visualisation
  quadMesh_integral.f90	\(~\)	compute an integral on a mesh

• Diffusion equation

  poisson_2d.f90	\(~\)	Poisson problem in 2D
  diffusion_Neumann.f90	\(~\)	a general diffusion equation with Neumann boundary condition
  diffusion_Dirichlet_Neumann.f90	\(~\)	a general diffusion equation with mixed Dirichlet-Neumann boundary condition

• Linear elasticity

  elasticity_Dirichlet_2D.f90	\(~\)	linear elasticity with Dirichlet boundary conditions
  elasticity_Neumann_2D.f90	\(~\)	linear elasticity with Neumann boundary conditions

• Eigenvalue problems

  eigen_Laplacian_2D.f90	\(~\)	compute the solution to the Laplace eigenproblem in 2D

• ODEs

  ode_Lin_0d.f90	\(~\)	a simple linear 0D ODE
  ode_cardio_0d.f90	\(~\)	a non linear ODE system in cardiac electrophysiology
  ode_monodomain_2d.f90	\(~\)	a parabolic reaction-diffusion equation coupled with an ODE system

Installation

Download the sources: https://plmlab.math.cnrs.fr/cpierre1/choral

Cmake is required.

• Configure
  • either edit the file "../config.cmake" to set your options before to run cmake

    mkdir build ; cd build ; cmake ..

  • or set your options with ccmake

    mkdir build ; cd build ; cmake .. ; ccmake ..

• Compile
  • to build the library

    make choral

  • to compile all programs and test

    make all

• Test

  make test

Author

Charles Pierre