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Documentation for Release 2024.1
The finite element implementations in the various Chaste solvers are described in the attached pdf.
Contents:
1 Finite element solution of simple equations 1.1 Poisson's equation 1.1.1 Applying Dirichlet boundary conditions 1.2 The heat equation 2 Chaste PDE solvers 2.1 SimpleLinearEllipticSolver 2.2 SimpleLinearParabolicSolver 2.3 SimpleNonlinearEllipticSolver 3 Cardiac electrophysiology 3.1 The monodomain equations 3.2 The bidomain equations 3.3 The bidomain equations with a perfusing bath 3.3.1 The bidomain problem with a bath, including stimuli and parameters 4 Solid mechanics 4.1 Formulation 4.1.1 Kinematics 4.1.2 Stress 4.1.3 Equilibrium equations 4.2 Hyper-elasticity and material laws 4.3 Weak form 4.4 Normal pressure on deformed surface boundary conditions 4.5 Finite element discretisation 4.6 Actual ordering of unknowns 4.7 FE residual/Jacobian for the case of normal pressure on deformed surface BCs 4.8 Test problems 4.9 Other implementation calculations 5 Cardiac electro-mechanics 5.1 Formulation 5.1.1 Test problem 5.2 Implicit or explicit schemes 5.3 Anisotropic passive material laws 5.4 Active stress generated in sheet direction 6 Fluid dynamics 6.1 Stokes' Flow
Finite Element Implementations