Syllabus
Solving a partial differential equation by finite element method using FEniCS.
- Introduction to Python language and typical HPC enviroment and tools.
- Overview of the basic components for finite element solution of partial differential equations: domain description and discretization, basis function implementation (parametric, non-parametric finite elements), boundary condition implementation, efficient linear system assembly, solution of large, sparse linear systems (direct, preconditioned iterative, multigrid methods)
- Nonlinear problems, fixed point method, Newton method
- Example applications: the Poisson equation, the convection-diffusion-reaction equation, the heat transfer equation, the Navier--Stokes equation, the elastic deformation equation, multi-phase flows, the levelset method
Annotation
Introduction to modern methods for numerical solution of systems of partial differential equations obtained by mathematical modeling of continuum mechanics problems (heat transfer, fluid flow, elastic deformation, etc.). The course includes overview of the basic software for numerical computation and its application to solution of PDEs. Major part includes overview and practical use of parallel HPC computational cluster, the basic numerical libraries (Blas, Lapack, Petsc, etc. ), finite element libraries (Fenics) and libraries for parallel computation
(MPI, OpenMP)