Calcul numérique des solides et structures non-linéaires 2022-2023

This repository collects the material to the class MU5MES01 of the Solid Mechanics Master of Sorbonne Université and ENPC

• Teachers:

  • Denis Duhamel (denis.duhamel@enpc.fr)

  • Claire Lestringant (claire.lestringant@sorbonne-universite.fr)

  • Corrado Maurini (corrado.maurini@sorbonne-universite.fr, tour 55-65, 414)

  • Sébastien Neukirch (sebastien.neukirch@sorbonne-universite.fr)

• You can find help on how to install and use FEniCS in INSTALL.md

• You can find some links to online resources in the file LINKS.md

• The preliminary program is available here syllabus.md

Numerical tools

In this class we will use the following open-source numerical tools:

• gmsh: Advanced meshing tool (https://gmsh.info)

• dolfinx: the finite element library, see https://docs.fenicsproject.org/dolfinx/v0.5.1/python/api.html.

  FEniCSx is a popular open-source computing platform for solving partial differential equations (PDEs). FEniCSx enables users to quickly translate scientific models into efficient finite element code. With the high-level Python and C++ interfaces to FEniCSx, it is easy to get started, but FEniCSx offers also powerful capabilities for more experienced programmers. FEniCSx runs on a multitude of platforms ranging from laptops to high-performance clusters.

• ufl (Unified Form Language): https://fenics.readthedocs.io/projects/ufl/en/latest/manual/introduction.html

  The Unified Form Language is an embedded domain specific language for definition of variational forms intended for finite element discretization. More precisely, it defines a fixed interface for choosing¨ finite element spaces and defining expressions for weak forms in a notation close to the mathematical one.

• PETSc https://petsc.org/release/overview/

  PETSc, the Portable, Extensible Toolkit for Scientific Computation, is intended for use in large-scale application projects. Many ongoing computational science projects are built around the PETSc libraries. PETSc is easy to use for beginners. Moreover, its careful design allows advanced users to have detailed control over the solution process. PETSc includes a large suite of parallel linear, nonlinear equation solvers and ODE integrators that are easily used in application codes written in C, C++, Fortran and Python. PETSc provides many of the mechanisms needed within parallel application codes, such as simple parallel matrix and vector assembly routines that allow the overlap of communication and computation. In addition, PETSc includes support for parallel distributed arrays useful for finite difference methods.

• pyvista: pyvista - PyVista package for 3D plotting and mesh analysis (https://docs.pyvista.org).

• paraview: ParaView is an open-source, multi-platform data analysis and visualization application (https://www.paraview.org).