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Course: Solving PDEs with Feel++
IntroductionThe finite element method is used in many fields of physics and engineering (mechanics of solids, fluids, bio-physics, electronics, …).
Researchers, PhD students and engineers often need to quickly solve a physical problem, and it is useful to have flexible tools to test new numerical methods or understand the behavior of the equations involved. Rewrite a calculation code for Solving their own problem then becomes tedious and often far from their area of expertise.
In addition to the specialized commercial tools, open source generalist toolkits have recently been developed: going beyond the simple library, they provide users with sophisticated tools (complex geometry, physical models, parallelism) while offering A simple handling of finite element methods.
These tools are also optimized and parallelized and therefore make it possible to test large problems.
ObjectivesThe aim of this training is to present several recent tools, which are both innovative in methods, and widely used (FreeFem ++, Feel ++, Firedrake), explaining each time their advantages and disadvantages. They may indeed be complementary to one another depending on the problem under study. Each of these tools has its own programming language. Participants will learn to use each of them correctly by appropriating their language.
These tools all offer different solutions to overcome the difficulties of programming the finite element method, and allow researchers, doctoral students and engineers to solve increasingly complex physical problems.
Abstract of the Feel++ CourseFeel++ (Finite Element Embedded Language in C++) is a C++ library for solving partial differential equations with the Galerkin type methods and among them the finite element method and the reduced basis method. It relies on a Domain Specific Embedded Language (DSEL) that allows to write very compact code focusing on the variational formulation of the problem in order to solve seamlessly from a one to thousands of cores on a supercomputer.
Feel++ supports a large range of finite elements as well as numerical methods for PDEs through the DSEL (Domain-Specific Embedded Languages). With some advanced mesh features, it enables advanced numerical methods for PDEs such as Hybridized Discontinuous Galerkin methods or Lagrange multipliers based methods. Solver-wise Feel++ takes advantage of PETSc and offers advanced and scalable solution strategies even in complex method settings. Feel++ easily allows to compare various algebraic strategies.
Feel++ comes with a set of Toolboxes (CFD, CSM, FSI, Thermodynamics and more to come in electro-magnetism) that enables the user through few data files (geometry, parameters and model description) to run right away simulation or build more complex models by coupling different physics.
This tutorial will explain how to solve finite element problems with Feel++ using the library covering various aspects of Feel++ features from simple problems to more advanced ones. We will also use the Toolboxes to quickly setup standard simulations problems and couple some of them. We will take some time to discuss solution strategies using Feel++ PETSc interface.
Feel++ and Feel++ Toolboxes will be provided through docker containers and should be readily available on attendees computers. Attendees are welcome to bring their own problems to discuss how they could possibly be solved using Feel++.
RegistrationIf you would like to register for this course, please fill in the following online form
Registration is final only upon receipt of the complete application.
Please complete the registration form (pdf) and send it by 15th November 2016 by mail to Isabelle.firstname.lastname@example.org or by mail to:
CNRS – Delegation Ile-de-France Sud – Human Resources Department
Av. Of the Terrace – Bât. 9
Registration fees are free for CNRS staff and those in mixed units. For others, please contact email@example.com.
– Matthieu Boileau (CNRS & IRMA)
– Loic Gouarin (CNRS & Mathematics Laboratory of Orsay)
– Pierre Navaro (CNRS & IRMAR)