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 rt January 25, 2007 10:46

Next generation FEM (scientific computing)

i read this impressive article today and recommend it for u if u have interest to knowe about next generation FEM (scientific somputing):

ROBERT C. KIRBY & ANDERS LOGG A Compiler for Variational Forms, ACM Transactions on Mathematical Software, Vol. 32, No. 3, September 2006, Pages 417â€"444.

also look at this link: http://www.fenics.org/

Abstract of mentioned paper:

As a key step towards a complete automation of the finite element method, we present a new algorithm for automatic and efficient evaluation of multilinear variational forms. The algorithm has been implemented in the form of a compiler, the FEniCS Form Compiler (FFC). We present benchmark results for a series of standard variational forms, including the incompressible Navierâ€" Stokes equations and linear elasticity. The speedup compared to the standard quadrature-based approach is impressive; in some cases the speedup is as large as a factor of 1000.

 Jonas Holdeman January 25, 2007 11:25

Re: Next generation FEM (scientific computing)

I have not read the article, but am very skeptical of the apparent claims. Maybe for some "academic" problems with simple geometries... But underneath any "compiler" interface, there is still the difficult and time-consuming problem/art of mesh generation. And there is the problem/art of dealing with problems at the very edge of convergence or stability, and with boundary conditions.

This would not be the first program to take a general specification of a problem and connect or link computational modules to solve the problem for simple geometries. But in the real world, problem-solving is an ART, applying the incomplete science and technology as it exists the time to the problem at hand.

 rt January 25, 2007 11:38

Re: Next generation FEM (scientific computing)

so look at paper for more about concept, certainly this project is not complete but it opens roadmap for next generation scientific computing compilers.

FCC is coupled with other FEniCS projects to perform simulation, look at FEniCS gallery (http://www.fenics.org/gallery/) there are some sample related to complex geometry (e.g. gear, or temperature around a hot dolphin)

 rt January 30, 2007 11:13

Re: Next generation FEM (scientific computing)

Note that mentioned method is only related to automation of generation of local stiffness matrix and its assembling stage in FEM procedure, not linear algebra stage (solution of system of eqs.) that is usually more time consuming (abstract of paper is slightly illusive)

so it can be attractive in fully explicit FE analysis.

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