On the efficiency of symbolic computations combined with code generation for finite element methods-Reference-Cited by-同舟云学术

On the efficiency of symbolic computations combined with code generation for finite element methods

Published:2010-01 Issue:1 Volume:37 Page:1-26
ISSN:0098-3500
Container-title:ACM Transactions on Mathematical Software
language:en
Short-container-title:ACM Trans. Math. Softw.

Author:

Alnæs Martin Sandve¹,Mardal Kent-André²

Affiliation:

1. Simula Research Laboratory, Lysaker, Norway

2. Simula Research Laboratory, Oslo, Oslo, Norway

Abstract

Efficient and easy implementation of variational forms for finite element discretization can be accomplished with metaprogramming. Using a high-level language like Python and symbolic mathematics makes an abstract problem definition possible, but the use of a low-level compiled language is vital for run-time efficiency. By generating low-level C++ code based on symbolic expressions for the discrete weak form, it is possible to accomplish a high degree of abstraction in the problem definition while surpassing the run-time efficiency of traditional hand written C++ codes. We provide several examples where we demonstrate orders of magnitude in speedup.

Funder

Norges Forskningsråd

Publisher

Association for Computing Machinery (ACM)

Subject

Applied Mathematics,Software

Link

https://dl.acm.org/doi/pdf/10.1145/1644001.1644007

Reference37 articles.

1. Alnæs M. Langtangen H.-P. Logg A. Mardal K.-A. and Skavhaug O. 2008. UFC Specification and User Manual. http//www.fenics.org/ufc/. Alnæs M. Langtangen H.-P. Logg A. Mardal K.-A. and Skavhaug O. 2008. UFC Specification and User Manual. http//www.fenics.org/ufc/.

2. Alnæs M. and Mardal K.-A. 2008. SyFi—Symbolic Finite Elements. http://www.fenics.org/syfi/. Alnæs M. and Mardal K.-A. 2008. SyFi—Symbolic Finite Elements. http://www.fenics.org/syfi/.

3. Unified framework for finite element assembly

4. Mixed finite element methods for linear elasticity with weakly imposed symmetry

Cited by 28 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Targeting performance and user-friendliness: GPU-accelerated finite element computation with automated code generation in FEniCS;Parallel Computing;2023-11

2. Analytical solutions of systems of linear retarded and neutral delay differential equations by the Laplace transform: featuring limit cycles;2023-09-06

3. The study of diffuse interface propagation of dynamic failure in advanced ceramics using the phase-field approach;Computer Methods in Applied Mechanics and Engineering;2023-02

4. Phase-Field Damage Modeling in Generalized Mechanics by Using a Mixed Finite Element Method (FEM);Creep in Structures VI;2023

5. Comparison of Symbolic Computations for Solving Linear Delay Differential Equations Using the Laplace Transform Method;Mathematical and Computational Applications;2022-09-23