Result: On the Efficiency of Symbolic Computations Combined with Code Generation for Finite Element Methods.

Title:
On the Efficiency of Symbolic Computations Combined with Code Generation for Finite Element Methods.
Authors:
ALNæS, MARTIN SANDVE1 martinal@simula.no, MARDA, KENT-ANDRÉ1 kent-and@simula.no
Source:
ACM Transactions on Mathematical Software. 2011, Vol. 37 Issue 1, p6-6:26. 26p.
Subject Terms:
*FINITE element method, *MATHEMATICAL programming, *PYTHON programming language, *PROGRAMMING languages, *C++, *MATHEMATICS
Database:
Academic Search Index

Further Information

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. [ABSTRACT FROM AUTHOR]