
De Rham Complexes for Weak Galerkin Finite Element Spaces
Two de Rham complex sequences of the finite element spaces are introduce...
read it

TSFC: a structurepreserving form compiler
A form compiler takes a highlevel description of the weak form of parti...
read it

A discrete elasticity complex on threedimensional Alfeld splits
We construct conforming finite element elasticity complexes on the Alfel...
read it

Bringing Trimmed Serendipity Methods to Computational Practice in Firedrake
We present an implementation of the trimmed serendipity finite element f...
read it

UFL Dual Spaces, a proposal
This white paper highlights current limitations in the algebraic closure...
read it

ATENSOR  REDUCE program for tensor simplification
The paper presents a REDUCE program for the simplification of tensor exp...
read it

Spin Summations: A HighPerformance Perspective
Besides tensor contractions, one of the most pronounced computational bo...
read it
Fast Evaluation of Finite Element Weak Forms Using Python Tensor Contraction Packages
In finite element calculations, the integral forms are usually evaluated using nested loops over elements, and over quadrature points. Many such forms (e.g. linear or multilinear) can be expressed in a compact way, without the explicit loops, using a single tensor contraction expression by employing the Einstein summation convention. To automate this process and leverage existing high performance codes, we first introduce a notation allowing trivial differentiation of multilinear finite element forms. Based on that we propose and describe a new transpiler from Einstein summation based expressions, augmented to allow defining multilinear finite element weak forms, to regular tensor contraction expressions. The resulting expressions are compatible with a number of Python scientific computing packages, that implement, optimize and in some cases parallelize the general tensor contractions. We assess the performance of those packages, as well as the influence of operand memory layouts and tensor contraction paths optimizations on the elapsed time and memory requirements of the finite element form evaluations. We also compare the efficiency of the transpiled weak form implementations to the Cbased functions available in the finite element package SfePy.
READ FULL TEXT
Comments
There are no comments yet.