Comparative study of finite element methods using the Time-Accuracy-Size (TAS) spectrum analysis

TL;DR

This paper introduces a comprehensive performance analysis framework for comparing finite element algorithms based on time, accuracy, and size, aiding optimal algorithm selection for PDE simulations.

Contribution

It extends the TAS spectrum model to include hardware and algorithmic tradeoffs, providing a new method for evaluating finite element discretizations.

Findings

The TAS spectrum analysis effectively compares different finite element methods.

Application to Poisson's equation demonstrates the framework's practical utility.

Insights into hardware and algorithmic tradeoffs in finite element simulations.

Abstract

We present a performance analysis appropriate for comparing algorithms using different numerical discretizations. By taking into account the total time-to-solution, numerical accuracy with respect to an error norm, and the computation rate, a cost-benefit analysis can be performed to determine which algorithm and discretization are particularly suited for an application. This work extends the performance spectrum model in Chang et. al. 2017 for interpretation of hardware and algorithmic tradeoffs in numerical PDE simulation. As a proof-of-concept, popular finite element software packages are used to illustrate this analysis for Poisson's equation.