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