Comparative study of finite element methods using the time-accuracy-size (TAS) spectrum analysis

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 [J. Chang et al., Concurrency and Computation Practice and Experience, 30(2017), e4401] for interpretation of hardware and algorithmic trade-offs in numerical PDE simulation. As a proof-of-concept, popular finite element software packages are used to illustrate this analysis for Poisson's equation.