## Comparative study of finite element methods using the time-accuracy-size (TAS) spectrum analysis.(English)Zbl 1417.65224

For comparison of different finite element methods using continuous and discontinuous Galerkin approaches, a performance analysis metrics is introduced. An extended performance spectrum model is presented, based on the work of J. Chang et al. [“A performance spectrum for parallel computational frameworks that solve PDEs”, Concurrency Comput. Pract. Exp. 30, No. 11, e4401 (2017; doi:10\.1002/cpe.4401)], which takes into account time-to-solution, accuracy of the solution and the problem size.
Thus hardware and algorithmic trade-offs can be interpreted. The proposed metrics are illustrated for the Poisson equation using various meshes on a $$2d$$ unit square and a unit cube, for the latter using parallel computations.

### MSC:

 65Y05 Parallel numerical computation 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

### Keywords:

finite elements; parallel computing; performance; accuracy

### Software:

PETSc; MOOSE ; PyOP2; deal.ii; COFFEE; Firedrake; FInAT; TSFC; FEniCS; DMPlex; libMesh; ML; pTatin3D; FIAT ; hypre; petsc4py
Full Text:

### References:

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