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arXiv · 2110.05804

Complexity of direct and iterative solvers on space-time formulations versus time--marching schemes for h-refined grids towards singularities

Marcin Skotniczny·Anna Paszynska·Sergio Rojas·Maciej Paszynski
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Abstract

We study computational complexity aspects for Finite Element formulations considering hypercubic space--time full and time--marching discretization schemes for $h$--refined grids towards singularities. We perform a relatively comprehensive study of comparing the computational time via time complexities of direct and iterative solvers. We focus on the space-time formulation with refined computational grids and on the corresponding time slabs, namely, computational grids obtained by taking the "cross-sections" of the refined space-time mesh. We compare the computational complexity of the space-time formulation and the corresponding time--marching scheme. Our consideration concerns the computational complexity of the multi-frontal solvers, the iterative solvers, as well as the static condensation. Numerical experiments with Octave confirm our theoretical findings.

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Marcin Skotniczny, Anna Paszynska, Sergio Rojas, Maciej Paszynski. 2021-10-12. Complexity of direct and iterative solvers on space-time formulations versus time--marching schemes for h-refined grids towards singularities. https://arxiv.org/abs/2110.05804

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