HPS Accelerated Spectral Solvers for Time Dependent Problems
Numerical Analysis
2018-11-13 v1
Abstract
A high-order convergent numerical method for solving linear and non-linear parabolic PDEs is presented. The time-stepping is done via an explicit, singly diagonally implicit Runge-Kutta (ESDIRK) method of order 4 or 5, and for the implicit solve, we use the recently developed "Hierarchial Poincare-Steklov (HPS)" method. The HPS method combines a multidomain spectral collocation discretization technique (a "patching method") with a nested-dissection type direct solver. In the context under consideration, the elliptic solve required in each time-step involves the same coefficient matrix, which makes the use of a direct solver particularly effective. The manuscript describes the methodology and presents numerical experiments.
Cite
@article{arxiv.1811.04555,
title = {HPS Accelerated Spectral Solvers for Time Dependent Problems},
author = {Tracy Babb and Per-Gunnar Martinsson and Daniel Appelo},
journal= {arXiv preprint arXiv:1811.04555},
year = {2018}
}