A parallel algorithm for solving linear parabolic evolution equations
Abstract
We present an algorithm for the solution of a simultaneous space-time discretization of linear parabolic evolution equations with a symmetric differential operator in space. Building on earlier work, we recast this discretization into a Schur-complement equation whose solution is a quasi-optimal approximation to the weak solution of the equation at hand. Choosing a tensor-product discretization, we arrive at a remarkably simple linear system. Using wavelets in time and standard finite elements in space, we solve the resulting system in linear complexity on a single processor, and in polylogarithmic complexity when parallelized in both space and time. We complement these theoretical findings with large-scale parallel computations showing the effectiveness of the method.
Cite
@article{arxiv.2009.08875,
title = {A parallel algorithm for solving linear parabolic evolution equations},
author = {Raymond van Venetië and Jan Westerdiep},
journal= {arXiv preprint arXiv:2009.08875},
year = {2021}
}