Details

Autor(en) / Beteiligte

• van Venetië, Raymond
• Westerdiep, Jan

Titel

A Parallel Algorithm for Solving Linear Parabolic Evolution Equations

Ist Teil von

• Parallel-In-Time Integration Methods, 2021, Vol.356, p.33-50

Ort / Verlag

Switzerland: Springer International Publishing AG

Erscheinungsjahr

2021

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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.