Parallelizing the Kolmogorov-Fokker-Planck Equation

TL;DR

This paper introduces the first parallel Schwarz waveform relaxation scheme for the Kolmogorov-Fokker-Planck equation, providing convergence proof, well-posedness analysis, and numerical validation.

Contribution

It presents a novel parallel algorithm for the Kolmogorov-Fokker-Planck equation with a new convergence proof and well-posedness analysis.

Findings

Successful parallel implementation demonstrated

Convergence of the scheme proven theoretically

Numerical tests confirm effectiveness

Abstract

We design the first parallel scheme based on Schwarz waveform relaxation methods for the Kolmogorov-Fokker-Planck equation. We introduce a new convergence proof for the algorithms. We also provide results about the existence and uniqueness of a solution for this equation with several boundary conditions, in order to prove that our algorithms are well-posed. Numerical tests are also provided.