Stochastic domain decomposition for time dependent adaptive mesh generation

TL;DR

This paper introduces a stochastic domain decomposition method for generating adaptive meshes in time-dependent PDE problems, enabling efficient parallel computation and improved mesh quality in physics and engineering simulations.

Contribution

It presents a novel stochastic domain decomposition approach for adaptive mesh generation coupled with physical PDEs, suitable for multi-core environments.

Findings

Method effectively generates high-quality adaptive meshes.

Parallel implementation shows promising performance.

Compared meshes demonstrate improved quality over single domain methods.

Abstract

The efficient generation of meshes is an important component in the numerical solution of problems in physics and engineering. Of interest are situations where global mesh quality and a tight coupling to the solution of the physical partial differential equation (PDE) is important. We consider parabolic PDE mesh generation and present a method for the construction of adaptive meshes in two spatial dimensions using stochastic domain decomposition that is suitable for an implementation in a multi- or many-core environment. Methods for mesh generation on periodic domains are also provided. The mesh generator is coupled to a time dependent physical PDE and the system is evolved using an alternating solution procedure. The method uses the stochastic representation of the exact solution of a parabolic linear mesh generator to find the location of an adaptive mesh along the (artificial) subdomain interfaces. The deterministic evaluation of the mesh over each subdomain can then be obtained completely independently using the probabilistically computed solutions as boundary conditions. The parallel performance of this general stochastic domain decomposition approach has previously been shown. We demonstrate the approach numerically for the mesh generation context and compare the mesh obtained with the corresponding single domain mesh using a representative mesh quality measure.