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.
Highlights
The numerical solution of many partial differential equations (PDEs) benefits from the construction of an adaptive grid automatically tuned by the solution itself
We present an efficient, parallel strategy for the solution of the moving mesh PDE based on a stochastic domain decomposition method proposed by Acebron et al [1]
In [5, 6] we have shown that the stochastic domain decomposition technique is an effective way for the parallel generation of adaptive meshes
Summary
The numerical solution of many partial differential equations (PDEs) benefits from the construction of an adaptive grid automatically tuned by the solution itself. Motivated by the alternating solution method, one of the authors has studied the parallel solution of the nonlinear MMPDE alone using a Schwarz based domain decomposition approach. In [10], a monolithic domain decomposition method, simultaneously solving a linear mesh generator coupled to the physical PDE, was presented for a shape optimization problem. Due to a stochastic representation for the solution of PDEs subject to periodic boundary conditions, we give, for the first time, a method to generate meshes for periodic problems using a stochastic domain decomposition approach.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
