Stochastic Domain Decomposition for Time Dependent Adaptive Mesh Generation (Journal of Mathematical Study, 2015)
The efficient generation of meshes is an important component in the numericalsolution of problems in physics and engineering. Of interest are situations whereglobal mesh quality and a tight coupling to the solution of the physical partial differentialequation (PDE) is important. We consider parabolic PDE mesh generationand present a method for the construction of adaptive meshes in two spatial dimensionsusing stochastic domain decomposition that is suitable for an implementationin a multi- or many-core environment. Methods for mesh generation on periodic domainsare also provided. The mesh generator is coupled to a time dependent physicalPDE and the system is evolved using an alternating solution procedure. The methoduses the stochastic representation of the exact solution of a parabolic linear mesh generatorto find the location of an adaptive mesh along the (artificial) subdomain interfaces.The deterministic evaluation of the mesh over each subdomain can then beobtained completely independently using the probabilistically computed solutions asboundary conditions. A small scaling study is provided to demonstrate the parallelperformance of this stochastic domain decomposition approach to mesh generation.We demonstrate the approach numerically and compare the mesh obtained with thecorresponding single domain mesh using a representative mesh quality measure.