A Conservative Parallel Iteration Scheme for Nonlinear Diffusion Equations on Unstructured Meshes (Communications in Computational Physics, 2020)
In this paper, a conservative parallel iteration scheme is constructed to solvenonlinear diffusion equations on unstructured polygonal meshes. The design is basedon two main ingredients: the first is that the parallelized domain decomposition isembedded into the nonlinear iteration; the second is that prediction and correctionsteps are applied at subdomain interfaces in the parallelized domain decompositionmethod. A new prediction approach is proposed to obtain an efficient conservativeparallel finite volume scheme. The numerical experiments show that our parallelscheme is second-order accurate, unconditionally stable, conservative and has linearparallel speed-up.