A parallel grid modification and domain decomposition algorithm for local phenomena capturing and load balancing

Lion's nonoverlapping Schwarz domain decomposition method based on a finite difference discretization is applied to problems with fronts or layers. For the purpose of getting accurate approximation of the solution by solving small linear systems, grid refinement is made on subdomains that contain fronts and layers and uniform coarse grids are applied on subdomains in which the solution changes slowly and smoothly. In order to balance loads among different processors, we employ small subdomains with fine grids for rapidly-changing-solution areas, and big subdomains with coarse grids for slowly-changing-solution areas. Numerical implementations in the SPMD mode on an nCUBE2 machine are conducted to show the efficiency and accuracy of the method.