Exploiting Domain Knowledge to Optimize Mesh Partitioning for Multi-Scale Methods

Multi-scale methods are widely used in complex scientific computing problems [1], [2] which allow problem domains to be decomposed into smaller parts and simulated with different spatial and temporal scales. This way, “the area of interest” is simulated at a finer granularity and higher computation cost while the rest of the system is approximated with a much coarser model. Recursive domain-decomposition [3], [4] is an attractive approach for multi-scale simulation where a large problem is decomposed into group of loosely-coupled subdomains. These subdomains are solved independently and the solutions of individual subdomains are coupled back to get the desired solution. This is illustrated as tree-like algorithmic approach with individual subdomains and shared interfaces are represented as leaf and interior nodes respectively. A recursive TreeSolve function call on root node gives the final solution for a single timestep iteration. Subdomains at smaller timescale will execute multiple times in each iteration.