Efficient Parabolic Solvers Scalable across Multi-Architectural Levels

High end computing hardware has been growing fast in both uniprocessor performance and parallel system scales. Steadily advancing but somewhat lagging behind is the speed of memory accesses. Thus, needed are software and algorithms behind software that adapt well with architectural features of high end computing hardware. Stable explicit implicit domain decomposition (SEIDD) is a class of numerical algorithms originally introduced for solving parabolic equations on parallel computers, which has adequately high parallelism, flexible controllability for load balancing, minimal communication cost, and good stability and efficiency. In this paper, we study the effectiveness of SEIDD in harnessing the computing power at the inter-processor level for parallel processing as well as the level of cache memories for fast memory accesses.