High Performance Large Sparse PDEs with Parabolic and Elliptic Types Using AGE Method on DPCS

Abstract

The computational analysis of three case studies using parallelization of Alternating Group Explicit (AGE) solver is presented. Based on (2×2) block system and splitting strategy, AGE with Douglas-Richford and Brian variances are applied to simulate the large sparse PDEs applications with parabolic and elliptic types. The applications are heat equation, food dehydration for preservation and breast cancer growth. The AGE method has proved to be stable and suitable for parallel computing as it possesses separately and independently. The performance of AGE is compared with classical iterative methods such as Red Black Gauss Seidel (RBGS) and Jacobi (JB) methods. Since the PDEs applications are large sparse problems, we apply the AGE method in three different applications with three different mathematical models. The parallel implementation is based on SIMD model and supported by distributed memory architecture. Therefore, some numerical analysis and parallel performance indicators are used to validate the superior of parallel AGE method in terms of time execution, speedup, efficiency and effectiveness. As a result, the performances of numerical analysis and parallel evaluation of AGE are found to be effective for solving three case studies in reducing data storage accesses and minimizing communication time on a distributed parallel computer system.