An improved parallel AGE method to solve incomplete blow-up problem through high performance computing system

Abstract

Incomplete blow-up is a condition under the quasilinear heat equation. The Porous Medium Equation (PME) with power source are admitting incomplete blow-up. It is used as one of the filtration process in the industry. This filtration process has been used globally in the medical and laboratory applications. Previously, the standard numerical procedure was Gauss Seidel method to solve this problem. We propose a new variance of the Alternating Group Explicit Scheme (AGE) algorithms to solve incomplete blow-up problem through High performance computing (HPC). HPC systems include of multiple (usually mass-produced) processors linked together in a single system with commercially available interconnects. This is in contrast to mainframe computers, which are generally monolithic in nature. Four important terms that are, convergent rate by the number of iteration, execution time, computational complexity and stability are considered in this study to evaluate the performances of this approach.