A Hierarchical Reduced Order Modeling for Distributed Memory Parallel Computers

Abstract

Proper orthogonal decomposition (POD) is a method for obtaining a basis for representing physical phenomena and has been used in reduced order models for fast analysis. To apply POD to large-scale problems, distributed memory parallel computing, in which parallel processes are allocated to each partitioned subdomain, is effective. On the other hand, Local POD, which obtains a basis for each decomposed subdomain, has been proposed to improve the computational efficiency of POD. Against this background, we propose a method to independently set subdomains where the basis is acquired and subdomains where parallel processes are allocated. Through its application to diffusion equations, we discuss the computing efficiency and parallel computational performance.