Using State-Of-The-Art Sparse Matrix Optimizations for Accelerating the Performance of Elmer

Multiphysics simulations are at the core of modern Computer Aided Engineering (CAE) allowing the analysis of multiple, simultaneously acting physical phenomena. These simulations often rely on Finite Element Methods (FEM) and the solution of large linear systems which, in turn, end up in multiple calls of the costly Sparse Matrix-Vector Multiplication (SpMV) kernel. We have recently proposed the Compressed Sparse eXtended (CSX) format, which applies aggressive compression to the column indexing structure of the CSR format and is able to provide an average performance improve- ment of more than 40% over multithreaded CSR implementations. This work integrates CSX into the Elmer multiphysics simulation software and evaluates its impact on the total execution time of the solver. Despite its preprocessing cost, CSX is able to improve by almost 40% the performance of the Elmer's SpMV component (using multithreaded CSR) and provides an up to 15% performance gain in the overall solver time after 1000 linear system iterations. To our knowledge, this is one of the rst attempts to evaluate the real impact of an innovative sparse-matrix storage format within a `production' multiphysics software