Singular Value Decomposition used for compression of results from the Finite Element Method

Abstract

A complex finite element analysis can produce large amount of data that is problematic to post-process in reasonable time. This paper describes application of Singular Value Decomposition (SVD) to the compression of results from finite element solvers. Although the idea of image compression method is an inspiration for this research work, the SVD compression algorithm used for compression of images cannot be directly used for FEM results. Differences and implementation challenges are discussed in the text. Quality of approximation is more important in scientific field than in computer graphics where the most significant factor is the human perception of the resulting image. Error estimation methods used during compression of finite element results are presented. The focus is also on the algorithm performance. SVD is a very computational intensive method. Therefore, various optimization techniques were investigated, e.g. randomized SVD. The method leads to the lower memory consumption, 10% of the original size or less, with negligible compression error.