A scalable parallel Gauss-Seidel and Jacobi solver for animal genetics

Abstract

A parallel solver based on data parallelism on distributed memory architectures is described. The familiar Gauss-Seidel and Jacobi iterations are used in an “iteration on data” scheme. Minimalization of interprocessor communication is obtained by a split of equations in two sets: Local and Global. Only members of the global set receive contributions from data on more than one processor, hence only global equations require communication during iterations for their solution. Linear and in some models even super linear scalability is obtained in a wide range of model sizes and numbers of parallel processors. The largest example tested in this study is a 3-trait calculation with 30.1 mio. equations.