On the Impact of the Heterogeneous Multicore and Many‐Core Platforms on Iterative Solution Methods and Preconditioning Techniques
Dimitar Lukarski, Maya G. Neytcheva · 2014
This chapter discusses the issue for a class of methods, broadly used in scientific computations, mainly the iterative solution methods. It shows how iterative methods can be performed efficiently on highly parallel, heterogeneous platforms. It also presents various methods and examples to show how this can be done, which includes mathematical description, as well as hardware-specific aspects. Then, it briefly discusses basic iterative techniques as well as two of the most often used projection-based methods: the conjugate gradient (CG) method, the generalized minimal residual (GMRES) method, and the multigrid (MG) method. It also describes the defect-correction technique as an illustration of an approach particularly suitable for solving linear systems on heterogeneous computers. Except the preconditioning phase, all routines in most of the iterative solution methods can be straightforwardly performed in parallel. Therefore, this chapter focuses on techniques for exposing fine-grained level of parallelism in the preconditioning phase.