Multi-GPU Acceleration of Algebraic Multi-Grid Preconditioners for Elliptic Field Problems

In this contribution, a multi-graphic processing unit (GPU) implementation of Krylov sub-space methods with algebraic multi-grid preconditioners is proposed. It is used to solve large linear systems stemming from finite element or finite difference discretizations of elliptic problems as they occur, e.g., in electrostatics. The distribution of data across multiple GPUs and the effects on memory and speed are discussed when using an approach that preserves the effects of fine-grained parallelism with shared memory on the GPU while distributing data across multiple GPUs with minimal communication effort.