Scalable multi-coloring preconditioning for multi-core CPUs and GPUs

Krylov space methods like conjugate gradient and GMRES are efficient and parallelizable approaches for solving huge and sparse linear systems of equations. But as condition numbers are increasing polynomially with problem size sophisticated preconditioning techniques are essential building blocks. However, many preconditioning approaches like Gauss-Seidel/SSOR and ILU are based on sequential algorithms. Introducing parallelism for preconditioners is mostly hampering mathematical efficiency. In the era of multi-core and many-core processors like GPUs there is a strong need for scalable and fine-grained parallel preconditioning approaches. In the framework of the multi-platform capable finite element package HiFlow3 we are investigating multi-coloring techniques for block Gauss-Seidel type preconditioners. Our approach proves efficiency and scalability across hybrid multi-core and GPU platforms.