Finite element solution of boundary value problems: theory and computation
Finite element solution of boundary value problems: theory and computation
BoomerAMG: a parallel algebraic multigrid solver and preconditioner
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Implementing sparse matrix-vector multiplication on throughput-oriented processors
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
HiFlow3: a flexible and hardware-aware parallel finite element package
Proceedings of the 9th Workshop on Parallel/High-Performance Object-Oriented Scientific Computing
Facing the Multicore-Challenge II
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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.