Factorized sparse approximate inverse preconditionings I: theory
SIAM Journal on Matrix Analysis and Applications
Parallel Preconditioning with Sparse Approximate Inverses
SIAM Journal on Scientific Computing
Multigrid
Robust Parallel Smoothing for Multigrid Via Sparse Approximate Inverses
SIAM Journal on Scientific Computing
Sparse approximate inverse smoothers for geometric and algebraic multigrid
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
Implementing sparse matrix-vector multiplication on throughput-oriented processors
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
Scalable multi-coloring preconditioning for multi-core CPUs and GPUs
Euro-Par 2010 Proceedings of the 2010 conference on Parallel processing
A parallel algebraic multigrid solver on graphics processing units
HPCA'09 Proceedings of the Second international conference on High Performance Computing and Applications
Parallel geometric-algebraic multigrid on unstructured forests of octrees
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Hi-index | 0.00 |
Multigrid methods are efficient and fast solvers for problems typically modeled by partial differential equations of elliptic type. We use the approach of matrix-based geometric multigrid that has high flexibility with respect to complex geometries and local singularities. Furthermore, it adapts well to the exigences of modern computing platforms. In this work we investigate multi-colored Gauß-Seidel type smoothers, the power(q)-pattern enhanced multi-colored ILU(p,q) smoothers with fill-ins, and factorized sparse approximate inverse (FSAI) smoothers. These approaches provide efficient smoothers with a high degree of parallelism. We describe the configuration of our smoothers in the context of the portable lmpLAtoolbox and the HiFlow 3 parallel finite element package. In our approach, a single source code can be used across diverse platforms including multicore CPUs and GPUs. Highly optimized implementations are hidden behind a unified user interface. Efficiency and scalability of our multigrid solvers are demonstrated by means of a comprehensive performance analysis on multicore CPUs and GPUs.