Parallel Smoothers Using Sparse Approximate Inverse

Sparse Approximate Inverse Smoothers For Geometric and Algebraic Multigrid

Sparse Approximate Inverse Smoother for Multigrid

Various forms of sparse approximate inverses (SAI) have been shown to be useful for preconditioning. Their potential usefulness in a parallel environment has motivated much interest in recent years. However, the capability of an approximate inverse in eliminating the local error has not yet been fully exploited in multigrid algorithms. A careful examination of the iteration matrices of these ap...

Sparse Approximate Inverse Smoothers For Geometric and Algebraic Multigrid

Towards a complete FEM-based simulation toolkit on GPUs: Unstructured Grid Finite Element Geometric Multigrid solvers with strong smoothers based on Sparse Approximate Inverses

We describe our FE-gMG solver, a finite element geometric multigrid approach for problems relying on unstructured grids. We augment our GPUand multicore-oriented implementation technique based on cascades of sparse matrix-vector multiplication by applying strong smoothers. In particular, we employ Sparse Approximate Inverse (SPAI) and Stabilised Approximate Inverse (SAINV) techniques. We focus ...

Parallel Smoothers for Matrix-based Multigrid Methods on Unstructured Meshes Using Multicore CPUs and GPUs

Multigrid methods are efficient and fast solvers for problems typically modeled by partial differential equations of elliptic type. For problems with complex geometries and local singularities stencil-type discrete operators on equidistant Cartesian grids need to be replaced by more flexible concepts for unstructured meshes in order to properly resolve all problem-inherent specifics and for mai...