Sparse Approximate Inverse Smoother for Multigrid

Mass Smoothers in Geometric Multigrid for Isogeometric Analysis

We investigate geometric multigrid methods for solving the large, sparse linear systems which arise in isogeometric discretizations of elliptic partial differential equations. In particular, we study a smoother which incorporates the inverse of the mass matrix as an iteration matrix, and which we call mass-Richardson smoother. We perform a rigorous analysis in a model setting and perform some n...

Sparse Approximate Inverse Smoothers For Geometric and Algebraic Multigrid

Sparse Approximate Inverse Smoothers For Geometric and Algebraic Multigrid

Multigrid Treatment and Robustness Enhancement for Factored Sparse Approximate Inverse Preconditioning

We investigate the use of sparse approximate inverse techniques (SAI) in a grid based multilevel ILU preconditioner (GILUM) to design a robust parallelizable precon-ditioner for solving general sparse matrix. Taking the advantages of grid based mul-tilevel methods, the resulting preconditioner outperforms sparse approximate inverse in robustness and eeciency. Conversely, taking the advantages o...

Compatible coarsening in the multigraph algorithm

We present some heuristics incorporating the philosophy of compatible relaxation into an existing algebraic multigrid method, the so-called multigraph solver of Bank and Smith [1]. In particular, approximate left and right eigenvectors of the iteration matrix for the smoother are used in computing both the sparsity pattern and the numerical values of the transfer matrices that correspond to res...