High performance sparse multifrontal solvers on modern GPUs

Breakthroughs in Sparse Solvers for GPUs

The CUDA Center of Excellence (CCOE) at UTK targets the development of innovative algorithms and technologies to tackle challenges in Heterogeneous High Performance Computing. Over the last year, the CCOE at UTK developed CUDA-based breakthrough technologies in sparse solvers for GPUs. Here, we describe the main ones – a sparse iterative solvers package, a communication-avoiding (CA) sparse ite...

Sparse Approximate Inverse Preconditioners for Iterative Solvers on GPUs

For the solution of large systems of linear equations, iterative solvers with preconditioners are typically employed. However, the design of preconditioners for the black-box case, in which no additional information about the underlying problem is known, is very difficult. The most commonly employed method of incomplete LU factorizations is a serial algorithm and thus not well suited for the ma...

Block Low-Rank (BLR) approximations to improve multifrontal sparse solvers

Matrices coming from elliptic Partial Differential Equations (PDEs) have been shown to have a lowrank property: well defined off-diagonal blocks of their Schur complements can be approximated by low-rank products. In the multifrontal context, this can be exploited within the fronts in order to obtain a substantial reduction of the memory requirement and an efficient way to perform many of the b...

Performance of PDE Sparse Solvers on Hypercubes

Preconditioned Krylov solvers on GPUs

In this paper, we study the effect of enhancing GPU-accelerated Krylov solvers with preconditioners. We consider the BiCGSTAB, CGS, QMR, and IDR( s ) Krylov solvers. For a large set of test matrices, we assess the impact of Jacobi and incomplete factorization preconditioning on the solvers’ numerical stability and time-to-solution performance. We also analyze how the use of a preconditioner imp...