Decoupled Block-Wise ILU(k) Preconditioner on GPU

TL;DR

This paper presents a GPU implementation of a decoupled block-wise ILU(k) preconditioner that allows flexible block sizes and levels, with detailed phases and numerical experiments demonstrating its effectiveness.

Contribution

It introduces a decoupled ILU(k) algorithm with symbolic and factorization phases tailored for GPU, supporting variable block sizes and levels for improved preconditioning.

Findings

Effective preconditioning on GPU demonstrated across different k levels.

Flexible block sizes enhance parallel efficiency.

Numerical results validate the method's performance.

Abstract

This research investigates the implementation mechanism of block-wise ILU(k) preconditioner on GPU. The block-wise ILU(k) algorithm requires both the level k and the block size to be designed as variables. A decoupled ILU(k) algorithm consists of a symbolic phase and a factorization phase. In the symbolic phase, a ILU(k) nonzero pattern is established from the point-wise structure extracted from a block-wise matrix. In the factorization phase, the block-wise matrix with a variable block size is factorized into a block lower triangular matrix and a block upper triangular matrix. And a further diagonal factorization is required to perform on the block upper triangular matrix for adapting a parallel triangular solver on GPU.We also present the numerical experiments to study the preconditioner actions on different k levels and block sizes.