Accelerated solution of Helmholtz equation with Iterative Krylov Methods on GPU

TL;DR

This paper evaluates GPU-accelerated linear algebra operations with complex double precision and demonstrates how iterative Krylov methods can efficiently solve acoustic Helmholtz equations, achieving significant speedups and robustness.

Contribution

It provides a detailed analysis of GPU-based complex arithmetic operations and applies iterative Krylov methods to solve Helmholtz equations efficiently in acoustic modeling.

Findings

Up to 27x speedup in dot product operations

Up to 10x speedup in sparse matrix-vector multiplication

Demonstrated robustness and efficiency of Krylov solvers in complex double precision

Abstract

This paper gives an analysis and an evaluation of linear algebra operations on Graphics Processing Unit (GPU) with complex number arithmetics with double precision. Knowing the performance of these operations, iterative Krylov methods are considered to solve the acoustic problem efficiently. Numerical experiments carried out on a set of acoustic matrices arising from the modelisation of acoustic phenomena within a cylinder and a car compartment are exposed, exhibiting the performance, robustness and efficiency of our algorithms, with a ratio up to 27x for dot product, 10x for sparse matrix-vector product and solvers in complex double precision arithmetics.