Implementation of a Stabilized Biconjugate Gradient Method for Block-Sparse Matrices on the CUDA Platform

Abstract

Implementation of a Stabilized Biconjugate Gradient Method for Block-Sparse Matrices on the CUDA Platform

G. V. Muratova, T. S. Martynova, P. A. Oganesyan, I. D. Ignatenko, V. V. Krylov

Incoming article date: 08.12.2025

The article addresses the solution of systems of linear algebraic equations arising in static and steady-state vibration problems solved by the finite element method. A block-sparse matrix format based on the CSR (Compressed Sparse Row) format is presented, along with its GPU implementation using CUDA. A stabilized biconjugate gradient method is implemented and applied to model problems of varying dimensions; a comparison with a reference implementation in MATLAB is also conducted.

Keywords: sparse matrices, finite element method, block matrices, GPU, parallel computing, systems of linear algebraic equations, biconjugate gradient method