GPU implementation of an incomplete Cholesky conjugate gradient solver for a FEM-generated system using full kernel consolidation

Author(s)

Sato, Andre Kubagawa ; Martins, Thiago Castro ; Tsuzuki, Marcos Sales Guerra

• Document type: Journal article
• Source: SOFT COMPUTING; v. 27, n. 14, p. 14-pg., 2023-05-07.

Abstract

The finite element method (FEM) is a widely used technique to solve partial differential equations and can thus be applied to describe different physical phenomena. Preconditioned conjugate gradient (PCG) is often employed to solve FEM-generated systems of linear equations. The parallelization of PCG algorithms has been contemplated by several works in the literature. In this work, a massive parallel incomplete Cholesky conjugate gradient (ICCG) algorithm for a graphics processing unit (GPU) is proposed. The method is particularly suited for Monte Carlo-based solutions to inverse problems. The solution adopted uses the cpJDS sparse matrix format to circumvent the difficulty in parallelizing the triangular solver by incorporating a coloring scheme. The cpJDS-based ICCG introduces a large number of synchronization points, adding a performance overhead, and its poor effects are minimized using a full kernel consolidation. Tests executed on a wide assortment of sparse matrices, with varying structures, showed that the proposed solution performs better that the CPU CG implementation for cases with medium-to-large matrices, achieving speed-ups of up to 60x. (AU)

• FAPESP's process: 09/07173-2 - Applying the simulated annealing to the electrical impedance tomography aiming the determination of absolute images
• Grantee: Marcos de Sales Guerra Tsuzuki
• Support Opportunities: Regular Research Grants
• FAPESP's process: 17/07799-5 - Interval Simulated Annealing implemented with GPGPU to obtain absolute images in electrical impedance tomography
• Grantee: Marcos de Sales Guerra Tsuzuki
• Support Opportunities: Regular Research Grants
• FAPESP's process: 20/15230-5 - Research Centre for Greenhouse Gas Innovation - RCG2I
• Grantee: Julio Romano Meneghini
• Support Opportunities: Research Grants - Research Centers in Engineering Program