Journal Article

FZJ-2025-03449

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png tfQMRgpu: a GPU-accelerated linear solver with block-sparse complex result matrix

Baumeister, P. F. (Corresponding author)FZJ* ; Nassyr, S.FZJ*

2025
Springer Science + Business Media B.V Dordrecht [u.a.]

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Please use a persistent id in citations: doi:10.1007/s11227-025-07145-6  doi:10.34734/FZJ-2025-03449

Abstract: We present tfQMRgpu, a GPU-accelerated iterative linear solver based on the transpose-free quasi-minimal residual (tfQMR) method. Designed for large-scale electronic structure calculations, particularly in the context of Korringa–Kohn–Rostoker density functional theory, tfQMRgpu efficiently handles block-sparse complex matrices arising from multiple scattering theory. The solver exploits GPU parallelism to accelerate convergence while leveraging memory-efficient sparse storage formats. By unifying the solution of multiple right-hand side (RHS) block vectors, tfQMRgpu significantly improves throughput, demonstrating up to a speedup on modern GPUs. Additionally, we introduce a flexible implementation framework that supports both explicit matrix-based and matrix-free operator formulations, such as high-order finite-difference stencils for real-space grid-based Green function calculations. Benchmarks on various NVIDIA GPUs demonstrate the solver’s efficiency, in some cases achieving over 56% of peak floating-point performance for block-sparse matrix multiplications. tfQMRgpu is open-source, providing interfaces for C, C++, Fortran, Julia, and Python, making it a versatile tool for high-performance computing applications that can benefit from the unification of RHS problems.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 5111 - Domain-Specific Simulation & Data Life Cycle Labs (SDLs) and Research Groups (POF4-511) (POF4-511)
2. 5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs) and Research Groups (POF4-511) (POF4-511)
3. 5122 - Future Computing & Big Data Systems (POF4-512) (POF4-512)
4. BMBF 01 1H1 6013, NRW 325 – 8.03 – 133340 - SiVeGCS (DB001492) (DB001492)
5. ATML-X-DEV - ATML Accelerating Devices (ATML-X-DEV) (ATML-X-DEV)

Appears in the scientific report 2025

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Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Engineering, Computing and Technology ; DEAL Springer ; Ebsco Academic Search ; Essential Science Indicators ; IF < 5 ; JCR ; Nationallizenz ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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