A massively parallel algorithm for Bordered Almost Block Diagonal Systems on GPUs

Abstract

In this paper, we present PARASOF, an algorithm for the solution of linear systems with BABD matrices on massively parallel computing systems like graphic processing units or GPUs. This algorithm is compared with the state-of-the-art algorithms, in particular SOF, from which it is inspired and takes the same stability properties. We detail its design and implementation issues and give the main figures of its theoretical and experimental performances.

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Funding

The authors received a doctoral grant funded by BeanTech s.r.l. “GPU computing for modeling, nonlinear optimization and machine learning.” This work was partially supported by INdAM-GNCS 2019 project “Tecniche innovative e parallele per sistemi lineari e nonlineari di grandi dimensioni, funzioni ed equazioni matriciali ed applicazioni.”

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Correspondence to M. Dessole.

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Dessole, M., Marcuzzi, F. A massively parallel algorithm for Bordered Almost Block Diagonal Systems on GPUs. Numer Algor 86, 1243–1263 (2021). https://doi.org/10.1007/s11075-020-00931-8

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Keywords

  • GPU
  • Parallel algorithms
  • BABD system
  • Batched routines
  • Optimal control
  • GPGPU computing