Linear Solvers for Power Grid Optimization Problems: A Review of GPU-Accelerated Linear Solvers

Kasia Swirydowicz; Eric Darve; Wesley Jones; Jonathan Maack; Shaked Regev; Mchael Saunders; Stephen Thomas; Slaven Peles

doi:10.1016/j.parco.2021.102870

Linear Solvers for Power Grid Optimization Problems: A Review of GPU-Accelerated Linear Solvers

Kasia Swirydowicz, Eric Darve, Wesley Jones, Jonathan Maack, Shaked Regev, Mchael Saunders, Stephen Thomas, Slaven Peles

Computational Science

Research output: Contribution to journal › Article › peer-review

18 Scopus Citations

Abstract

The linear equations that arise in interior methods for constrained optimization are sparse symmetric indefinite, and they become extremely ill-conditioned as the interior method converges. These linear systems present a challenge for existing solver frameworks based on sparse LU or LDL^T decompositions. We benchmark five well known direct linear solver packages on CPU- and GPU-based hardware, using matrices extracted from power grid optimization problems. The achieved solution accuracy varies greatly among the packages. None of the tested packages delivers significant GPU acceleration for our test cases. For completeness of the comparison we include results for MA57, which is one of the most efficient and reliable CPU solvers for this class of problem.

Original language	American English
Article number	102870
Number of pages	9
Journal	Parallel Computing
Volume	111
DOIs	https://doi.org/10.1016/j.parco.2021.102870 https://doi.org/10.1016/j.parco.2021.102870
State	Published - Jul 2022

Bibliographical note

Publisher Copyright:
© 2021

NREL Publication Number

NREL/JA-2C00-81949

Keywords

GPU
Grid optimization
Solvers
Sparse linear equations

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abstract = "The linear equations that arise in interior methods for constrained optimization are sparse symmetric indefinite, and they become extremely ill-conditioned as the interior method converges. These linear systems present a challenge for existing solver frameworks based on sparse LU or LDLT decompositions. We benchmark five well known direct linear solver packages on CPU- and GPU-based hardware, using matrices extracted from power grid optimization problems. The achieved solution accuracy varies greatly among the packages. None of the tested packages delivers significant GPU acceleration for our test cases. For completeness of the comparison we include results for MA57, which is one of the most efficient and reliable CPU solvers for this class of problem.",

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AU - Swirydowicz, Kasia

AU - Darve, Eric

AU - Jones, Wesley

AU - Maack, Jonathan

AU - Regev, Shaked

AU - Saunders, Mchael

AU - Thomas, Stephen

AU - Peles, Slaven

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N2 - The linear equations that arise in interior methods for constrained optimization are sparse symmetric indefinite, and they become extremely ill-conditioned as the interior method converges. These linear systems present a challenge for existing solver frameworks based on sparse LU or LDLT decompositions. We benchmark five well known direct linear solver packages on CPU- and GPU-based hardware, using matrices extracted from power grid optimization problems. The achieved solution accuracy varies greatly among the packages. None of the tested packages delivers significant GPU acceleration for our test cases. For completeness of the comparison we include results for MA57, which is one of the most efficient and reliable CPU solvers for this class of problem.

AB - The linear equations that arise in interior methods for constrained optimization are sparse symmetric indefinite, and they become extremely ill-conditioned as the interior method converges. These linear systems present a challenge for existing solver frameworks based on sparse LU or LDLT decompositions. We benchmark five well known direct linear solver packages on CPU- and GPU-based hardware, using matrices extracted from power grid optimization problems. The achieved solution accuracy varies greatly among the packages. None of the tested packages delivers significant GPU acceleration for our test cases. For completeness of the comparison we include results for MA57, which is one of the most efficient and reliable CPU solvers for this class of problem.

KW - GPU

KW - Grid optimization

KW - Solvers

KW - Sparse linear equations

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JO - Parallel Computing

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Linear Solvers for Power Grid Optimization Problems: A Review of GPU-Accelerated Linear Solvers

Abstract

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Keywords

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