Scalability analysis of direct and iterative solvers used to model charging of superconducting pancake solenoids

Muhammad Mohebujjaman; Syuńichi Shiraiwa; Brian Labombard; John C. Wright; Kiran K. Uppalapati

doi:10.1088/2631-8695/acbd85

Scalability analysis of direct and iterative solvers used to model charging of superconducting pancake solenoids

Muhammad Mohebujjaman, Syuńichi Shiraiwa, Brian Labombard, John C. Wright, Kiran K. Uppalapati

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2 Scopus citations

Abstract

A mathematical model for the charging simulation of non-insulated superconducting pancake solenoids is presented. Numerical solutions are obtained by the simulation model using a variety of solvers. A scalability analysis is performed for both direct and preconditioned iterative solvers for four different pancakes solenoids with varying number of turns and mesh elements. It is found that even with two extremely different time scales in the system an iterative solver combination (FGMRES-GMRES) in conjunction with the parallel Auxiliary Space Maxwell Solver (AMS) preconditioner outperforms a parallelized direct solver (MUMPS). In general, the computational time of the iterative solver is found to increase with the number of turns in the solenoids and/or the conductivity assumed for the superconducting material.

Original language	English (US)
Article number	015045
Journal	Engineering Research Express
Volume	5
Issue number	1
DOIs	https://doi.org/10.1088/2631-8695/acbd85
State	Published - Mar 2023

All Science Journal Classification (ASJC) codes

General Engineering

Keywords

direct solver
iterative solver
non-insulated superconductor
scalability analysis
superconductor

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10.1088/2631-8695/acbd85

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title = "Scalability analysis of direct and iterative solvers used to model charging of superconducting pancake solenoids",

abstract = "A mathematical model for the charging simulation of non-insulated superconducting pancake solenoids is presented. Numerical solutions are obtained by the simulation model using a variety of solvers. A scalability analysis is performed for both direct and preconditioned iterative solvers for four different pancakes solenoids with varying number of turns and mesh elements. It is found that even with two extremely different time scales in the system an iterative solver combination (FGMRES-GMRES) in conjunction with the parallel Auxiliary Space Maxwell Solver (AMS) preconditioner outperforms a parallelized direct solver (MUMPS). In general, the computational time of the iterative solver is found to increase with the number of turns in the solenoids and/or the conductivity assumed for the superconducting material.",

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AU - Mohebujjaman, Muhammad

AU - Shiraiwa, Syuńichi

AU - Labombard, Brian

AU - Wright, John C.

AU - Uppalapati, Kiran K.

PY - 2023/3

Y1 - 2023/3

N2 - A mathematical model for the charging simulation of non-insulated superconducting pancake solenoids is presented. Numerical solutions are obtained by the simulation model using a variety of solvers. A scalability analysis is performed for both direct and preconditioned iterative solvers for four different pancakes solenoids with varying number of turns and mesh elements. It is found that even with two extremely different time scales in the system an iterative solver combination (FGMRES-GMRES) in conjunction with the parallel Auxiliary Space Maxwell Solver (AMS) preconditioner outperforms a parallelized direct solver (MUMPS). In general, the computational time of the iterative solver is found to increase with the number of turns in the solenoids and/or the conductivity assumed for the superconducting material.

AB - A mathematical model for the charging simulation of non-insulated superconducting pancake solenoids is presented. Numerical solutions are obtained by the simulation model using a variety of solvers. A scalability analysis is performed for both direct and preconditioned iterative solvers for four different pancakes solenoids with varying number of turns and mesh elements. It is found that even with two extremely different time scales in the system an iterative solver combination (FGMRES-GMRES) in conjunction with the parallel Auxiliary Space Maxwell Solver (AMS) preconditioner outperforms a parallelized direct solver (MUMPS). In general, the computational time of the iterative solver is found to increase with the number of turns in the solenoids and/or the conductivity assumed for the superconducting material.

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KW - iterative solver

KW - non-insulated superconductor

KW - scalability analysis

KW - superconductor

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Scalability analysis of direct and iterative solvers used to model charging of superconducting pancake solenoids

Abstract

All Science Journal Classification (ASJC) codes

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