Evaluation of massively parallel linear sparse solvers on unstructured finite element meshes

Korić, Seid; Lu, Qiyue; Guleryuz, Erman

doi:10.1016/j.compstruc.2014.05.009

Cited by 33 publications

(22 citation statements)

References 17 publications

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“…Iterative solvers and assembly-free methods have been widely used for reducing the memory requirements at the cost of increasing the processing time of the solve step. The solve step is responsible for 70-80% of the total computational time [4] when iterative solvers are used, and thus it becomes the bottleneck of the analysis. Nevertheless, the use of High-Performance Computing (HPC) techniques can alleviate the computational cost of iterative solvers in large finite element models, which allows to solve the finite element problems within a reasonable computational time [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Efficient matrix-free GPU implementation of Fixed Grid Finite Element Analysis

Martínez-Frutos

Herrero-Pérez

2015

Finite Elements in Analysis and Design

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Section: Introductionmentioning

confidence: 99%

Efficient matrix-free GPU implementation of Fixed Grid Finite Element Analysis

Martínez-Frutos

Herrero-Pérez

2015

Finite Elements in Analysis and Design

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“…Based on this assumption, sequential wall clock times are calculated for each problem size and then equation 6is used to calculate Speedup on larger core counts. Note that this assumption is close to reality since the factorization in WSMP indeed scales ideally or even super-linearly on lower number of cores for multi-million equation problem sizes given enough memory is provided [16].…”

Section: Resultsmentioning

confidence: 78%

Sparse matrix factorization in the implicit finite element method on petascale architecture

Korić

Gupta²

2016

Computer Methods in Applied Mechanics and Engineering

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The performance of the massively parallel direct multifrontal solver Watson Sparse Matrix Package (WSMP) for solving large sparse systems of linear equations arising in implicit finite element method on unstructured (free) meshes in solid mechanics was evaluated on one of the most powerful supercomputers currently available to the open science community-the sustained petascale high performance computing system of Blue Waters. We have performed full-scale benchmarking tests up to 65,536 cores using assembled global stiffness matrices and load vectors ranging from 11-40 million unknowns extracted from "real-world" commercial implicit finite element analysis (FEA) applications. The results show that a direct multifrontal factorization method with a hybrid parallel implementation in WSMP performs exceedingly well on a petascale high-performance computing (HPC) system, and delivers superior factorization time and parallel scalability, thus opening the door for the high fidelity modeling of complex industrial structures and assemblies in real scale.

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“…In some cases, a problem specific preconditioner will be highly effective, yet it is often difficult to parallelize the code without losing either its efficiency or scalability on modern HPC platforms. Koric et al (2014) has recently explored several configurations of solvers, preconditioners, and their parameters in the libraries PETSc and hypre and found that no iterative preconditioned solver combination could correctly solve the highly ill-conditioned system of equations from the structural finite element simulations.…”

Section: Direct and Iterative Methodsmentioning

confidence: 99%

Evaluation of parallel direct sparse linear solvers in electromagnetic geophysical problems

Puzyrev

Korić

Wilkin

2016

Computers & Geosciences

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High performance computing is absolutely necessary for large-scale geophysical simulations. In order to obtain a realistic image of a geologically complex area, industrial surveys collect vast amounts of data making the computational cost extremely high for the subsequent simulations. A major computational bottleneck of modeling and inversion algorithms is solving the large sparse systems of linear ill-conditioned equations in complex domains with multiple right hand sides. Recently, parallel direct solvers have been successfully applied to multi-source seismic and electromagnetic problems. These methods are robust and exhibit good performance, but often require large amounts of memory and have limited scalability. In this paper, we evaluate modern direct solvers on large-scale modeling examples that previously were considered unachievable with these methods. Performance and scalability tests utilizing up to 65,536 cores on the Blue Waters supercomputer clearly illustrate the robustness, efficiency and competitiveness of direct solvers compared to iterative techniques. Wide use of direct methods utilizing modern parallel architectures will allow modeling tools to accurately support multi-source surveys and 3D data acquisition geometries, thus promoting a more efficient use of the electromagnetic methods in geophysics.The authors would like to thank the MUMPS and PARDISO developers for providing free academic licenses and Dr. Anshul Gupta for access to his solver library which is not publicly available. We also would like to thank the Private Sector Program and the Blue Waters sustained-petascale computing project at the\ud National Center for Supercomputing Applications (NCSA), which is supported by the National Science Foundation (awards OCI-\ud 0725070 and ACI-1238993) and the state of Illinois. The shared-memory tests were performed on the MareNostrum supercomputer of the Barcelona Supercomputer Center. The first author\ud acknowledges funding from the Repsol-BSC Research Center through the AURORA project and support from the RISE Horizon 2020 European Project GEAGAM (644602). The authors wish to thank Jef Caers and two anonymous reviewers for their valuable\ud comments that significantly helped to improve this paper.Peer ReviewedPostprint (author's final draft

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Evaluation of massively parallel linear sparse solvers on unstructured finite element meshes

Cited by 33 publications

References 17 publications

Efficient matrix-free GPU implementation of Fixed Grid Finite Element Analysis

Efficient matrix-free GPU implementation of Fixed Grid Finite Element Analysis

Sparse matrix factorization in the implicit finite element method on petascale architecture

Evaluation of parallel direct sparse linear solvers in electromagnetic geophysical problems

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