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Direct Solution of FEM Models: Are Sparse Direct Solvers the Best Strategy?
[article]
2020
arXiv
pre-print
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sparse direct solver libraries, while maintaining approximately comparable or slightly slower serial serial execution speed but with significantly better parallel and GPU processing prospects. ...
A brief summary of direct solution approaches for finite element methods (FEM) in computational electromagnetics (CEM) is given along with an alternative direct solution based on domain decomposition ( ...
to state-of-the-art sparse matrix direct solvers. ...
arXiv:2002.05019v1
fatcat:mavfugwtm5df5jym4kewjvja24
Direct finite-element solver of linear complexity for system-level signal and power integrity co-analysis
2014
2014 IEEE International Symposium on Electromagnetic Compatibility (EMC)
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Comparisons with the finite element methods that employ the most advanced direct sparse solvers have demonstrated the clear advantages of the proposed high-capacity linear-complexity direct solver. ...
In this paper, we develop a fast direct finite-element solver of linear (optimal) complexity for solving large-scale system-level signal and power integrity problems. ...
The authors would like to thank Dr. Jason Morsey at IBM Corporation for providing package structures and measured data. ...
doi:10.1109/isemc.2014.6899063
fatcat:z5wzeqchs5dyrf4jqapo4sbgru
A direct finite-element-based solver of significantly reduced complexity for solving large-scale electromagnetic problems
2009
2009 IEEE MTT-S International Microwave Symposium Digest
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A comparison with state-of-theart sparse matrix solvers has shown the advantages of the proposed solver. ...
Based on the observation that the sparse matrix resulting from a finite-element-based analysis can be represented by an matrix without any approximation, and the inverse of this sparse matrix has a data-sparse ...
Numerical experiments and a comparison with state-of-the-art sparse matrix solvers have demonstrated its superior performance. ...
doi:10.1109/mwsym.2009.5165661
fatcat:6z4rnt6dfzapdm2t6zjbrnu5pq
An H-LU Based Direct Finite Element Solver Accelerated by Nested Dissection for Large-scale Modeling of ICs and Packages
2010
PIERS Online
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A comparison with the state-of-the-art direct finite element solver that employs the most advanced sparse matrix solution has shown a clear advantage of the proposed solver. ...
Applications to large-scale package modeling involving millions of unknowns have demonstrated the accuracy and almost linear complexity of the proposed direct solver. ...
In addition, we compare the proposed direct solver with the state-of-the-art direct sparse solver such as UMFPACK 5.0 [9]. ...
doi:10.2529/piers091220163114
fatcat:2gillxqebjg3nhgwlxlwlrnz7y
On Solving Groundwater Flow and Transport Models with Algebraic Multigrid Preconditioning
[article]
2020
arXiv
pre-print
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Contrarily, a sparse direct solver was the most efficient for the pure advective transport processes such as the forward travel time simulations. ...
The new solver was compared with traditional preconditioned iterative methods and direct sparse solvers on several two- and three-dimensional benchmark problems spanning homogeneous and heterogeneous formations ...
Concluding Remarks This paper compares the performances of many preconditioned sparse iterative solvers implemented in the AMGCL library and selected state-of-the-art sparse direct solvers for steady-state ...
arXiv:2001.05798v2
fatcat:tdjgydw2bvh5jf4wliogia5reu
Towards efficient SPICE-accurate nonlinear circuit simulation with on-the-fly support-circuit preconditioners
2012
Proceedings of the 49th Annual Design Automation Conference on - DAC '12
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to 8 reduction in memory usage, when compared with the simulator powered by the state-of-the-art direct solver KLU. ...
solvers, allowing for on-the-fly updates during transient simulations when adopted in Krylov-subspace iterative solvers. ...
factor of eight when compared with the SPICE simulator powered by the state-of-the-art direct matrix solver KLU [1] . ...
doi:10.1145/2228360.2228564
dblp:conf/dac/ZhaoF12
fatcat:rvtdb5egvzgrln7ax232ak6vjy
Fast Block Linear System Solver Using Q-Learning Schduling for Unified Dynamic Power System Simulations
[article]
2021
arXiv
pre-print
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The simulation on some large power systems shows that our solver is 2-6 times faster than KLU, which is the state-of-the-art sparse solver for circuit simulation problems. ...
We present a fast block direct solver for the unified dynamic simulations of power systems. This solver uses a novel Q-learning based method for task scheduling. ...
Numerical experiments on some large power systems shows that our solver is 2-6 times faster than classical sparse solver(KLUthe state-of-the-art sparse solver for circuit simulation problems). ...
arXiv:2110.05843v1
fatcat:kyje65ejerfmnntzhqxxct757m
A direct finite element solver of linear complexity for large-scale 3-D circuit extraction in multiple dielectrics
2013
Proceedings of the 50th Annual Design Automation Conference on - DAC '13
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Numerical experiments demonstrate a clear advantage of the proposed solver as compared with existing finite-element solvers that employ state-of-theart direct sparse matrix solutions. ...
We develop a direct finite-element solver of linear (optimal) complexity to extract broadband circuit parameters such as S-parameters of arbitrarily shaped 3-D interconnects in inhomogeneous dielectrics ...
Comparisons with state-of-the-art direct FEM solvers that employ the most advanced direct sparse matrix solutions as well as a commercial iterative FEM solver have shown a clear advantage of the proposed ...
doi:10.1145/2463209.2488906
dblp:conf/dac/ZhouLJ13
fatcat:trqgt2pv3rabpgnhgtmz4blwzy
A GPU-Based Transient Stability Simulation Using Runge-Kutta Integration Algorithm
2013
International Journal of Smart Grid and Clean Energy
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The differential equations of dynamic components are evaluated in GPU, while the linear network equations are solved in CPU using sparse direct solver. ...
Simulation on IEEE 22-bus power system with 6 generators is reported to validate the feasibility of the proposed method. ...
Further, the proposed method utilizes the data-parallel computational capability of GPU and the efficiency of the state-of-art sparse direct solvers under CPU. ...
doi:10.12720/sgce.2.1.32-39
fatcat:3mh6ko7mdrbxtf76kyv2nen3u4
A Parallel Sparse Hybrid Solver And Its Relations To Graphs And Hypergraphs
2012
Zenodo
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In this whitepaper, we review the state-of-the-art hybrid solver, which uses generalized form DS factorization, for solving system of equations of the form Ax = f, and this solver's relations to graphs ...
The partitioning objective of GP relates to minimizing the number of nonzeros in the reduced system, whereas the partitioning objective of HP exactly models minimizing the size of the reduced system. ...
Acknowledgements The HPC resources used in this work were provided by the Department of Computer Engineering, Middle East Technical University, Turkey. ...
doi:10.5281/zenodo.807072
fatcat:rlmhhj5urzcaljfmtai3dnvyoa
Task-Based Sparse Hybrid Linear Solver for Distributed Memory Heterogeneous Architectures
[chapter]
2017
Lecture Notes in Computer Science
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We illustrate our discussion with the MaPHyS sparse hybrid solver relying on the PaStiX and Chameleon dense and sparse direct libraries, respectively. ...
In this paper, we propose to extend a sparse hybrid solver for handling distributed memory heterogeneous platforms. ...
to compute x Ii , done by the sparse direct solver. ...
doi:10.1007/978-3-319-58943-5_7
fatcat:snj53iv5lzgnrbudiqkjwombsu
A New Architecture for Optimization Modeling Frameworks
[article]
2016
arXiv
pre-print
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We introduce cvxflow, an open-source convex optimization modeling framework in Python based on the ideas in this paper, and show that it outperforms the state of the art. ...
We propose a new architecture for optimization modeling frameworks in which solvers are expressed as computation graphs in a framework like TensorFlow rather than as standalone programs built on a low-level ...
running on GPU, the existing state-of-the-art method for solving large convex problems to moderate accuracy. ...
arXiv:1609.03488v2
fatcat:lsqhowdnlbaotlodee7fdzmxfe
Ginkgo: A high performance numerical linear algebra library
2020
Journal of Open Source Software
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Ginkgo is a production-ready sparse linear algebra library for high performance computing on GPU-centric architectures with a high level of performance portability and focuses on software sustainability ...
, a collaborative effort of the U.S. ...
Department of Energy Office of Science and the National Nuclear Security Administration. . Ginkgo: A high performance numerical linear algebra library. ...
doi:10.21105/joss.02260
fatcat:4pd44vwhwjeq5aoprhpltsgtna
Learning the Markov Decision Process in the Sparse Gaussian Elimination
[article]
2021
arXiv
pre-print
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Finally, we recast the sparse solver into the framework of Q-Learning. ...
Our learning-based algorithm could help improve the performance of sparse solver, which has been verified in some numerical experiments. ...
In many literatures, this method is also called direct method [4, 5] , or direct sparse solver in the case of sparse matrix. At the age of Gauss (1777-1855), the number of equations is very small. ...
arXiv:2109.14929v1
fatcat:xchy5ytk2ndnrl3cwcwr6foyoa
A Parallel Sparse Direct Solver via Hierarchical DAG Scheduling
2014
ACM Transactions on Mathematical Software
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The proposed parallel sparse direct solver is evaluated for the particular problems arising from the hp-Finite Element Method where conventional sparse direct solvers do not scale well. ...
We present a scalable parallel sparse direct solver for multi-core architectures based on Directed Acyclic Graph (DAG) scheduling. ...
Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF. ...
doi:10.1145/2629641
fatcat:qbiygwm4b5bi7b2mtp6mm323qe
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