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Direct Solution of FEM Models: Are Sparse Direct Solvers the Best Strategy? [article]

Javad Moshfegh, Marinos N. Vouvakis
2020 arXiv   pre-print
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

Bangda Zhou, Dan Jiao
2014 2014 IEEE International Symposium on Electromagnetic Compatibility (EMC)  
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

Haixin Liu, Dan Jiao
2009 2009 IEEE MTT-S International Microwave Symposium Digest  
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

Haixin Liu, Dan Jiao
2010 PIERS Online  
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]

M. A. Sbai, A. Larabi
2020 arXiv   pre-print
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

Xueqian Zhao, Zhuo Feng
2012 Proceedings of the 49th Annual Design Automation Conference on - DAC '12  
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]

Yingshi Chen and Xinli Song and HanYang Dai and Tao Liu and Wuzhi Zhong and Guoyang Wu
2021 arXiv   pre-print
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

Bangda Zhou, Haixin Liu, Dan Jiao
2013 Proceedings of the 50th Annual Design Automation Conference on - DAC '13  
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

Zhijun Qin, Yunhe Hou
2013 International Journal of Smart Grid and Clean Energy  
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

Mustafa Gündoğan
2012 Zenodo  
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]

Emmanuel Agullo, Luc Giraud, Stojce Nakov
2017 Lecture Notes in Computer Science  
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]

Matt Wytock, Steven Diamond, Felix Heide, Stephen Boyd
2016 arXiv   pre-print
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

Hartwig Anzt, Terry Cojean, Yen-Chen Chen, Goran Flegar, Fritz Göbel, Thomas Grützmacher, Pratik Nayak, Tobias Ribizel, Yu-Hsiang Tsai
2020 Journal of Open Source Software  
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]

Yingshi Chen
2021 arXiv   pre-print
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

Kyungjoo Kim, Victor Eijkhout
2014 ACM Transactions on Mathematical Software  
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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