Parallel FETI‐DP algorithm for efficient simulation of large‐scale EM problems
Abstract
Summary An efficient parallelization of the dual‐primal finite‐element tearing and interconnecting (FETI‐DP) algorithm is presented for large‐scale electromagnetic simulations. As a nonoverlapping domain decomposition method, the FETI‐DP algorithm formulates a global interface problem, whose iterative solution is accelerated with a solution of a global corner problem. To achieve a good load balance for parallel computation, the original computational domain is decomposed into subdomains with similar sizes and shapes. The subdomains are then distributed to processors based on their close proximity to minimize inter‐processor communication. The parallel generalized minimal residual method, enhanced with the iterative classical Gram‐Schmidt orthogonalization scheme to reduce global communication, is adopted to solve the global interface problem with a fast convergence rate. The global corner‐related coarse problem is solved iteratively with a parallel communication‐avoiding biconjugate gradient stabilized method to minimize global communication, and its convergence is accelerated by a diagonal preconditioner constructed from the coarse system matrix. To alleviate neighboring communication overhead, the non‐blocking communication approach is employed in both generalized minimal residual and communication‐avoiding biconjugate gradient stabilized iterative solutions. Three numerical examples are presented to demonstrate the accuracy, scalability, and capability of the proposed parallel FETI‐DP algorithm for electromagnetic modeling of general objects and antenna arrays.more »
- Authors:
-
- Center for Computational Electromagnetics, Department of Electrical and Computer Engineering University of Illinois at Urbana‐Champaign 306 N Wright Street Urbana 61801 IL USA
- Publication Date:
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1401655
- Resource Type:
- Publisher's Accepted Manuscript
- Journal Name:
- International Journal of Numerical Modelling. Electronic Networks, Devices and Fields
- Additional Journal Information:
- Journal Name: International Journal of Numerical Modelling. Electronic Networks, Devices and Fields Journal Volume: 29 Journal Issue: 5; Journal ID: ISSN 0894-3370
- Publisher:
- Wiley Blackwell (John Wiley & Sons)
- Country of Publication:
- United Kingdom
- Language:
- English
Citation Formats
Zhang, Kedi, and Jin, Jian‐Ming. Parallel FETI‐DP algorithm for efficient simulation of large‐scale EM problems. United Kingdom: N. p., 2016.
Web. doi:10.1002/jnm.2153.
Zhang, Kedi, & Jin, Jian‐Ming. Parallel FETI‐DP algorithm for efficient simulation of large‐scale EM problems. United Kingdom. https://doi.org/10.1002/jnm.2153
Zhang, Kedi, and Jin, Jian‐Ming. Thu .
"Parallel FETI‐DP algorithm for efficient simulation of large‐scale EM problems". United Kingdom. https://doi.org/10.1002/jnm.2153.
@article{osti_1401655,
title = {Parallel FETI‐DP algorithm for efficient simulation of large‐scale EM problems},
author = {Zhang, Kedi and Jin, Jian‐Ming},
abstractNote = {Summary An efficient parallelization of the dual‐primal finite‐element tearing and interconnecting (FETI‐DP) algorithm is presented for large‐scale electromagnetic simulations. As a nonoverlapping domain decomposition method, the FETI‐DP algorithm formulates a global interface problem, whose iterative solution is accelerated with a solution of a global corner problem. To achieve a good load balance for parallel computation, the original computational domain is decomposed into subdomains with similar sizes and shapes. The subdomains are then distributed to processors based on their close proximity to minimize inter‐processor communication. The parallel generalized minimal residual method, enhanced with the iterative classical Gram‐Schmidt orthogonalization scheme to reduce global communication, is adopted to solve the global interface problem with a fast convergence rate. The global corner‐related coarse problem is solved iteratively with a parallel communication‐avoiding biconjugate gradient stabilized method to minimize global communication, and its convergence is accelerated by a diagonal preconditioner constructed from the coarse system matrix. To alleviate neighboring communication overhead, the non‐blocking communication approach is employed in both generalized minimal residual and communication‐avoiding biconjugate gradient stabilized iterative solutions. Three numerical examples are presented to demonstrate the accuracy, scalability, and capability of the proposed parallel FETI‐DP algorithm for electromagnetic modeling of general objects and antenna arrays. Copyright © 2016 John Wiley & Sons, Ltd.},
doi = {10.1002/jnm.2153},
journal = {International Journal of Numerical Modelling. Electronic Networks, Devices and Fields},
number = 5,
volume = 29,
place = {United Kingdom},
year = {Thu Mar 17 00:00:00 EDT 2016},
month = {Thu Mar 17 00:00:00 EDT 2016}
}
https://doi.org/10.1002/jnm.2153
Web of Science
Works referenced in this record:
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
journal, January 1998
- Karypis, George; Kumar, Vipin
- SIAM Journal on Scientific Computing, Vol. 20, Issue 1
Application of the FETI method to ASCI problems?scalability results on 1000 processors and discussion of highly heterogeneous problems
journal, January 2000
- Bhardwaj, Manoj; Day, David; Farhat, Charbel
- International Journal for Numerical Methods in Engineering, Vol. 47, Issue 1-3
The second generation FETI methods and their application to the parallel solution of large-scale linear and geometrically non-linear structural analysis problems
journal, April 2000
- Farhat, Charbel; Pierson, Kendall; Lesoinne, Michel
- Computer Methods in Applied Mechanics and Engineering, Vol. 184, Issue 2-4
Feti-Dph: a Dual-Primal Domain Decomposition Method for Acoustic Scattering
journal, September 2005
- Farhat, Charbel; Avery, Philip; Tezaur, Radek
- Journal of Computational Acoustics, Vol. 13, Issue 03
A parallel finite-element tearing and interconnecting algorithm for solution of the vector wave equation with PML absorbing medium
journal, January 2000
- Wolfe, C. T.; Navsariwala, U.; Gedney, S. D.
- IEEE Transactions on Antennas and Propagation, Vol. 48, Issue 2
Parallel implementation of the FETI-DPEM algorithm for general 3D EM simulations
journal, May 2009
- Li, Yu-Jia; Jin, Jian-Ming
- Journal of Computational Physics, Vol. 228, Issue 9
Nonconformal FETI-DP Methods for Large-Scale Electromagnetic Simulation
journal, September 2012
- Xue, Ming-Feng; Jin, Jian-Ming
- IEEE Transactions on Antennas and Propagation, Vol. 60, Issue 9
An Augmented Incomplete Factorization Approach for Computing the Schur Complement in Stochastic Optimization
journal, January 2014
- Petra, Cosmin G.; Schenk, Olaf; Lubin, Miles
- SIAM Journal on Scientific Computing, Vol. 36, Issue 2
Review of domain-decomposition methods for the implementation of FEM on massively parallel computers
journal, January 1995
- Hamandi, L.; Lee, R.; Ozguner, F.
- IEEE Antennas and Propagation Magazine, Vol. 37, Issue 1
A Scalable Nonoverlapping and Nonconformal Domain Decomposition Method for Solving Time-Harmonic Maxwell Equations in $\mathbb{R}^3$
journal, January 2012
- Peng, Zhen; Lee, Jin-Fa
- SIAM Journal on Scientific Computing, Vol. 34, Issue 3
Avoiding Communication in Nonsymmetric Lanczos-Based Krylov Subspace Methods
journal, January 2013
- Carson, Erin; Knight, Nicholas; Demmel, James
- SIAM Journal on Scientific Computing, Vol. 35, Issue 5
One way domain decomposition method with second order transmission conditions for solving electromagnetic wave problems
journal, February 2010
- Peng, Zhen; Rawat, Vineet; Lee, Jin-Fa
- Journal of Computational Physics, Vol. 229, Issue 4
Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
journal, March 1992
- van der Vorst, H. A.
- SIAM Journal on Scientific and Statistical Computing, Vol. 13, Issue 2
A FEM Domain Decomposition Method for Photonic and Electromagnetic Band Gap Structures
journal, February 2006
- Vouvakis, M. N.; Cendes, Z.; Lee, J. -F.
- IEEE Transactions on Antennas and Propagation, Vol. 54, Issue 2
A Domain Decomposition Method for Electromagnetic Radiation and Scattering Analysis of Multi-Target Problems
journal, August 2008
- Zhao, Kezhong; Rawat, Vineet; Lee, Jin-Fa
- IEEE Transactions on Antennas and Propagation, Vol. 56, Issue 8
Non-conformal domain decomposition method with second-order transmission conditions for time-harmonic electromagnetics
journal, August 2010
- Peng, Zhen; Lee, Jin-Fa
- Journal of Computational Physics, Vol. 229, Issue 16
Finite Elements for Electrical Engineers
book, January 2012
- Silvester, Peter P.; Ferrari, Ronald L.
- Cambridge University Press
A two-level domain decomposition method for the iterative solution of high frequency exterior Helmholtz problems
journal, April 2000
- Farhat, Charbel; Macedo, Antonini; Lesoinne, Michel
- Numerische Mathematik, Vol. 85, Issue 2
A New Dual-Primal Domain Decomposition Approach for Finite Element Simulation of 3-D Large-Scale Electromagnetic Problems
journal, October 2007
- Li, Yu-Jia; Jin, Jian-Ming
- IEEE Transactions on Antennas and Propagation, Vol. 55, Issue 10
A preconditioned dual–primal finite element tearing and interconnecting method for solving three-dimensional time-harmonic Maxwell's equations
journal, October 2014
- Xue, Ming-Feng; Jin, Jian-Ming
- Journal of Computational Physics, Vol. 274
A Hybrid Conformal/Nonconformal Domain Decomposition Method for Multi-Region Electromagnetic Modeling
journal, April 2014
- Xue, Ming-Feng; Jin, Jian-Ming
- IEEE Transactions on Antennas and Propagation, Vol. 62, Issue 4