Domain Decomposition Preconditioning for Surface Integral Equations in Solving Challenging Electromagnetic Scattering Problems

Peng, Zhen; Hiptmair, Ralf; Shao, Yang; MacKie-Mason, Brian

doi:10.1109/tap.2015.2500908

Cited by 93 publications

(31 citation statements)

References 67 publications

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“…Both the simulation capability and modeling fidelity of the proposed solver are expected to scale with the exponential growth in computing power. To realize this objective, advances have been made on three fronts: (i) a geometry-adaptive discontinuous Galerkin boundary element method (DG-BEM) [1], which permits the use of nonconformal surface discretizations and facilitates the mesh generation task for high-definition objects; (ii) a non-overlapping additive Schwarz domain decomposition (DD) method for the iterative solution of the DG-BEM matrix equations, which leads to scalable convergence in the DD iterations [2], [3]; (iii) parallel and adaptive computational algorithms to reduce the time complexity of very large-scale simulations via distributed memory HPC architectures.…”

Section: Technical Approachmentioning

confidence: 99%

High-performance surface integral equation solvers towards extreme-scale electromagnetic modeling and simulation

Peng

MacKie-Mason

2016

2016 IEEE/ACES International Conference on Wireless Information Technology and Systems (ICWITS) and Applied Computational Elect

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This work investigates an adaptive, parallel and scalable integral equation solver for very large-scale electromagnetic modeling and simulation. A complicated surface model is decomposed into a collection of components, all of which are discretized independently and concurrently using a discontinuous Galerkin boundary element method. An additive Schwarz domain decomposition method is proposed next for the efficient and robust solution of linear systems resulting from discontinuous Galerkin discretizations. The work leads to a rapidly-convergent integral equation solver that is scalable for large multi-scale objects. Furthermore, it serves as a basis for parallel and scalable computational algorithms to reduce the time complexity via advanced distributed computing systems. Numerical experiments are performed on large computer clusters to characterize the performance of the proposed method. Finally, the capability and benefits of the resulting algorithms are exploited and illustrated through different types of real-world applications on high performance computing systems.

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Section: Technical Approachmentioning

confidence: 99%

High-performance surface integral equation solvers towards extreme-scale electromagnetic modeling and simulation

Peng

MacKie-Mason

2016

2016 IEEE/ACES International Conference on Wireless Information Technology and Systems (ICWITS) and Applied Computational Elect

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“…Moreover, the stability and convergence have been validated for targets with sharp edges and corners. Along the line of this research, we herein employ a non-symmetric interior penalty formulation [34]. Although it results in non-symmetric coupling matrices after the finite dimensional discretization, it enjoys the remarkable property of discrete ellipticity of the weak formulation and well-posedness of the discrete formulation.…”

Section: Discontinuous Galerkin Formulationmentioning

confidence: 99%

ADAPTIVE AND PARALLEL SURFACE INTEGRAL EQUATION SOLVERS FOR VERY LARGE-SCALE ELECTROMAGNETIC MODELING AND SIMULATION (Invited Paper)

MacKie-Mason¹,

Greenwood²,

Peng³

2015

PIER

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Abstract-This work investigates an adaptive, parallel and scalable integral equation solver for very large-scale electromagnetic modeling and simulation. A complicated surface model is decomposed into a collection of components, all of which are discretized independently and concurrently using a discontinuous Galerkin boundary element method. An additive Schwarz domain decomposition method is proposed next for the efficient and robust solution of linear systems resulting from discontinuous Galerkin discretizations. The work leads to a rapidly-convergent integral equation solver that is scalable for large multi-scale objects. Furthermore, it serves as a basis for parallel and scalable computational algorithms to reduce the time complexity via advanced distributed computing systems. Numerical experiments are performed on large computer clusters to characterize the performance of the proposed method. Finally, the capability and benefits of the resulting algorithms are exploited and illustrated through different types of real-world applications on high performance computing systems.

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“…In the DG method, the computational domain is first divided into smaller subdomains. By independently meshing each subdomain and developing a preconditioner based on the domain decomposition, the mesh generation process can be significantly simplified, and the condition of the matrix is improved . DG‐SIE methods have been developed for PEC targets and for homogeneous dielectric objects .…”

Section: Introductionmentioning

confidence: 99%

A discontinuous Galerkin surface integral equation method for scattering from IBC targets

Kong

Ylä‐Oijala

Sihvola

2019

Int J Numerical Modelling

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A discontinuous Galerkin (DG) surface integral equation method is proposed for electromagnetic scattering from targets with the impedance boundary condition (IBC). We present electric field integral equation (EFIE), magnetic field integral equation (MFIE), and self‐dual integral equation formulations for the problem and study their numerical performance. On the basis of the results of these experiments, DG is developed for EFIE and MFIE (DG‐EFIE and DG‐MFIE). The convergence of the iterative solutions and the solution accuracy of DG‐EFIE and DG‐MFIE are further investigated for a wide range of surface impedances. The numerical performance of these formulations is found to be nearly complementary with respect to the surface impedance. The capability of the proposed DG solution strategy for calculating scattering from large multiscale IBC targets is demonstrated.

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Domain Decomposition Preconditioning for Surface Integral Equations in Solving Challenging Electromagnetic Scattering Problems

Cited by 93 publications

References 67 publications

High-performance surface integral equation solvers towards extreme-scale electromagnetic modeling and simulation

High-performance surface integral equation solvers towards extreme-scale electromagnetic modeling and simulation

ADAPTIVE AND PARALLEL SURFACE INTEGRAL EQUATION SOLVERS FOR VERY LARGE-SCALE ELECTROMAGNETIC MODELING AND SIMULATION (Invited Paper)

A discontinuous Galerkin surface integral equation method for scattering from IBC targets

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