A Domain Decomposition Method for Boundary Integral Equations Using a Transmission Condition Based on the Near-Zone Couplings

Wiedenmann, Oliver; Eibert, Thomas F.

doi:10.1109/tap.2014.2322881

Cited by 30 publications

(12 citation statements)

References 30 publications

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“…Instead, one usually turns to preconditioned Krylov subspace iterative methods. When such iterative solutions are employed, the efficient and parallel computation of effective preconditioners poses an immense challenge [6,12,[36][37][38][39][40][41][42]. This work proposes a one-level non-overlapping additive Schwarz DD preconditioner [43] for the solution of the DG-BEM linear system equation, Ax = b.…”

Section: Domain Decomposition Solvermentioning

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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Section: Domain Decomposition Solvermentioning

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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“…It is desirable for computational electromagnetic to provide efficient algorithms for such challenging problems. Today, fast algorithms, parallel algorithms, and domain decomposition methods (DDM) [1] [13] have been regarded as approaches to solve complex electromagnetic problems.…”

Section: Introductionmentioning

confidence: 99%

Integral Equation-Based Nonoverlapping DDM Using the Explicit Boundary Condition

Zheng

Zhou

Wang

2015

IEEE Trans. Antennas Propagat.

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A new integral equation-based nonoverlapping domain decomposition method (NDDM) is proposed for analyzing electromagnetic (EM) scattering from electrically large PEC objects whose MLFMA models are too large for the user's computer to accommodate. The integral equation is first built on the entire PEC surface, and the entire surface is partitioned into some nonoverlapping subsurfaces. The RWG functions are used to expand the surface current on the entire surface. Then, each full-RWG function across some boundary curve is split into two half-RWG functions whose unknown coefficients are constrained by the boundary current continuity (using the explicit boundary condition). The convergence of the outer-iterative scheme of the proposed NDDM is investigated theoretically and demonstrated to be very good, and hence a very large problem can be effectively solved in an ordinary computer. Some numerical examples are provided to demonstrate the correctness and robustness of the proposed method, and to compare the proposed method with the existing overlapping DDMs having similar attributes.Index Terms-Domain decomposition method (DDM), electromagnetic (EM) scattering, full-RWG function, half-RWG function, method of moments (MoM), nonoverlapping subdomain.

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“…Convergence properties in DD depend on the transmission conditions between sub-domains [24]; in [22] these are implemented by adding an artificial perfect electric conductor (PEC) surface to close each of the subdomains upon tearing; surface current cancellation within each pair of artificial inter-domain surfaces is then enforced in the solution scheme. A recent work [25] proposes an overlapping DD method in which the transmission conditions among the overlapped sub-domains are enforced in each inner solver by using the global near field matrix; a suitably reduced version of the whole near field matrix is used in the inner solvers for each sub-problem.…”

Section: Introductionmentioning

confidence: 99%

A Nonconformal Domain Decomposition Scheme for the Analysis of Multiscale Structures

Bautista

Vipiana

Francavilla

et al. 2015

IEEE Trans. Antennas Propagat.

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We present a Domain Decomposition (DD) framework for the analysis of impenetrable structures; it allows for the EFIE and CFIE, and for open, closed, and open-closed structures. The DD results in an effective preconditioner for large and complex problems exploiting iterative solution and fast factorizations. The domain decomposition employs specialized transmission conditions among the domains, and the use of discontinuous Galerkin (DG) allows conformal as well as nonconformal discretizations of domain boundaries; the nonconformal nature of the decomposition gives considerable flexibility in the meshing. The strategy is highly parallelizable, as all the operations involving the sub-domains can performed in parallel. The proposed scheme is implementation independent and can be easily merged with existing electromagnetic codes.

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A Domain Decomposition Method for Boundary Integral Equations Using a Transmission Condition Based on the Near-Zone Couplings

Cited by 30 publications

References 30 publications

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

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

Integral Equation-Based Nonoverlapping DDM Using the Explicit Boundary Condition

A Nonconformal Domain Decomposition Scheme for the Analysis of Multiscale Structures

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