EFIE Modeling of High-Definition Multiscale Structures

Vipiana, F.; Francavilla, M. A.; Vecchi, G.

doi:10.1109/tap.2010.2048855

Cited by 86 publications

(73 citation statements)

References 26 publications

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“…The coexistence of an electrically large aircraft carrier platform and electrically small fine features reflects into disparate mesh sizes. It may cause the so-called "mixed-frequency" problem [12,27] and result in an extremely ill-conditioned matrix equation.…”

Section: Introductionmentioning

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: Introductionmentioning

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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“…The mesh quality and resolution is one of the key issues in the solution of this kind of problems [1], [2]. A fine mesh is required to obtain an accurate current description on the surface.…”

Section: Introductionmentioning

confidence: 99%

Automatic h-refinement through a-posteriori error estimation and discontinous Galerkin

Vasquez

Francavilla

Vipiana

et al. 2015

2015 IEEE International Conference on Computational Electromagnetics

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“…The usage of higher order hierarchical basis functions typically increases the condition number of the system matrix, thereby deteriorating the convergence. Even though advanced preconditioning strategies have been developed [4], [5], in particular to improve the conditioning of the BI matrix, for complex and/or large geometries, iterative solution techniques are still prone to fail.…”

Section: Introductionmentioning

confidence: 99%

A direct hierarchical multilevel preconditioner for the solution of finite element-boundary integral equations

Wiedenmann

Eibert

2014

The 8th European Conference on Antennas and Propagation (EuCAP 2014)

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Boundary integral (BI) equations in combination with fast solvers such as the multilevel fast multipole method are very well suited for solving electromagnetic scattering and radiation problems. In order to consider dielectric objects, the BI approach can be extended to the hybrid finite element-boundary integral (FE-BI) method. By using hierarchical higher order basis functions for the expansion of the unknowns, very accurate results can be obtained. To accelerate the convergence of iterative solvers, the usage of preconditioning methods is indispensable. In this work, a very efficient multilevel preconditioner is presented which is based on a factorization of the submatrices containing the interactions of the zeroth order divergence-conforming basis functions in the BI formulation and the corresponding lowest order curl-conforming basis of the FE method. Moreover, it is shown that the number of fill-ins can be effectively reduced by exploiting advanced reordering algorithms.Index Terms-finite element method, boundary integral method, higher order, preconditioning. I. INTRODUCTIONBoundary integral (BI) equation methods are a versatile tool for the solution of electromagnetic scattering and radiation problems since they require only a surface discretization and the radiation condition is fulfilled automatically. While they are best suited if applied on metallic objects, dielectric materials can be easily incorporated by using a hybrid finite element-boundary integral (FE-BI) formulation [1]. In contrast to the finite element method, which is a local technique that results in a sparse matrix, the BI formulation leads to a fully populated system matrix due to the global nature of the integral operator. However, the usage of fast solvers like the multilevel fast multipole method (MLFMM) [2] reduces the complexity of the BI method considerably, so that the combined FE-BI system can be conveniently solved by iterative solution methods. If higher order basis functions [3] are deployed for the expansion of the unknowns, very accurate results can be obtained in a very efficient way for a wide range of problems.One major drawback of the depicted method is the lack of robustness due to possible convergence problems of the iterative solver. The usage of higher order hierarchical basis functions typically increases the condition number of the system matrix, thereby deteriorating the convergence. Even though advanced preconditioning strategies have been developed [4], [5], in particular to improve the conditioning of the BI matrix, for complex and/or large geometries, iterative solution techniques are still prone to fail.

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EFIE Modeling of High-Definition Multiscale Structures

Cited by 86 publications

References 26 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)

Automatic h-refinement through a-posteriori error estimation and discontinous Galerkin

A direct hierarchical multilevel preconditioner for the solution of finite element-boundary integral equations

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