A FEM Domain Decomposition Method for Photonic and Electromagnetic Band Gap Structures

Vouvakis, Marinos N.; Cendes, Z.J.; Lee, Jin‐Fa

doi:10.1109/tap.2005.863095

Cited by 148 publications

(77 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We have thus tested the convergence of the method with respect to α i . For the same value of the stopping criterion of the GMRES algorithm, we have noted in Table 2 which is the value suggested in [33]. As one can remark, this value is also an optimal value in terms of iterations for our proposed method.…”

Section: Numerical Resultsmentioning

confidence: 78%

See 1 more Smart Citation

Scattered Field Computation With an Extended Feti-Dpem2 Method

Voznyuk¹,

Tortel²,

Litman³

2013

PIER

View full text Add to dashboard Cite

Abstract-Due to the increasing number of applications in engineering design and optimization, more and more attention has been paid to full-wave simulations based on computational electromagnetics. In particular, the finite-element method (FEM) is well suited for problems involving inhomogeneous and arbitrary shaped objects. Unfortunately, solving large-scale electromagnetic problems with FEM may be time consuming. A numerical scheme, called the dual-primal finite element tearing and interconnecting method (FETI-DPEM2), distinguishes itself through the partioning on the computation domain into non-overlapping subdomains where incomplete solutions of the electrical field are evaluated independently. Next, all the subdomains are "glued" together using a modified Robin-type transmission condition along each common internal interface, apart from the corner points where a simple Neumann-type boundary condition is imposed. We propose an extension of the FETI-DPEM2 method where we impose a Robin type boundary conditions at each interface point, even at the corner points. We have implemented this Extended FETI-DPEM2 method in a bidimensional configuration while computing the field scattered by a set of heterogeneous, eventually anistropic, scatterers. The results presented here will assert the efficiency of the proposed method with respect to the classical FETI-DPEM2 method, whatever the mesh partition is arbitrary defined.

show abstract

Section: Numerical Resultsmentioning

confidence: 78%

“…This method has been applied in many domains like mechanics [19,20], acoustic wave propagation [21][22][23], and in electromagnetism [24][25][26][27][28][29][30][31][32]. For example, related DDM methods have been developed for simulating the interactions of photonic crystals with electromagnetic waves [33,34].…”

Section: Introductionmentioning

confidence: 99%

Scattered Field Computation With an Extended Feti-Dpem2 Method

Voznyuk¹,

Tortel²,

Litman³

2013

PIER

View full text Add to dashboard Cite

show abstract

“…Recently, a non-overlapping finite element domain decomposition method has been applied successfully in electromagnetic scattering and radiation problems [17][18][19][20][21][22][23][24]. Numerical experiments demonstrate the efficient performance of DDM, especially for periodic structures.…”

Section: Introductionmentioning

confidence: 99%

“…In order to improve the convergence of the conventional FE-BI-MLFMA and save the computer memory, a non-overlapping domain decomposition method presented in [19,20] is applied to FE-BI-MLFMA effectively. Additionally, a novel mixed absorbing boundary condition and block symmetry successive over relaxation (ABC-SSOR) preconditioner is proposed to further accelerate the convergence.…”

Section: Introductionmentioning

confidence: 99%

Domain Decomposition Fe-Bi-Mlfma Method for Scattering by 3d Inhomogeneous Objects

Gao¹,

Yang²,

Sheng³

2013

PIER

View full text Add to dashboard Cite

Abstract-The hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) is a powerful method for calculating scattering by inhomogeneous objects. However, the conventional FE-BI-MLFMA often suffers from iterative convergence problems. A non-overlapping domain decomposition method (DDM) is applied to FE-BI-MLFMA to speed up the iterative convergence. Furthermore, a preconditioner based on absorbing boundary condition and symmetric successive over relaxation (ABC-SSOR) is constructed to further accelerate convergence of the DDM-FE-BI-MLFMA. Numerical experiments demonstrate the efficiency of the proposed preconditioned DDM-FE-BI-MLFMA.

show abstract

“…It is not easy to satisfy the memory requirement to solve large-scale problem using MOM even on most powerful computers. One of the approaches to overcome such a problem is the domain decomposition method, which has found wide applications in the EM community [8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Algorithm for Em Scattering by Electrically Large Dielectric Objects Using MR-Qeb Iterative Scheme and Cg-FFT Method

Zhao¹,

Cui²,

Li³

2007

PIER

View full text Add to dashboard Cite

Abstract-In this paper, an efficient algorithm is presented to analyze the electromagnetic scattering by electrically large-scale dielectric objects. The algorithm is based on the multi-region and quasiedge buffer (MR-QEB) iterative scheme and the conjugate gradient (CG) method combined with the fast Fourier transform (FFT). This algorithm is done by dividing the computational domain into small sub-regions and then solving the problem in each sub-region with buffer area using the CG-FFT method. Considering the spurious edge effects, local quasi-edge buffer regions are used to suppress these unwanted effects and ensure the stability. With the aid of the CG-FFT method, the proposed algorithm is very efficient, and can solve very largescale problems which cannot be solved using the conventional CG-FFT method in a personal computer. The accuracy and efficiency of the proposed algorithm are verified by comparing numerical results with analytical Mie-series solutions for dielectric spheres.

show abstract

A FEM Domain Decomposition Method for Photonic and Electromagnetic Band Gap Structures

Cited by 148 publications

References 30 publications

Scattered Field Computation With an Extended Feti-Dpem2 Method

Scattered Field Computation With an Extended Feti-Dpem2 Method

Domain Decomposition Fe-Bi-Mlfma Method for Scattering by 3d Inhomogeneous Objects

An Efficient Algorithm for Em Scattering by Electrically Large Dielectric Objects Using MR-Qeb Iterative Scheme and Cg-FFT Method

Contact Info

Product

Resources

About