An efficient perfectly matched layer based multilevel fast multipole algorithm for large planar microwave structures

Ginste, Dries Vande; Michielssen, E.; Olyslager, F.; Zutter, D. De

doi:10.1109/tap.2006.874320

Cited by 36 publications

(29 citation statements)

References 41 publications

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“…This scheme has, e.g., also been applied to scattering from and radiation by intricate dielectric objects such as printed circuit board antennas [17,18] and to photonic crystal waveguides [19]. The reader is encouraged to consult these references to gain familiarity with the MLFMM scheme.…”

Section: Sgm-mlfmmmentioning

confidence: 99%

Efficient uncertainty quantification of large two-dimensional optical systems with a parallelized stochastic Galerkin method

Zubac¹,

Fostier²,

Zutter³

et al. 2015

Opt. Express

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It is well-known that geometrical variations due to manufacturing tolerances can degrade the performance of optical devices. In recent literature, polynomial chaos expansion (PCE) methods were proposed to model this statistical behavior. Nonetheless, traditional PCE solvers require a lot of memory and their computational complexity leads to prohibitively long simulation times, making these methods non-tractable for large optical systems. The uncertainty quantification (UQ) of various types of large, two-dimensional lens systems is presented in this paper, leveraging a novel parallelized Multilevel Fast Multipole Method (MLFMM) based Stochastic Galerkin Method (SGM). It is demonstrated that this technique can handle large optical structures in reasonable time, e.g., a stochastic lens system with more than 10 million unknowns was solved in less than an hour by using 3 compute nodes. The SGM, which is an intrusive PCE method, guarantees the accuracy of the method. By conjunction with MLFMM, usage of a preconditioner and by constructing and implementing a parallelized algorithm, a high efficiency is achieved. This is demonstrated with parallel scalability graphs. The novel approach is illustrated for different types of lens system and numerical results are validated against a collocation method, which relies on reusing a traditional deterministic solver. The last example concerns a Cassegrain system with five random variables, for which a speed-up of more than 12× compared to a collocation method is achieved.

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Section: Sgm-mlfmmmentioning

confidence: 99%

Efficient uncertainty quantification of large two-dimensional optical systems with a parallelized stochastic Galerkin method

Zubac¹,

Fostier²,

Zutter³

et al. 2015

Opt. Express

Self Cite

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“…Both terms are acquired through an interpolation process centered on the respective face side. Replacing (17)- (19) into (16), we derive…”

Section: Explicit Multimodal Formulationmentioning

confidence: 99%

“…whose important property is the incorporation of (12)- (19) in the temporal integration process. Herein, to achieve higherorder accuracy, a 3-stage scheme is devised.…”

Section: Explicit Multimodal Formulationmentioning

confidence: 99%

“…The strength of such undesired phenomena depends on the magnitude and abruptness of the grid wave mode velocity distribution and may be crucial in diverse large-scale applications. Pursuing the constant improvement of these important drawbacks, an assortment of proficient algorithms has been hitherto presented [19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

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Combined FVTD/PSTD Schemes with Enhanced Spectral Accuracy for the Design of Large-Scale EMC Applications

Kantartzis

Dimitriadis

Tsiboukis

2012

AEM

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A generalized conformal time-domain method with adjustable spectral accuracy is introduced in this paper for the consistent analysis of large-scale electromagnetic compatibility problems. The novel 3-D hybrid schemes blend a stenciloptimized finite-volume time-domain and a multimodal Fourier-Chebyshev pseudo-spectral time-domain algorithm that split the overall space into smaller and flexible areas. A key asset is that both techniques are updated independently and interconnected by robust boundary conditions. Also, combining a family of spatial derivative approximators with controllable precision in general curvilinear coordinates, the proposed method launches a conformal field flux formulation to derive electromagnetic quantities in regions with fine details. For advanced grid reliability at dissimilar media interfaces, dispersion-reduced adaptive operators, which assign the proper weights to each spatial increment, are developed. So, the resulting discretization yields highly rigorous and computationally affordable simulations, devoid of lattice errors. Numerical results, addressing detailed comparisons of various realistic applications with reference or measurement data verify our methodology and reveal its significant applicability.

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“…As planarly layered media are of huge practical importance in microwave design, upon the conception of the perfectly matched layer (PML) -detailed mathematically by Prof. F. Olyslager in [1] -an efficient FMM for 2D microstrip configurations was designed [2]. A specialized Multilevel Fast Multipole Algorithm (MLMFA) for 3D layered structures, based on the application of PMLs, was presented in [3], [4] and later improved upon by means of Singular Value Decompositions [5]. It was found that PML-based FMMs could also be devised for photonic crystals [6].…”

Section: Introductionmentioning

confidence: 99%

Recent advances in boundary element methods applied to conducting and dielectric electromagnetic scattering problems

Cools

Bogaert

Fostier

et al. 2010

2010 URSI International Symposium on Electromagnetic Theory

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Abstract-Boundary element methods (BEMs) are an increasingly popular approach to the modeling of electromagnetic scattering both by perfect conductors and dielectric objects. Several mathematical, numerical, and computational techniques pullulated from the research into BEMs, enhancing its efficiency. The Fast Multipole Method (FMM) and its descendants accelerate the matrix-vector product that constitutes the BEM's computational bottleneck. In particular, dedicated FMMs have been conceived for the computation of the electromagnetic scattering at complex metallic and/or dielectric objects in free space and in layered background media. Calderón preconditioning of the BEM's system matrix lowers the number of matrix-vector products required to reach an accurate solution, and thus the time to reach it. Parallelization distributes the remaining workload over a battery of affordable computational nodes, diminishing the wall-clock computation time. In honor of our former colleague and mentor, Prof. F. Olyslager, an overview of some dedicated BEMs for large and complex EM problems developed within the Electromagnetics Group at Ghent University is presented. Recent results that ramified from Prof. Olyslager's scientific endeavors are included in the survey.

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An efficient perfectly matched layer based multilevel fast multipole algorithm for large planar microwave structures

Cited by 36 publications

References 41 publications

Efficient uncertainty quantification of large two-dimensional optical systems with a parallelized stochastic Galerkin method

Efficient uncertainty quantification of large two-dimensional optical systems with a parallelized stochastic Galerkin method

Combined FVTD/PSTD Schemes with Enhanced Spectral Accuracy for the Design of Large-Scale EMC Applications

Recent advances in boundary element methods applied to conducting and dielectric electromagnetic scattering problems

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