A Calderón Preconditioner for High Dielectric Contrast Media

Gossye, Michiel; Huynen, Martijn; Ginste, Dries Vande; Zutter, D. De; Rogier, Hendrik

doi:10.1109/tap.2017.2778014

Cited by 26 publications

(30 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This equation is uniquely solvable. However, the eigenvalue spectrum of the system matrix, P, in (17) is not bounded from below nor above, meaning that dense-mesh breakdown will occur. This leads to a slow iterative convergence and inaccurate solutions when solving the discretized problem.…”

Section: Cp-pmchwt Equationmentioning

confidence: 99%

“…The derivation of a novel formulation that remains well-conditioned for high magnetic contrast media is given in Section 2.2. The derivation of a comparable method for high dielectric contrast media [17] is described in Section 2.3.…”

Section: Cp-pmchwt Equationmentioning

confidence: 99%

“…However, in Section 2.3, a formulation that remains well-conditioned for high dielectric contrasts is summarized. The full derivation is given in [17].…”

Section: Derivation Of a Cp For High Magnetic Contrastsmentioning

confidence: 99%

“…In [17], a Calderón preconditioned single-source equation, based on the DtN operator, was introduced that does not suffer from dense-mesh breakdown for electromagnetic scattering problems involving arbitrarily high dielectric contrasts (including conductive or negative index media). In this paper, we present a comparable method, based on the Neumann-to-Dirichlet (NtD) operator Y, that does not break down when arbitrarily high permeabilities are present.…”

Section: Introductionmentioning

confidence: 99%

“…Next, the derivation of the novel formulation is given. It is compared to the CP-PMCHWT and the method in [17]. In Section 3, the discretization of the proposed method is discussed.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Electromagnetic modeling of high magnetic contrast media using Calderón preconditioning

Gossye

Ginste

Rogier

2019

Computers & Mathematics with Applications

Self Cite

View full text Add to dashboard Cite

In this contribution, we present a Calderón preconditioner for a novel singlesource equation to efficiently model electromagnetic scattering problems involving high magnetic contrasts. Through analysis of the spectral properties of the system matrix after discretization, it is shown that this formulation does not break down when high permeabilities are present, which was an unresolved problem of the Calderón preconditioned Poggio-Miller-Chan-Harrington-Wu-Tsai method. The adopted discretization scheme, which involves Rao-Wilton-Glisson and Buffa-Christiansen basis functions, allows for an easy integration in existing commercial Method of Moments software. The efficiency and accuracy of the presented method is corroborated by numerical examples.

show abstract

Section: Cp-pmchwt Equationmentioning

confidence: 99%

Section: Cp-pmchwt Equationmentioning

confidence: 99%

“…However, in Section 2.3, a formulation that remains well-conditioned for high dielectric contrasts is summarized. The full derivation is given in [17].…”

Section: Derivation Of a Cp For High Magnetic Contrastsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Next, the derivation of the novel formulation is given. It is compared to the CP-PMCHWT and the method in [17]. In Section 3, the discretization of the proposed method is discussed.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Electromagnetic modeling of high magnetic contrast media using Calderón preconditioning

Gossye

Ginste

Rogier

2019

Computers & Mathematics with Applications

Self Cite

View full text Add to dashboard Cite

show abstract

Benchmarking preconditioned boundary integral formulations for acoustics

Wout

Haqshenas

Gélat

et al. 2021

Numerical Meth Engineering

View full text Add to dashboard Cite

The boundary element method (BEM) is an efficient numerical method for simulating harmonic wave propagation. It uses boundary integral formulations of the Helmholtz equation at the interfaces of piecewise homogeneous domains. The discretization of its weak formulation leads to a dense system of linear equations, which is typically solved with an iterative linear method such as GMRES. The application of BEM to simulating wave propagation through large-scale geometries is only feasible when compression and preconditioning techniques reduce the computational footprint. Furthermore, many different boundary integral equations exist that solve the same boundary value problem. The choice of preconditioner and boundary integral formulation is often optimized for a specific configuration, depending on the geometry, material characteristics, and driving frequency. On the one hand, the design flexibility for the BEM can lead to fast and accurate schemes. On the other hand, efficient and robust algorithms are difficult to achieve without expert knowledge of the BEM intricacies. This study surveys the design of boundary integral formulations for acoustics and their acceleration with operator preconditioners. Extensive benchmarks provide valuable information on the computational characteristics of several hundred different models for multiple reflection and transmission of acoustic waves.

show abstract