Hybrid Volume-Surface Integral Equation

Volakis, John L.; Sertel, Kubilay; Usner, B.C.

doi:10.1007/978-3-031-01694-3_4

Cited by 5 publications

(8 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Additionally, the free space permittivity ε 0 and the free space permeability µ 0 are considered as the background medium without loss of generality. In addition, Maxwell’s equations in free space are defined as (Volakis and Sertel, 2012): where M(x , z) and J(x , z) are a magnetic current source and an electric current source, respectively. In the first stage of solution’s procedure, the Maxwell’s equations inside the scatterer are represented in the form of volume integral equation.…”

Section: Forward Formulationmentioning

confidence: 99%

“…In the first stage of solution’s procedure, the Maxwell’s equations inside the scatterer are represented in the form of volume integral equation. Consequently, the presence of the investigated structure in free space can be expressed in terms of magnetic polarization and electric polarization currents given by (Volakis and Sertel, 2012): …”

Section: Forward Formulationmentioning

confidence: 99%

“…This leads to an electric field in the y -direction. With harmonic time dependence of e −iωt , the Maxwell’s equations within the structure may be descried as (Volakis and Sertel, 2012): where E(x , z) and H(x , z) are the electric field and the magnetic field, respectively. The operating frequency is given by ω /2 π .…”

Section: Forward Formulationmentioning

confidence: 99%

See 2 more Smart Citations

A novel representation of electromagnetic field interaction with vertically stratified structures

Elkattan

Kamel

2023

COMPEL

View full text Add to dashboard Cite

Purpose The purpose of this study is to develop an efficient model to solve the electromagnetic forward problem using a novel semi-analytical approach to compute the electromagnetic fields because of the presence of a scatterer. Design/methodology/approach The proposed model involves a novel formulation of a complete orthonormal set of radiating/nonradiating polarization currents. Furthermore, an integral equation-based representation is derived, and the appropriate boundary conditions are imposed to get the scattered electromagnetic field. An error term is introduced to evaluate the obtained results. Findings The proposed model was tested using several examples at different frequencies. The results of this study show that the novel representation exhibits fast convergence behavior and achieves highly accurate results, when compared to the results provided by the transmission line method. Originality/value The derived formulations presented in this study are significant in the electromagnetic forward modelling field because of the meaningful physical representation they provide. This is an important aspect that leads to precise calculation of electromagnetic fields for various applications.

show abstract

Section: Forward Formulationmentioning

confidence: 99%

Section: Forward Formulationmentioning

confidence: 99%

See 1 more Smart Citation

A novel representation of electromagnetic field interaction with vertically stratified structures

Elkattan

Kamel

2023

COMPEL

View full text Add to dashboard Cite

show abstract

“…Using the potentials in eq 2, the scattered components of the electromagnetic fields can be represented with either a direct − or indirect formulation . In this work, we have used the indirect formulation for the electromagnetic fields given by with tangential density currents m and j , and where the coefficients in eq multiplying the vector potentials are such that enforcing the continuity of the tangential components of the fields across Γ results in a Müller system of integral equations with only weakly singular integral operators. − The tangential components of eq evaluated at the boundary Γ can be expressed in terms of the boundary integral operators that result from taking the cross product with the normal vector n ( r ) and the limit as r → r ′, namely with r ∈ Γ.…”

Section: Full-wave Analysis Of Nanophotonic Structures Using Boundary...mentioning

confidence: 99%

“…To solve the system of Maxwell’s equations in eq , we use a three-dimensional boundary integral representation − for the electromagnetic fields. This approach has several advantages over volumetric methods (e.g., finite-differences), including the fact that only material interfaces need to be discretized (as opposed to the entire simulation volumes) and that the geometrical features of the devices are parametrically represented, avoiding material staircasing errors.…”

Section: Full-wave Analysis Of Nanophotonic Structures Using Boundary...mentioning

confidence: 99%

Fast Inverse Design of 3D Nanophotonic Devices Using Boundary Integral Methods

Garza

Sideris

2022

ACS Photonics

View full text Add to dashboard Cite

Recent developments in the computational automated design of electromagnetic devices, otherwise known as inverse design, have significantly enhanced the design process for nanophotonic systems. Inverse design can both reduce design time considerably and lead to high-performance, nonintuitive structures that would otherwise have been impossible to develop manually. Despite the successes enjoyed by structure optimization techniques, most approaches leverage electromagnetic solvers that require significant computational resources and suffer from slow convergence and numerical dispersion. Recently, a fast simulation and boundary-based inverse design approach based on boundary integral equations was demonstrated for two-dimensional nanophotonic problems. In this work, we introduce a new full-wave three-dimensional simulation and boundary-based optimization framework for nanophotonic devices also based on boundary integral methods, which achieves high accuracy even at coarse mesh discretizations while only requiring modest computational resources. The approach has been further accelerated by leveraging GPU computing, a sparse block-diagonal preconditioning strategy, and a matrix-free implementation of the discrete adjoint method. As a demonstration, we optimize three different devices: a 1:2 1550 nm power splitter and two nonadiabatic mode-preserving waveguide tapers. To the best of our knowledge, the tapers, which span 40 wavelengths in the silicon material, are the largest silicon photonic waveguiding devices to have been optimized using full-wave 3D solution of Maxwell's equations.

show abstract

Comparative performance of the finite element method and the boundary element fast multipole method for problems mimicking transcranial magnetic stimulation (TMS)

Htet

Saturnino²,

Burnham

et al. 2019

J. Neural Eng.

View full text Add to dashboard Cite

Objective. A study pertinent to the numerical modeling of cortical neurostimulation is conducted in an effort to compare the performance of the finite element method (FEM) and an original formulation of the boundary element fast multipole method (BEM-FMM) at matched computational performance metrics. Approach. We consider two problems: (i) a canonic multi-sphere geometry and an external magnetic-dipole excitation where the analytical solution is available and; (ii) a problem with realistic head models excited by a realistic coil geometry. In the first case, the FEM algorithm tested is a fast open-source getDP solver running within the SimNIBS 2.1.1 environment. In the second case, a high-end commercial FEM software package ANSYS Maxwell 3D is used. The BEM-FMM method runs in the MATLAB® 2018a environment. Main results. In the first case, we observe that the BEM-FMM algorithm gives a smaller solution error for all mesh resolutions and runs significantly faster for high-resolution meshes when the number of triangular facets exceeds approximately 0.25 M. We present other relevant simulation results such as volumetric mesh generation times for the FEM, time necessary to compute the potential integrals for the BEM-FMM, and solution performance metrics for different hardware/operating system combinations. In the second case, we observe an excellent agreement for electric field distribution across different cranium compartments and, at the same time, a speed improvement of three orders of magnitude when the BEM-FMM algorithm used. Significance. This study may provide a justification for anticipated use of the BEM-FMM algorithm for high-resolution realistic transcranial magnetic stimulation scenarios.

show abstract

Hybrid Volume-Surface Integral Equation

Cited by 5 publications

References 0 publications

A novel representation of electromagnetic field interaction with vertically stratified structures

A novel representation of electromagnetic field interaction with vertically stratified structures

Fast Inverse Design of 3D Nanophotonic Devices Using Boundary Integral Methods

Comparative performance of the finite element method and the boundary element fast multipole method for problems mimicking transcranial magnetic stimulation (TMS)

Contact Info

Product

Resources

About