Two-Dimensional Boundary-Value Problems

Polycarpou, Anastasis C.

doi:10.1007/978-3-031-01689-9_2

Cited by 4 publications

(8 citation statements)

References 25 publications

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“…Numerical analyzes and simulations were performed using the frequency domain Finite Element Method 40 in the infrared electromagnetic spectrum range (1000–2500 nm) using licensed COMSOL Multiphysics software 41 . The relative permittivity of gold , , is based on the Drude–Lorentz model 42 , and for the aluminum dioxide we consider = 3.24 along the simulated and analyzed spectrum.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Programmable nanophotonic planar resonator filter-absorber based on phase-change InSbTe

Oliveira,

de Souza,

Rodriguez-Esquerre

2023

Sci Rep

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Reconfigurable plasmonic-photonic electromagnetic devices have been incessantly investigated for their great ability to optically modulate through external stimuli to meet today's emerging needs, with chalcogenide phase-change materials being promising candidates due to their remarkably unique electrical and optics, enabling new perspectives in recent photonic applications. In this work, we propose a reconfigurable resonator using planar layers of stacked ultrathin films based on Metal-dielectric-PCM, which we designed and analyzed numerically by the Finite Element Method (FEM). The structure is based on thin films of Gold (Au), aluminum oxide (Al2O3), and PCM (In3SbTe2) used as substrate. The modulation between the PCM phases (amorphous and crystalline) allows the alternation from the filter to the absorber structure in the infrared (IR) spectrum (1000–2500 nm), with an efficiency greater than 70% in both cases. The influence of the thickness of the material is also analyzed to verify tolerances for manufacturing errors and dynamically control the efficiency of transmittance and absorptance peaks. The physical mechanisms of field coupling and transmitted/absorbed power density are investigated. We also analyzed the effects on polarization angles for Transversal Electric (TE) and Transversal Magnetic (TM) polarized waves for both cases.

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Section: Numerical Simulationsmentioning

confidence: 99%

Programmable nanophotonic planar resonator filter-absorber based on phase-change InSbTe

Oliveira,

de Souza,

Rodriguez-Esquerre

2023

Sci Rep

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“…This equation can be solved using numerical, analytical or semianalytical methods depending on the complexity of the brain model. Two of the most commonly used numerical methods are the finite difference method (FDM) [ 63 , 64 , 65 , 66 , 67 ] and the finite element method (FEM) [ 64 , 68 , 69 , 70 ].…”

Section: Solutions Of Tms Field Bvpsmentioning

confidence: 99%

“…The Weighted residual Galerkin method [ 68 , 69 ] is one of the most widely used FEMs. In this case, the starting point is Equation (32), which considers the domain of a single element (

), and the weak formulation [ 68 , 69 ] and the residual for the element ( e ) can be written as:

…”

Section: Solutions Of Tms Field Bvpsmentioning

confidence: 99%

“…According to the Garlerkin formulation [ 68 ], the weight function ( w ) should be set equal to the interpolation functions:

…”

Section: Solutions Of Tms Field Bvpsmentioning

confidence: 99%

“…Due to the fact that the normal vector of the faces shared by two neighbor elements has opposite directions [ 68 , 69 ], the integral

cancels for interior element boundaries, and

is different from zero only for the outer boundaries. Furthermore, if the simulation is performed considering an air box circumscribing the brain, in the air,

; therefore,

.…”

Section: Solutions Of Tms Field Bvpsmentioning

confidence: 99%

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A Review of Formulations, Boundary Value Problems and Solutions for Numerical Computation of Transcranial Magnetic Stimulation Fields

Pérez-Benítez,

Martínez-Ortiz,

Aguila-Muñoz

2023

Brain Sciences

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Since the inception of the transcranial magnetic stimulation (TMS) technique, it has become imperative to numerically compute the distribution of the electric field induced in the brain. Various models of the coil-brain system have been proposed for this purpose. These models yield a set of formulations and boundary conditions that can be employed to calculate the induced electric field. However, the literature on TMS simulation presents several of these formulations, leading to potential confusion regarding the interpretation and contribution of each source of electric field. The present study undertakes an extensive compilation of widely utilized formulations, boundary value problems and numerical solutions employed in TMS fields simulations, analyzing the advantages and disadvantages associated with each used formulation and numerical method. Additionally, it explores the implementation strategies employed for their numerical computation. Furthermore, this work provides numerical expressions that can be utilized for the numerical computation of TMS fields using the finite difference and finite element methods. Notably, some of these expressions are deduced within the present study. Finally, an overview of some of the most significant results obtained from numerical computation of TMS fields is presented. The aim of this work is to serve as a guide for future research endeavors concerning the numerical simulation of TMS.

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Interactive and educational simulation tool for permanent magnet synchronous machines

Schugardt,

Kaiser,

Avcilar

et al. 2024

COMPEL

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Purpose This paper aims to present an interactive design and simulation tool for permanent magnet synchronous machines based on the finite-element-method. The tool is intended for education and research on electrical machines. Design/methodology/approach A coupling between the software MATLAB and finite element method magnetics is used. Several functionalities are included as modular scripts and represented in the form of a graphical user interface. Included are fully parametrized motor models, automatic winding generations and the evaluation of torque waveforms, core losses and speed-torque-diagrams. A survey was conducted to determine how the motivation of students concerning the covered topics is influenced by using the tool. Findings Due to its simplicity and the intuitive visualization of the results, the tool provides direct access to the topic of electrical machines without having to deal with separate scripts. The modular structure of the software allows simple extensions with new functions. Because students can directly contribute to the tool with their own work, their motivation for using and extending it increases. Originality/value The presented tool offers more functionalities compared to similar free software packages, e.g. the calculation of core losses and speed-torque diagrams. Also, it is designed in such a way that it can be easily understood and extended by students.

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Two-Dimensional Boundary-Value Problems

Cited by 4 publications

References 25 publications

Programmable nanophotonic planar resonator filter-absorber based on phase-change InSbTe

Programmable nanophotonic planar resonator filter-absorber based on phase-change InSbTe

A Review of Formulations, Boundary Value Problems and Solutions for Numerical Computation of Transcranial Magnetic Stimulation Fields

Interactive and educational simulation tool for permanent magnet synchronous machines

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