scholarly journals Comparative Performance of the Finite Element Method and the Boundary Element Fast Multipole Method for Problems Mimicking Transcranial Magnetic Stimulation (TMS)

2018 ◽  
Author(s):  
Aung Thu Htet ◽  
Guilherme B. Saturnino ◽  
Edward H. Burnham ◽  
Gregory M. Noetscher ◽  
Aapo Nummenmaa ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transcranial Magnetic Stimulation ◽  
High Resolution ◽  
Boundary Element ◽  
Magnetic Stimulation ◽  
Performance Metrics ◽  
Fast Multipole Method ◽  
The Finite Element Method ◽  
First Case

AbstractA 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. 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.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.This study may provide a justification for anticipated use of the BEM-FMM algorithm for high-resolution realistic transcranial magnetic stimulation scenarios.

scholarly journals Acoustic Noise Computation of Electrical Motors Using the Boundary Element Method

Energies ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 245
Author(s):  
Sabin Sathyan ◽  
Ugur Aydin ◽  
Anouar Belahcen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Finite Element Simulation ◽  
Acoustic Noise ◽  
The Finite Element Method ◽  
Magnetic Forces ◽  
Element Simulation ◽  
Element Method

This paper presents a numerical method and computational results for acoustic noise of electromagnetic origin generated by an induction motor. The computation of noise incorporates three levels of numerical calculation steps, combining both the finite element method and boundary element method. The role of magnetic forces in the production of acoustic noise is established in the paper by showing the magneto-mechanical and vibro-acoustic pathway of energy. The conversion of electrical energy into acoustic energy in an electrical motor through electromagnetic, mechanical, or acoustic platforms is illustrated through numerical computations of magnetic forces, mechanical deformation, and acoustic noise. The magnetic forces were computed through 2D electromagnetic finite element simulation, and the deformation of the stator due to these forces was calculated using 3D structural finite element simulation. Finally, boundary element-based computation was employed to calculate the sound pressure and sound power level in decibels. The use of the boundary element method instead of the finite element method in acoustic computation reduces the computational cost because, unlike finite element analysis, the boundary element approach does not require heavy meshing to model the air surrounding the motor.

scholarly journals Elongation determination using finite element and boundary element method

2015 ◽  
Vol 61 (4) ◽  
pp. 389-394
Author(s):  
Piotr Kisała ◽  
Waldemar Wójcik ◽  
Nurzhigit Smailov ◽  
Aliya Kalizhanova ◽  
Damian Harasim
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Experimental Studies ◽  
Numerical Algorithms ◽  
Mathematical Structure ◽  
The Finite Element Method ◽  
Fbg Sensor ◽  
Element Method

AbstractThis paper presents an application of the finite element method and boundary element method to determine the distribution of the elongation. Computer simulations were performed using the computation of numerical algorithms according to a mathematical structure of the model and taking into account the values of all other elements of the fiber Bragg grating (FBG) sensor. Experimental studies were confirmed by elongation measurement system using one uniform FBG.

scholarly journals The implementation of the boundary element method to the Helmholtz equation of acoustics

2021 ◽  
pp. 13-19
Author(s):  
Sergey Sivak ◽  
Mihail Royak ◽  
Ilya Stupakov ◽  
Aleksandr Aleksashin ◽  
Ekaterina Voznjuk
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Numerical Methods ◽  
Helmholtz Equation ◽  
Boundary Value Problems ◽  
Boundary Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Element Method

Introduction: To solve the Helmholtz equation is important for the branches of engineering that require the simulation of wave phenomenon. Numerical methods allow effectiveness’ enhancing of the related computations. Methods: To find a numerical solution of the Helmholtz equation one may apply the boundary element method. Only the surface mesh constructed for the boundary of the three-dimensional domain of interest must be supplied to make the computations possible. This method’s trait makes it possible toconduct numerical experiments in the regions which are external in relation to some Euclidian three-dimensional subdomain bounded in the three-dimensional space. The later also provides the opportunity of not using additional geometric techniques to consider the infinitely distant boundary. However, it’s only possible to use the boundary element methods either for the homogeneous domains or for the domains composed out of adjacent homogeneous subdomains. Results: The implementation of the boundary elementmethod was committed in the program complex named Quasar. The discrepancy between the analytic solution approximation and the numerical results computed through the boundary element method for internal and external boundary value problems was analyzed. The results computed via the finite element method for the model boundary value problems are also provided for the purpose of the comparative analysis done between these two approaches. Practical relevance: The method gives an opportunityto solve the Helmholtz equation in an unbounded region which is a significant advantage over the numerical methods requiring the volume discretization of computational domains in general and over the finite element method in particular. Discussion: It is planned to make a coupling of the two methods for the purpose of providing the opportunity to conduct the computations in the complex regions with unbounded homogeneous subdomain and subdomains with substantial inhomogeneity inside.

scholarly journals Numerical Analysis of Microwave Scattering from Layered Sea Ice Based on the Finite Element Method

2018 ◽  
Vol 10 (9) ◽  
pp. 1332 ◽  
Author(s):  
Xu Xu ◽  
Camilla Brekke ◽  
Anthony Doulgeris ◽  
Frank Melandsø
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Sea Ice ◽  
Scattering Problem ◽  
The Finite Element Method ◽  
Microwave Scattering ◽  
Scattering Model ◽  
Salinity Profile ◽  
First Case ◽  
Element Method

A two-dimensional scattering model based on the Finite Element Method (FEM) is built for simulating the microwave scattering of sea ice, which is a layered medium. The scattering problem solved by the FEM is formulated following a total- and scattered-field decomposition strategy. The model set-up is first validated with good agreements by comparing the results of the FEM with those of the small perturbation method and the method of moment. Subsequently, the model is applied to two cases of layered sea ice to study the effect of subsurface scattering. The first case is newly formed sea ice which has scattering from both air–ice and ice–water interfaces. It is found that the backscattering has a strong oscillation with the variation of sea ice thickness. The found oscillation effects can increase the difficulty of retrieving the thickness of newly formed sea ice from the backscattering data. The second case is first-year sea ice with C-shaped salinity profiles. The scattering model accounts for the variations in the salinity profile by approximating the profile as consisting of a number of homogeneous layers. It is found that the salinity profile variations have very little influence on the backscattering for both C- and L-bands. The results show that the sea ice can be considered to be homogeneous with a constant salinity value in modelling the backscattering and it is difficult to sense the salinity profile of sea ice from the backscattering data, because the backscattering is insensitive to the salinity profile.

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