Numerical calculation of singular integrals for different formulations of Boundary Element

@article{Sikora2017NumericalCO,
  title={Numerical calculation of singular integrals for different formulations of Boundary Element},
  author={J S Sikora and Krzysztof Polakowski and Beata Pańczyk},
  journal={Przegląd Elektrotechniczny},
  year={2017},
  volume={1},
  pages={183-187}
}
This paper presents a method of regularization for the numerical calculation of singular integrals used in different formulations of Boundary Element Method. The singular integrals arise when elements of order higher than zero are used for discretization. Very often in the Diffusive Optical Tomography for infant head modeling, triangular or square curvilinear boundary elements of the second order are used hence, our interest in the subject of effective and accurate calculation of singular… Expand

Figures and Tables from this paper

Quadrature Rules for Functions with a Mid-Point Logarithmic Singularity in the Boundary Element Method Based on the x = tp Substitution
Quadrature rules for evaluating singular integrals that typically occur in the boundary element method (BEM) for two-dimensional and axisymmetric threedimensional problems are considered. This paperExpand
The Boundary Element Method in Acoustics: A Survey
  • Kirkup
  • Engineering
  • Applied Sciences
  • 2019
The boundary element method (BEM) in the context of acoustics or Helmholtz problems is reviewed in this paper. The basis of the BEM is initially developed for Laplace’s equation. The boundaryExpand

References

SHOWING 1-10 OF 13 REFERENCES
Solving Boundary Integral Problems with BEM++
TLDR
BEM++ is a novel open-source library for the solution of boundary integral equations for Laplace, Helmholtz and Maxwell problems in three space dimensions and is a C++ library with Python bindings for all important features, making it possible to integrate the library into other C++ projects or to use it directly via Python scripts. Expand
Calculation of the improper integrals for Fourier boundary element method
Abstract. The traditional Boundary Element Method (BEM) is a collection of numerical techniques for solving some partial differential equations. The classical BEM produces a fully populatedExpand
The regularising transformation integration method for boundary element kernels. Comparison with series expansion and weighted Gaussian integration methods
Abstract The paper is concerned with singular integrands arising from three dimensional potential problems in the Boundary Element Method. These consist of the product of a shape function, a JacobianExpand
Diffuse photon propagation in multilayered geometries.
TLDR
This paper presents solutions for the multilayered diffuse light propagation for a three-layer concentric sphere model using a series expansion method and for a general layered geometry using the boundary element method (BEM) and results are presented comparing these solutions to an independent Monte Carlo model. Expand
Optical tomography in medical imaging
We present a review of methods for the forward and inverse problems in optical tomography. We limit ourselves to the highly scattering case found in applications in medical imaging, and to theExpand
Substructuring Methods for 3-D BEM Multilayered Model for Diffuse Optical Tomography Problems
Diffuse optical tomography (DOT) is an emerging functional medical imaging modality with aims to recover the optical properties of biological tissue. The forward problem of the light propagation ofExpand
BOUNDARY ELEMENT METHOD MODYFICATIONS FOR USE IN SOME IMPEDANCE AND OPTICAL TOMOGRAPHY APPLICATIONS
The article presents two elements associated with the practice of application of the boundary element method. The first is associated with BEM ability to analyze an open boundary objects andExpand
Tomography Visualization Methods for Monitoring Gases in the Automotive Systems
Taking into consideration growing ecology and safety demands, there are a need for more accurate and cheaper ways to monitor workflows of gases, which can be used in automotive applications. SuchExpand
Preparation of Papers for Publication in IEEE Transactions on Consumer Electronics
  • IEEE Transactions on Consumer Electronics
  • 2006
The downloaded document is a template for Microsoft Word versions 6.0 or later. Please download the electronic template from http://ewh.ieee.org/soc/ces/papersub.html to prepare your manuscript. ReadExpand
Open source BEM library
This article presents the project of the new open source boundary element method library. It discusses main goals of the project and its characteristics consistent with the 'good open sourceExpand
...
1
2
...