# 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}
}```
• Published 5 November 2017
• Mathematics
• Przegląd Elektrotechniczny
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
2 Citations

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#### References

SHOWING 1-10 OF 13 REFERENCES
Solving Boundary Integral Problems with BEM++
• Computer Science, Mathematics
• ACM Trans. Math. Softw.
• 2015
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
• Mathematics
• 2013
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
• Mathematics
• 1989
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.
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
• Physics
• IEEE Transactions on Magnetics
• 2008
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
• Physics
• 2017
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