Nystrom method for the Muller boundary integral equations on a dielectric body of revolution: axially symmetric problem

2015 ◽  
Vol 9 (11) ◽  
pp. 1186-1192 ◽  
Author(s):  
Vitaliy S. Bulygin ◽  
Yuriy V. Gandel ◽  
Ana Vukovic ◽  
Trevor M. Benson ◽  
Phillip Sewell ◽  
...  
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Body Of Revolution ◽  
Symmetric Problem ◽  
Axially Symmetric ◽  
Dielectric Body ◽  
Nyström Method ◽  
Nystrom Method

The method of hypersingular integral equations in the problem of electromagnetic wave diffraction by a dielectric body with a partial perfectly conducting coating

2017 ◽  
Vol 32 (6) ◽  
Author(s):  
Alexey V. Setukha ◽  
Elizaveta N. Bezobrazova
Keyword(s):  
Electromagnetic Wave ◽  
Integral Equations ◽  
Numerical Scheme ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
The Body ◽  
Dielectric Body ◽  
Piecewise Constant ◽  
Conducting Coating ◽  
Monochromatic Electromagnetic Wave

AbstractA problem of scattering of a monochromatic electromagnetic wave by a homogeneous dielectric body is considered. A part of the boundary of the body is a perfectly conducting thin surface. The problem is reduced to a system of the boundary integral equations containing integrals with strong singularity, the integrals are understood in terms of Hadamard final part. A numerical solution scheme is constructed on the base of approximate solution of these equations using the methods of piecewise-constant approximations and collocation. The constructed numerical scheme is tested on a model example.

scholarly journals APPLICATION OF THE METHOD OF BOUNDARY INTEGRAL EQUATIONS FOR NON-STATIONARY PROBLEM OF THERMAL CONDUCTIVITY IN AXIALLY SYMMETRIC DOMAIN

2017 ◽  
Vol 1 ◽  
pp. 61-68
Author(s):  
Grigoriy Zrazhevsky ◽  
Vera Zrazhevska
Keyword(s):  
Thermal Conductivity ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Symmetric Domain ◽  
Singular Integral Equations ◽  
Initial Boundary ◽  
Boundary Integral ◽  
Fourier Series Expansion ◽  
Axially Symmetric ◽  
Initial Boundary Problem

The article considers the non-stationary initial-boundary problem of thermal conductivity in axially symmetric domain in Minkowski space, formulated as equivalent boundary integral equation. Using the representation of the solution in the form of a Fourier series expansion, the problem is reformulated as an infinite system of two-dimensional singular integral equations regarding expansion coefficients. The paper presents and investigates the explicit form for fundamental solutions used in the integral representation of the solution in the domain and on the border. The obtained results can be used in the construction of efficient numerical boundary element method for estimation of structures behavior under the influence of intense thermal loads in real-time.

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