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Approximate methods for calculating hypersingular integrals
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2021 Background. Hypersingular integrals are now finding more and more fields of application – aerodynamics, elasticity theory, electrodynamics and geophysics.
I.V. Boykov, P.V. Aykashev
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Boundary regularized integral equation formulation of the Helmholtz equation in acoustics [PDF]
Royal Society Open Science, 2015 A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically.
Qiang Sun +3 more
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Axioms, 2022 The article is devoted to the issue of construction of an optimal with respect to order passive algorithms for evaluating Cauchy and Hilbert singular and hypersingular integrals with oscillating kernels.
Vladimir Roudnev, Alla Boykova
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Regular, Singular and Hypersingular Integrals over Fractal Contours
Mathematics, 2023 The paper is devoted to the approximate calculation of Riemann definite integrals, singular and hypersingular integrals over closed and open non-rectifiable curves and fractals.
Vladimir Roudnev, Alla Boykova
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Hypersingular integrals at a corner [PDF]
Engineering Analysis With Boundary Elements, 1993 Abstract For a smooth boundary, hypersingular integrals can be defined as a limit from the interior, the approach direction being taken, for convenience, normal to the surface. At a boundary corner, the limit process, with a necessarily non-normal approach direction, provides a valid definition of the hypersingular equation, as long as the same ...
L J Gray, Lisa L Manne
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Researches in Mathematics, 2020 We introduce a family of Balakrishnan-Rubin type hypersingular integrals depending on a parameter $\varepsilon $ and generated by the Generalized Poisson semigroup.
S.E. Sinem, E. Melih, Ç. Selim
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IET Microwaves, Antennas &Propagation, Volume 17, Issue 4, Page 301-312, March 2023., 2023 The modal analysis of rectangular dielectric resonators are addressed using different combined surface integral equations (T‐Muller, N‐Muller, PMCHWT, and TENENH). All developed formulations are discretised through the method of moments with rooftop basis functions over flat quadrilaterals represented as bilinear surfaces, with razor‐blade functions ...
Moein Nazari +3 more
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Journal of Geophysical Research: Solid Earth, Volume 128, Issue 2, February 2023., 2023 Abstract Geothermal energy, featured as a renewable low‐carbon energy resource, exhibits great potential in mitigating global warming. However, efficient mining of geothermal energy from hot dry rock remains challenging due to the lack of a thermoporoelastic modeling approach that allows for integrated simulation of hydrofracturing and fluid ...
Sanbai Li, Dongxiao Zhang
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Boundedness on Hardy-Sobolev Spaces for Hypersingular Marcinkiewicz Integrals with Variable Kernels
Journal of Inequalities and Applications, 2008 The existence and boundedness on Sobolev spaces and Hardy-Sobolev spaces for the hypersingular Marcinkiewicz integrals with variable kernels are derived.
Songyan Zhang, Xiao Yu, Xiangxing Tao
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Windowed Green function method for wave scattering by periodic arrays of 2D obstacles
Studies in Applied Mathematics, Volume 150, Issue 1, Page 277-315, January 2023., 2023 Abstract This paper introduces a novel boundary integral equation (BIE) method for the numerical solution of problems of planewave scattering by periodic line arrays of two‐dimensional penetrable obstacles. Our approach is built upon a direct BIE formulation that leverages the simplicity of the free‐space Green function but in turn entails evaluation ...
Thomas Strauszer‐Caussade +3 more
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