Results 11 to 20 of about 145 (135)
Advances in Mathematical Physics, Volume 2023, Issue 1, 2023., 2023 In this study, the Fredholm hypersingular integral equation of the first kind with a singular right‐hand function on the interval [−1, 1] is solved. The discontinuous solution on the domain [−1, 1] is approximated by a piecewise polynomial, and a collocation method is introduced to evaluate the unknown coefficients. This method, which can be applied to
M. R. Elahi +4 more
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Advances in Mathematical Physics, 2021 We present a fast and accurate numerical scheme for approximating hypersingular integrals with highly oscillatory Hankel kernels. The main idea is to first change the integration path by Cauchy’s theorem, transform the original integral into an integral ...
Qinghua Wu, Mengjun Sun
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Rapid Methods for the Resolution of Contact Problems in Static Linear Elasticity
Mathematical Problems in Engineering, Volume 2023, Issue 1, 2023., 2023 In this paper, the two‐dimensional Signorini static contact problem in linear elasticity is presented. We present the weak formulation of the frictional contact problems, and the boundary integral operators are used to propose a boundary variational formulation whose resolution by the generalized Newton method is presented.
Laurent Tchoualag +3 more
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Div–curl problems and H1‐regular stream functions in 3D Lipschitz domains
Mathematical Methods in the Applied Sciences, Volume 45, Issue 3, Page 1097-1117, February 2022., 2022 We consider the problem of recovering the divergence‐free velocity field U ∈ L2(Ω) of a given vorticity F=curlU on a bounded Lipschitz domain Ω⊂ℝ3. To that end, we solve the ‘div–curl problem’ for a given F ∈ H−1(Ω). The solution is expressed in terms of a vector potential (or stream function) A ∈ H1(Ω) such that U=curlA. After discussing existence and
Matthias Kirchhart, Erick Schulz
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Вісник Харківського національного університету імені В.Н. Каразіна. Серія: Математичне моделювання, інформаційні технології, автоматизовані системи управління, 2020 To study the frequencies and modes of vibrations of a circular plate immersed in a liquid, a new approach has been developed. The technic is based on the use of hypersingular integral equations and the method of prescribed shapes.
Ivan Vierushkin, Elena Strelnikova
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Exact Solutions of the 3D Fractional Helmholtz Equation by Fractional Differential Transform Method
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 In this work, we applied the fractional reduced differential transform method (FRDTM) to find the exact solutions of the three‐dimensional fractional Helmholtz equation (FHE) and compared our outcomes with the tenth‐order approximate solutions for diverse fractional orders.
Saleh Alshammari +2 more
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ARGOS: An adaptive refinement goal‐oriented solver for the linearized Poisson–Boltzmann equation
Journal of Computational Chemistry, Volume 42, Issue 26, Page 1832-1860, October 5, 2021., 2021 An adaptive refinement goal oriented solver (ARGOS) of the linearized Poisson–Boltzmann equation for the calculation of the electrostatic interaction between molecules is developed and tested. It can efficiently handle discontinuous dielectric coefficients, singular charge densities, and the complicated geometry of molecular domains in three spatial ...
Svetoslav Nakov +3 more
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IET Microwaves, Antennas &Propagation, Volume 15, Issue 10, Page 1159-1170, 12 August 2021., 2021 Abstract Considered is the plane‐wave scattering from and absorption by a thin circular dielectric disk. The analysis uses a set of the singular integral equations for the effective electric and magnetic currents, derived using the generalized boundary conditions on the disk median section.
Mario Lucido +2 more
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Journal of Inequalities and Applications, 2020 Hypersingular integrals have appeared as effective tools for inversion of multidimensional potential-type operators such as Riesz, Bessel, Flett, parabolic potentials, etc.
Melih Eryiğit +2 more
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A generalized method for scattering from wide cavities with specified wave functions
IET Microwaves, Antennas &Propagation, Volume 15, Issue 1, Page 69-79, 8 January 2021., 2021 Abstract This study developed a generalized solution based on modal expansion for scattering by large cavities with known wave functions placed in an infinite perfect electric plane. Under the assumption of a large cavity, to reduce simulation time and simplify expressions, the half‐space above cavity with a strong singular Green's function is ...
Mehdi Bozorgi
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