Results 41 to 50 of about 1,219,987 (236)
Approximate methods for calculating hypersingular integrals
University proceedings. Volga region. Physical and mathematical sciences, 2021 Background. Hypersingular integrals are now finding more and more fields of application – aerodynamics, elasticity theory, electrodynamics and geophysics. Moreover, their calculation in an analytical form is possible only in very special cases. Therefore, approximate methods for calculating hypersingular integrals are an urgent problem in computational
I.V. Boykov, P.V. Aykashev
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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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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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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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Hypersingular Integral Equations of Prandtl’s Type: Theory, Numerical Methods, and Applications
Axioms, 2022 In this paper, we propose and justify a spline-collocation method with first-order splines for approximate solution of nonlinear hypersingular integral equations of Prandtl’s type.
Ilya Boykov +2 more
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Scattering by thin shells in fluids: Fast solver and experimental validation [PDF]
JASA Express Letters, 2021 A numerical model facilitating fast analysis of acoustic scattering by thin shells immersed in fluids is presented. The shell is simulated by an effective boundary condition, in which the inertial properties of the shell are taken into account while the ...
Evgeny Chernokozhin +2 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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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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Computer Assisted Methods in Engineering and Science, 2017 Singular and hypersingular integral equations appear frequently in engineering problems. The approximate solution of these equations by using various numerical methods is well known.
Nikolaos I. Ioakimidis
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