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Approximate solution for a class of hypersingular integral equations
Applied Mathematics Letters, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
B N Mandal
exaly +2 more sources
A General Algorithm for the Numerical Solution of Hypersingular Boundary Integral Equations
Journal of Applied Mechanics, Transactions ASME, 1992 The limiting process that leads to the formulation of hypersingular boundary integral equations is first discussed in detail. It is shown that boundary integral equations with hypersingular kernels are perfectly meaningful even at non-smooth boundary points, and that special interpretations of the integrals involved are not necessary.
M Guiggiani, T J Rudolphi, F J Rizzo
exaly +6 more sources
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
wiley +1 more source
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
wiley +1 more source
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
wiley +1 more source
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
wiley +1 more source
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
wiley +1 more source
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
wiley +1 more source
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
wiley +1 more source
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
wiley +1 more source