Results 11 to 20 of about 186 (123)
A rough hypersingular integral operator with an oscillating factor
Journal of Mathematical Analysis and Applications, 2006 Let \(W_\alpha^p({\mathbb R}^n)\) be the homogeneous Sobolev space and let \(H^r({\mathbb S}^{n-1})\) be the Hardy space on the unit sphere \({\mathbb S}^{n-1}\). Denote by \(\langle\Omega,\phi\rangle\) the pairing between a distribution \(\Omega\) and a \(C^\infty\)-function \(\phi\) on \({\mathbb S}^{n-1}\).
Chen, Daning, Fan, Dashan, Le, Hung Viet
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Journal of Integral Equations and Applications, 2022 While an integration by parts formula for the bilinear form of the hypersingular boundary integral operator for the transient heat equation in three spatial dimensions is available in the literature, a proof of this formula seems to be missing. Moreover, the available formula contains an integral term including the time derivative of the fundamental ...
Raphael Watschinger, Günther Of
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Comput. Math. Appl., 2014 We propose and analyze an overlapping Schwarz preconditioner for the $p$ and $hp$ boundary element method for the hypersingular integral equation in 3D. We consider surface triangulations consisting of triangles. The condition number is bounded uniformly in the mesh size $h$ and the polynomial order $p$.
Thomas Führer +3 more
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Kolmogorov-type inequalities for hypersingular integrals with homogeneous characteristics
Researches in MathematicsIn this article we obtain sharp Kolmogorov-type inequalities that estimate the uniform norm of a hypersingular integral operator $$ D^{w,\Omega}_K f(x): = \int_{C} w(|t|_K) (f(x+t) - f(x))\Omega(t)dt, x\in C, $$ using the uniform norm of the ...
V.F. Babenko +2 more
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Journal of Inequalities and Applications, 2011 Let , the authors introduce in this paper a class of the hypersingular Marcinkiewicz integrals along surface with variable kernels defined by , where with .
Ruiying Wei, Yin Li
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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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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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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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