Ultra-weak Formulation of a Hypersingular Integral Equation on Polygons and DPG Method with Optimal Test Functions [PDF]
SIAM Journal on Numerical Analysis, 2013 We present an ultra-weak formulation of a hypersingular integral equation on closed polygons and prove its well-posedness and equivalence with the standard variational formulation.
N. Heuer, Felipe Pinochet
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Computing methods of hypersingular integral applied to eddy-current testing
, 2002 International audienceThe detection of thin-opening cracks is an important part of the eddy-current nondestructive testing (NDT). The integral formulation is well adapted for this modelization if the geometry of the tested piece is simple.
Burais, Noël, Beltrame, Philippe
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Multi-Component BEM for the Helmholtz Equation: A Normal Derivative Method
Shock and Vibration, 2012 We describe a multi-component boundary element method for predicting wave energy distributions in a complex built-up system with material properties changing discontinuously at boundaries between sub-components.
H.A.M. Ben Hamdin, G. Tanner
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BPX Preconditioner for Hypersingular Integral Equations
Journal of Integral Equations and Applications, 1998 The BPX preconditioner [cf. \textit{J. H. Bramble, J. E. Pasciak} and \textit{J. Xu}, Math. Comput. 55, No. 191, 1-22 (1990; Zbl 0703.65076)] for the Galerkin approximation of hypersingular integral equations is presented. The condition number of the preconditioned matrix is shown to behave as \(O(h^{-\varepsilon})\) where \(\varepsilon\) is small and ...
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Transformation of hypersingular integrals and black-box cubature [PDF]
Mathematics of Computation, 2000 In this paper, we will consider hypersingular integrals as they arise by transforming elliptic boundary value problems into boundary integral equations. First, local representations of these integrals will be derived. These representations contain so-called finite-part integrals.
Sauter, S A, Lage, C
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QUADRATURE FORMULAS WITH MULTIPLE NODES FOR THE HILBERT HYPERSINGULAR INTEGRAL [PDF]
, 2017 Для гиперсингулярного интеграла Гильберта построены и исследованы квадратурные формулы с кратными узлами.For the Hilbert hypersingular integral quadrature formulas with multiple nodes are constructed and studied.334 ...
Солиев Ю.С.
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Taming hypersingular integrals using dimensional continuation
Physical Review E, 2012 We use the method of dimensional continuation to isolate singularities in integrals containing products of Green's functions or their derivatives. Rules for the extraction of the finite part of so-called hypersingular integrals are developed, which should be useful in methods based on boundary integral techniques in science and engineering.
Zehao, Li, L R, Ram-Mohan
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Effective semi-analytic integration for hypersingular Galerkin boundary integral equations for the Helmholtz equation in 3D [PDF]
, 2014 summary:We deal with the Galerkin discretization of the boundary integral equations corresponding to problems with the Helmholtz equation in 3D. Our main result is the semi-analytic integration for the bilinear form induced by the hypersingular operator.
Zapletal, Jan, Bouchala, Jiří
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A Comprehensive Review of Boundary Integral Formulations of Acoustic Scattering Problems
Sultan Qaboos University Journal for Science, 2000 This is a review presenting an overview of the developments in boundary integral formulations of the acoustic scattering problems. Generally, the problem is formulated in one of two ways viz.
S.I. Zaman
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Dual boundary element method for axisymmetric crack analysis
, 2002 In this paper a dual boundary element formulation is developed and applied to the evaluation of stress intensity factors in, and propagation of, axisymmetric cracks.
Wrobel, LC, Lacerda, LA
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