A Critical Study Of Hypersingular And Strongly Singular Boundary Integral Representations Of Potential Gradient
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by London, SW7 2BY 1992 - Imperial Spiral - Imperial College
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During the course of his graduate studies at PUC-Rio, he worked as a A Symbolic Computation of Singular Boundary Integrals. 187 derivatives of the potential on the circle x2 + y2 = (0.4)2 interior and the gradient BIE (traction BIE) on the other crack face. is hypersingular, and C0,a if the kernel is strongly singular.
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by JT Katsikadelis 2003 Cited by 19 discretization and the integration are restricted on the boundary. Therefore  Graciani E, Mantic V, Parıs F, Can˜as J. A critical study of hypersingular and strongly singular boundary integral representations of potential gradient. Comput
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Shape Optimization Directly from CAD: an - -ORCA
by H Lian 2015 Cited by 2 structural analysis, and to discretize the material differentiation form of caused by the evaluation of strongly singular integrals and jump possible without his help. A preferred boundary representation should have the capability of ysis is a critical step in gradient-based shape optimization algorithms.
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by GJD Chapman 2005 Cited by 10 A weakly singular integral equation approach for water wave problems of enlightening discussions throughout the course of this study. 5.4.1 Boundary element approach fluid velocity may be written as the gradient of a scalar potential 1. Dimension Weakly singular Strongly singular Hypersingular.
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by S López Peña 2010 Cited by 1 Surface Mixed Potential Integral Equation (MPIE) formulations together with the Method of In second place, a study which allows setting the relationship between invaluable help in the most critical situations during the development of this manuscript. IEs formulated in terms of fields lead to strong singular GF, whereas
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by O Bruno Cited by 1 gives rise to highly-favorable spectral properties thus making it possible to produce accurate tably, boundary integral equations require much smaller discretizations, for a Equations (which result from representations of acoustic fields by means of of double layer potentials, and associated hypersingular kernels and
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4.4 Hypersingular Boundary Integral: Quadratic Element. 93 is moving boundary problems, as the critical surface velocity is often a function of the gradient. A accurate representation of the car surface would demand a highly refined volume mesh, and potentially be highly useful for choosing new trial geometries. Thus
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by LJ Gray 1990 Cited by 76 Keywords: Boundary elements, comers, hypersingular integrals, Laplace A critical discussion of these modifications can term is highly singular, and has been termed hypersingulur and the surface gradient with respect to X is differentiation with respect to z. From the representation of the potential in (2.3), the.
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by M Taus 2015 Cited by 10 Isogeometric analysis is applied to boundary integral equations corresponding for weakly-singular, singular, and hyper-singular integral operators. They involve the representation formula that allows one to determine the solution u scheme is critical for numerical integration for CAD parametrizations.
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by E Graciani 2000 Cited by 19 A critical study of hypersingular and strongly singular boundary integral representations of potential gradient. E. Graciani, V. Manticœ, F. Parı¬s, J. Canƒas.
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by LJ Gray 2018 velocity gradients, and thus an efficient algorithm for post-processing Boundary integral analysis for fluids has primarily involved potential (inviscid irro- putation is clearly very expensive and it involves the hypersingular lar and strongly singular boundary integral representations of potential gradient.
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My initiation on gradient-based optimisation arose from this research stay. sense, the Singular, Hypersingular and Dual Boundary Integral Equations for two- and three- all strongly singular and hypersingular surface integrals to weakly singular surface integrals possible to use the representation provided by the mesh.
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The study has This latter choice is therefore a crucial factor in the MoM. ment - boundary integral (FE-BI)  method that combines differential- and (2.4b). Another useful representation is the mixed-potential form in which both vector Other forms of the EFIE involve both strongly singular and hypersingular integrals.
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hypersingular boundary integral equation to obtain a new solution. One can obtain the gradient of the potential, for points p G B, by differentiation under In this equation, the first integral is strongly singular, and the second one is hypersingular. and similarly for s/( N. Smoothness of the boundary is critical here, and the
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by MR Swager 2010 Cited by 2 evaluation of the (finite) hypersingular Galerkin integral. This limit process is also the basis for the algorithm for post-processing of the surface gradient. A critical aspect in the analysis of the hypersingular kernel is to establish the exis- singular and strongly singular boundary integral representations of potential gradi-.
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by S Kirkup 2019 Cited by 34 Keywords: boundary element method; acoustics; Helmholtz equation where Ψ(p, t) is the scalar time-dependent velocity potential related to the element is the combination the panel and the functional representation. values of the singular and hypersingular integrals in the BEM solution of Laplace's
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APPENDIX A MATHEMATICAL PRELIMINARIES AND
A critical study of hypersingular and strongly singular boundary integral representations of potential gradient. Comp. Mech., 25:542 559, 2000. 107. L. J. Gray.
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by LJ Gray Cited by 26 In a boundary integral analysis, rst order function derivatives, e.g., bound- ary potential gradient or stress tensor, can be accurately computed using a re- Key words. boundary integral method, surface derivatives, hypersingular Integral equations employ a direct representation of the surface and can work directly.
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4 Jul 2014 1.5 Boundary integral equations and representations This Fast Multipole accelerated BEM is then applied to study seismic These effects lead to some (possibly strong) motion amplification and since only the domain boundaries and possible interfaces are discretized. singular element integrals.
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by BZ Lu Cited by 303 developments in boundary element methods, interface methods, adaptive have been produced in this area and directed to studies of diverse biological deed, the quality of the potential near the molecular surface is actually critically depen- evaluation methods for all the strong singular and hypersingular integrals as.
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