# 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

by R Jeans Cited by 2 This study is concerned with innovative methods for the solution of A variational boundary element formulation of the acoustic problem with a novel solution to numerically approximate the highly singular integral velocity potential difference across thin shell off 6.1 Representation of plate problem

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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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2.5.2 Weakly non-uniform flow potential wave equation 6.5.1.3 Analysis of the results 4.6 Schematic representation of the weakly-coupled approach; scattering of a flow [31, 32, 33, 34] and mean flow with small velocity gradient [35, 36]. treatment of hyper-singular integrals developed by the boundary element

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space representations of spherical harmonics expansion (SE) based multilevel fast multipole 4.4.1 Geometrical Configuration for Near Singular Integrals 42.

### ICES REPORT 15-12 Isogeometric Analysis of Boundary

by M Taus 2015 Isogeometric analysis is applied to boundary integral equations They involve the representation formula that allows one to determine where (∇T u)(x) is the tangential gradient of u on Γ. With this approximation, the hyper-singular scheme is critical for numerical integration for CAD parametrizations.

### Electrohydrodynamics of Particles and Drops in Strong

C.2 Regularisation of hypersingular integral the drop electrohydrodynamics boundary element problem. The rigorous course and research work at University particle than outside, and if the electric field strength exceeds a critical value Ec Taking the dot product of Eq. (2.29) with the local potential gradient ∇φe

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by GO Ribeiro 2009 Cited by 13 1Dealing with singular integrals, including strongly-singular. (Cauchy principal value standard, or the hypersingular boundary integral equations, respectively. gradient of the integral representation for the potential at the interior point y, followed So the analysis using quadratic element is the most critical with regard to

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by JT Katsikadelis 2003 Cited by 19 discretization and the integration are restricted on the boundary. Therefore [9] 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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by L Desiderio 2017 Cited by 5 tion, Randomized Singular Value Decomposition, 3D Elastodynamics, Forced Vi- 1.3.1 Integral Representation and Boundary Integral Equation 22 propagation in complex media is crucial for many topics going from understanding the This tragic event was the starting point of the pioneering studies of John.

### Modelling Surface Waves using the Hypersingular Boundary

by A Farooq 2013 1.2 The Boundary Element Method 3 Hypersingular Boundary Integral Equation. 88 2.14 Co-ordinate system used for the analysis of Rayleigh wave propa- concludes with a possible application of surface waves in the pressure die casting Integral equation representations of boundary value problems gener-.

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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.

### Contribution to Integral Equation Techniques for - Infoscience

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

### Boundary integral equation method for electromagnetic and

by K Chen 2016 Cited by 2 In this thesis, the boundary integral equation method (BIEM) is studied and applied singularity subtraction scheme are proposed for performing singular and nearly researchers relied highly on their analytic skills to solve those models, which power dissipation, significant delay to critical paths, and noise and jitter to

### APPLICATION OF NYSTRÖM METHOD FOR THE SOLUTION

by G SELÇUK 2014 4.4.2 Bicubic Spline Representation of Surface Function 64 with evaluation of weakly singular and strongly singular integrals is extensive, few studies address evaluation of hypersingular integrals for the solution of The method is employed for the solution of frequency-domain boundary value

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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

### Regularized integral equation methods for elastic scattering

by OP Bruno 2020 Cited by 6 boundary integral methods only require discretization of the tials [21], which ensures the validity of the critical property of unique solvability; the resulting integral which result in strongly singular and hyper-singular kernels, representation leading to a hyper-singular integral operator is used [2,20].

### UNIVERSITY OF CINCINNATI - ETD (OhioLINK)

by X Chen Cited by 2 1.2 A Brief Review of the Boundary Element Method representation called boundary integral equations (BIE) and then the problem is solved are the issues of singular and nearly-singular integrals, possible very critical for the BEM application in advanced materials, since 39:Temperature Gradient.

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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

### Boundary element methods for earthquake - EarthArXiv

by TB Thompson 2019 Cited by 4 A wide range of studies of fault slip and earthquake mechanics have cal integration of the hypersingular (O(1/r3)) divergent integrals in most BEM formulations. 73 the strongly nonlinear effects of nonplanar fault and Earth surface geometry on Critically, the traction on the fault surface does not appear in equation (4).

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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.

### ICES REPORT 15-12 Isogeometric Analysis of Boundary

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.

### The boundary integral method for magnetic billiards - Uni-DUE

by K Hornberger 2000 Cited by 29 We introduce a boundary integral method for two-dimensional quantum billiards in particular at strong fields and semiclassical values of the magnetic length. It involves the regular Green function in the position space representation. We of dealing with singular (and possibly even hypersingular [19]) operators.

### Durham E-Theses - CORE

by R SIMPSON Cited by 5 Boundary Element Method to allow accurate analysis of 2D crack problems. The following project would not be possible without the generous funding 4.4 Strongly singular and hypersingular integrals for models which are linear elastic and exhibit high stress gradients, the BEM is an (b)3D representation of point.

### Evaluation of supersingular integrals: second-order boundary

by MNJ Moore 2007 Cited by 21 The boundary integral representation of second-order derivatives of the primary derivatives on the boundary, e.g. the potential gradient or stress tensor. boundary limit scheme, the gradient hypersingular integral in Equation (1) J. A critical study of hypersingular and strongly singular boundary integral.

### A critical study of hypersingular and strongly singular

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.

### Boundary Integral Analysis for the Non-homogeneous 3D

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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by R Hiptmair Cited by 3 isogeometric analysis in electromagnetism by R. Vazquez, page 506. Looking with boundary integral equation methods hold exciting promises (see the contri- [4] McLean, W. Strongly elliptic systems and boundary integral equations. the contribution [21] relies on use of first kind (singular or hypersingular) integral.

### A BOUNDARY ELEMENT APPROACH TO ACOUSTIC

by R Visser 2004 Cited by 60 This study adopts the Helmholtz integral equation as a basis for modeling acoustic particle acceleration is proportional to the gradient of the pressure: ation of the singular parts is possible without increasing the number of degrees the radiating boundary to circumvent the hypersingular behavior.

### Recent Advances and Emerging Applications of the Boundary

by YJ Liu 2011 Cited by 158 dealing with the singular and hypersingular integrals in the BIEs. Ten representative domain V with boundary S, we obtain the following representation integral: scale, critical research and industrial problems using the advanced. BEM are constitutive behaviors, evolving domains, strong gradients and.

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The study has This latter choice is therefore a crucial factor in the MoM. ment - boundary integral (FE-BI) [43] 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.

### Chapter 4 Boundary Element Method for Multi-Region

by XW Gao 1999 Cited by 8 developed, for accurate evaluation of the strongly singular domain integrals pertaining to interior 4.2.2 Traction Representation of System Equations In general, it is not possible to obtain analytical solutions for stress analysis of practical Regularization of hypersingular boundary integral equations is described by.

### Applications of the MLPG Method in Engineering & Sciences

MLPG method, and thus, several trends and ideas for future research interest are boundary integral equation (LBIE) method [Zhu, Zhang and Atluri (1998); Atluri tra and Ching (2002)] or solutions of non-hyper-singular traction and The strong formulation for tor Ek is defined as a negative gradient of electric potential.

### Analysis of hypersingular residual error estimates in boundary

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

### Numerical-asymptotic boundary integral methods - CentAUR

by S Chandler-Wilde 2012 Cited by 198 analysis and numerical analysis of highly oscillatory boundary integral op- erators and on mann data can be obtained, for example, by solving the combined potential (acoustic) adjoint double-layer operator and the (acoustic) hypersingular The singular critical points are evaluated via a rotation and translation pro-.

### FUNDAMENTAL SOLUTION BASED NUMERICAL METHODS

by CY Lee 2016 I greatly acknowledge the generous University Research method of fundamental solutions (MFS), the boundary element method (BEM) and Chapter 4 Evaluation of hypersingular line integral by complex-step derivative 1: Schematic representation of a 2D section of possible computational domain 28.

### Galerkin Boundary Integral Analysis for the 3D Helmholtz

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-.

### The Boundary Element Method in Acoustics: A Survey

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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by C Karadogan 2005 Cited by 2 Historical development of the Boundary integral equation methods. 18 DRBEM analysis of the Axisyninietric transient heat conduction critical change in their amount may cause While the problem representation in terms of partial differential equations They include: regular, near singular, weakly singular, strongly.

### 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.

### Durham Research Online

by Y Gong 2019 Cited by 14 Hybrid nearly singular integration for isogeometric boundary element Since CAD and BEM both require only a boundary representation the methods have been used for elasticity problems [41 43] and potential problems [44]. arises from the strongly singular nature of the integral of the flux kernel,

### Boundary Integral Evaluation of Surface - CiteSeerX

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.

### Boundary element solutions for broad-band 3-D geo

by Z Ren 2013 Cited by 24 hill model was used to study the effects of displacement currents in the radio- The surface integral methods contain weak, strong or even hyper singular The potential field will satisfy the inhomogeneous scalar Helmholtz equation Such a representation shows that the electromagnetic fields inside a homogeneous.

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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.

### On a critical appreciation of the hyper-singular boundary

by S Guimaraes 1970 Cited by 3 ABSTRACT. The present paper discusses the application of the hyper- singular boundary integral equation, the so called traction formulation, to solve Linear

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by B Zinser 2016 the hyper-singular integrals are computed using an interpolated quadrature sphere's boundary when z = 0 and the charge is inside the sphere at protein depends greatly on the complicated geometry and the electrostatic potential On the other hand, for the study of colloidal media involv- its integral representation.

### ANALYSIS OF ITERATIVE METHODS FOR THE SOLUTION

by C Ke 1989 Chcii Ke. This thesis is concerned with the numerical solution of boundary integral equa- tions and the 4 Conjugate Gradient Method for Smooth Integral Equations. 74 mental solution of Helrnlioltz equation, will play a crucial rolo. Note that the operator Nk defined in (1.20) is hyper singular, so its existence can only be

### Fracture Analysis of Piezoelectric Composites - UNSWorks

by C Li 2014 The singular stress and electric displacement fields around a crack tip of piezoelectric materials using the scaled boundary finite element method. 3.3.3 Solutions for displacement and electric potential functions can be aligned using the process of polarizing, by which a strong electric field is Hypersingular BEM for.