Hypersingular boundary integral equations have an additional free term
Computational Mechanics, 1995 In this paper it is shown that hypersingular boundary integral equations may have an additional free term which has been erroneously omitted in former ...
M Guiggiani
exaly +2 more sources
Semi Bounded Solution of Hypersingular Integral Equations of the First Kind on the Rectangle
, 2020 A hypersingular integral equations (HSIEs) of the first kind on the interval [ 1 ; 1 ] with the assumption that kernel of the hypersingular integral is constant on the diagonal of the domain is considered. Truncated series of Chebyshev polynomials of the
Z. Eshkuvatov +4 more
semanticscholar +2 more sources
On Fredholm property of hypersingular integral operators in special classes of functions
Известия высших учебных заведений. Поволжский регион: Физико-математические наукиBackground. Hypersingular integral equations on a segment that arise in many issues of mathematical physics are considered. Materials and methods. Hypersingular equations are studied in special classes of functions, which are represented by Fourier ...
Yu.G. Smirnov
doaj +2 more sources
The Modified Trapezoidal Rule for Computing Hypersingular Integral on Interval
Journal of Applied Mathematics, 2013 The modified trapezoidal rule for the computation of hypersingular integrals in boundary element methods is discussed. When the special function of the error functional equals zero, the convergence rate is one order higher than the general case.
Jin Li, Xiuzhen Li
doaj +2 more sources
Volume integration in the hypersingular boundary integral equation
Engineering Analysis with Boundary Elements, 2013 The evaluation of volume integrals that arise in conjunction with a hypersingular boundary integral formulation is considered. In a recent work for the standard (singular) boundary integral equation, the volume term was decomposed into an easily computed
Andress, James, Ye, Wenjing, Gray, L. J.
core +4 more sources
Solution of a hypersingular integral equation of the second kind
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1997 A straightforward analysis involving the complex function-theoretic method is employed to determine the closed-form solution of a special hypersingular integral equation of the second kind, and its known solution is ...
Mandal, BN +3 more
core +2 more sources
Direct Evaluation of Hypersingular Galerkin Surface Integrals
SIAM Journal on Scientific Computing, 2004 A direct algorithm for evaluating hypersingular integrals arising in a threedimensional Galerkin boundary integral analysis is presented. By integrating two of the four dimensions analytically, the coincident integration, defined as a limit to the ...
L. J. Gray, J. M. Glaeser, T. Kaplan
core +3 more sources
A Unified Trapezoidal Quadrature Method for Singular and Hypersingular Boundary Integral Operators on Curved Surfaces [PDF]
SIAM Journal on Numerical Analysis, 2022 This paper describes a trapezoidal quadrature method for the discretization of singular and hypersingular boundary integral operators (BIOs) that arise in solving boundary value problems for elliptic partial differential equations.
Bowei Wu, P. Martinsson
semanticscholar +1 more source
An integration by parts formula for the bilinear form of the hypersingular boundary integral operator for the transient heat equation in three spatial dimensions [PDF]
Journal of Integral Equations and Applications, 2021 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,
R. Watschinger, G. Of
semanticscholar +1 more source
Water wave scattering by a thin vertical submerged permeable plate
Mathematical Modelling and Analysis, 2021 An alternative approach is proposed here to investigate the problem of scattering of surface water waves by a vertical permeable plate submerged in deep water within the framework of linear water wave theory.
Rupanwita Gayen +2 more
doaj +1 more source