Integral Operators in Crack Problems and their Perturbations in the Direction of the Crack Extension [PDF]
, 1991 The perturbation, in the direction of the crack extension, of the elastostatic hypersingular integral operator for crack problems is calculated rigorously. A variational form including this perturbation is written in terms of the energy release rate. The
NISHIMURA, Naoshi, OHTSUKA, Kohji
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Optimal operator preconditioning for Galerkin boundary element methods on 3-dimensional screens
, 2020 We consider first-kind weakly singular and hypersingular boundary integral operators for the Laplacian on screens in R3 and their Galerkin discretization by means of low-order piecewise polynomial boundary elements.
Jerez-Hanckes, C +2 more
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Hierarchical bases on the standard and dual graph for stable solutions of the EFIE operator
, 2014 International audienceThis paper presents a dual generalized Haar basis for the electric field integral equation (EFIE) that regularizes the vector and the scalar potential on structured and unstructured meshes.
Andriulli, Francesco +5 more
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About Some Boundary Integral Operators on the Unit Disk Related to the Laplace Equation
, 2017 International audienceWe introduce four integral operators related to the Laplace equation in three dimensions on the circular unit disk. Two of them are related to the weakly singular operator and the other two are related to the hypersingular operator.
Nédélec, Jean-Claude +3 more
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The Rate of Convergence of Hypersingular Equations Numerical Computation
, 2018 Numerical methods for solving hypersingular equations based on Chebyshev polynomials of the second kind with a weight taking into account the Meixner physical conditions on the edge are developed.
Eminov, S. I., Petrova, S. Yu.
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Some generalizations of the hypersingular integral operators [PDF]
Studia Mathematica, 1973 openaire +2 more sources
MESH-INDEPENDENT OPERATOR PRECONDITIONING FOR BOUNDARY ELEMENTS ON OPEN CURVES
, 2014 Boundary value problems for the Poisson equation in the exterior of an open bounded Lipschitz curve C can be recast as first-kind boundary integral equations featuring weakly singular or hypersingular boundary integral operators (BIOs).
Hiptmair, Ralf +2 more
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Advanced materials modelling via fractional calculus: challenges and perspectives. [PDF]
Philos Trans A Math Phys Eng Sci, 2020 Failla G, Zingales M.
europepmc +1 more source
Integral equation formulations of exterior acoustic scattering problems [PDF]
The work presented in this thesis is particularly concerned with a robust integral equation formulation of acoustic scattering and radiation problems, which are essentially exterior Neumann boundary-value problems.
Zaman, S. I.
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Additive Schwarz Methods for Integral Equations of the First Kind
, 2007 This paper gives a survey on additive Schwarz methods applied to the h and p versions of the boundary element method. We consider weakly singular and hypersingular integral equations, namely the single layer potential operator and the normal derivative ...
Ernst P. Stephan
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