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Showing 1 to 11 of 11 for “"Singular integrals"”.
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Martingales, Singular Integrals, and Fourier Multipliers
… <em>Lp</em>-boundedness, 1 < <em>p</em> < ∞, of singular integrals and Fourier multipliers. We will use a combination of analytic and probabilistic methods to study analytic properties of these constructions and obtain results which cannot be obtained using probability alone.</p> <p>In …
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Relations between two classes of singular integrals
… paper in which they discussed a certain kind of singular integral, and used some of their results to establish differential properties of solutions of Poisson's equation. Recently, Jones made some observations on the fundamental solution of the heat equation and gave another class of singular …
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The dual boundary element method applied to semi-infinite surface cracks in two-dimensions
… with these methods are integrations of the singular integrals which cannot be accuartely evaluated via standard Gauss quadrature schemes. An analytical integration scheme has therefore been implemented to overcome this difficulty. The SIFs are recovered as a post-processing step using the …
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Resolução de problemas viscoelásticos utilizando o método dos elementos de contorno
… numerical Gaussian technigues for computing the singular integrals are tested. Here, finite part integration and third degree coordinate transformations are included. For accurate representation of traction discontinuities on the boundary, the so-called interpolated element is tested. ln this …
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Análise elástica bidimensional de problemas com simetria cíclica pelo método dos elementos de contorno
… normal vector or of the boundary variables. Singular integrals are carried out numerically with the use of a cubic transformation of the coordinates. The program developed also permits the analysis of problems presenting simple or double symmetry and, in order to compare the computational …
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Numerical Methods for Simulating Fluid Motion Driven By Immersed Interface
… mesh. We first describe a method for computing singular or nearly singular integrals, evaluated at a point on or near the curve. To improve accuracy of the numerical quadrature, we add corrections for the errors arising from discretization, which are found by asymptotic analysis. When used to …
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Efficient high-order integral equation methods for the heat equation
… the heat layer potentials contains convolution integrals in both space and time whose direct evaluation requires O(NS2NT2) work and O(NSNT) storage, where NS is the total number of discretization points in the spatial boundary and NT is the total number of time steps. This is excessively …
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The Hilbert Transform as an Average of Dyadic Shift Operators
In this thesis we discuss Petermichls characterization of the Hilbert transform as an average of dyadic shift operators following the presentation by Thomas Hytonen [Hyt]. A linear and bounded operator T in L2(R) that commutes with translations, dilations and anticommutes with reflections must be a …
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Layer potential evaluations on distributed memory machines
… equations is evaluating layer potentials with singular kernels. Quadrature by Expansion (QBX) is a quadrature method to evaluate such layer potentials accurately for targets near or on the source boundary, by forming expansions in the high-accuracy region away from the boundary, and evaluating …
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High-order numerical methods for layer potential evaluation
… practical challenges associated with issues of singular/near-singular quadrature and efficient scaling. Quadrature by Expansion (QBX) is a quadrature method that addresses many of the issues encountered in the evaluation of layer potentials, by providing a high-order and kernel/dimension …