Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula [PDF]
Applied Optics, 2006 The numerical calculation of the Rayleigh-Sommerfeld diffraction integral is investigated. The implementation of a fast-Fourier-transform (FFT) based direct integration (FFT-DI) method is presented, and Simpson's rule is used to improve the calculation accuracy. The sampling interval, the size of the computation window, and their influence on numerical
Shen, F. B., Wang, Anbo
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A bi‐cubic transformation for the numerical evaluation of the Cauchy principal value integrals in boundary methods [PDF]
International Journal for Numerical Methods in Engineering, 1989 AbstractThe numerical strategies employed in the evaluation of singular integrals existing in the Cauchy principal value (CPV) sense are, undoubtedly, one of the key aspects which remarkably affect the performance and accuracy of the boundary element method (BEM).Thus, a new procedure, based upon a bi‐cubic co‐ordinate transformation and oriented ...
Cerrolaza Rivas, Miguel +1 more
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Numerical Integral Transform Methods for Random Hyperbolic Models with a Finite Degree of Randomness [PDF]
Mathematics, 2019 This paper deals with the construction of numerical solutions of random hyperbolic models with a finite degree of randomness that make manageable the computation of its expectation and variance. The approach is based on the combination of the random Fourier transforms, the random Gaussian quadratures and the Monte Carlo method.
M. Consuelo Casabán +2 more
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Curvelets, Wave Atoms, and Wave Equations [PDF]
, 2006 We argue that two specific wave packet families---curvelets and wave atoms---provide powerful tools for representing linear systems of hyperbolic differential equations with smooth, time-independent coefficients.
Demanet, Laurent
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A Super-Algebraically Convergent, Windowing-Based Approach to the Evaluation of Scattering from Periodic Rough Surfaces [PDF]
, 2008 We introduce a new second-kind integral equation method to solve direct rough surface scattering problems in two dimensions. This approach is based, in part, upon the bounded obstacle scattering method that was originally presented in Bruno et al. [2004]
Monro, John Anderson
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Integral transforms solution for flow development in wavy wall ducts [PDF]
, 2011 Purpose – The purpose of this paper is to provide an analysis of two‐dimensional laminar flow in the entrance region of wavy wall ducts as obtained from the solution of the steady Navier‐Stokes equations for incompressible flow.
Renato M. Cotta +7 more
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Journal of Mathematics and Computer Science, 2013 In this paper we use differential transform method for solving nonlinear and linear Volterra integral equation with the kernel as ( − ) by using an efficient technique. We approximate the kernel of integral equation with Taylor series and make integral equation simpler by using some techniques that when we use differential transform method,
Hadis Seiheii +2 more
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Numerical solution of nonlinear Hammerstein integral equations via Sinc collocation method based on double exponential transformation [PDF]
Mathematical Sciences, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fariborzi Araghi, Mohammad Ali +1 more
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Simulation Capabilities for Challenging Medical Imaging and Treatment Planning Problems [PDF]
, 2011 Advanced numerical solvers and associated simulation tools, such as, for example, numerical algorithms based on novel spectral methods, efficient time-stepping and domain meshing techniques for solution of Partial Differential Equations (PDEs ...
Beni, Catherine Elizabeth
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Metric Based Upscaling for Partial Differential Equations with a Continuum of Scales [PDF]
, 2007 Numerical upscaling of problems with multiple scale structures have attracted increasing attention in recent years. In particular, problems with non-separable scales pose a great challenge to mathematical analysis and simulation.
Zhang, Lei
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