Comparison of four software packages applied to a scattering problem

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• 作者：Albertsen ; Niels Christian ; Chesneaux ; Jean-Marie ; et. al.
• 关键词：Boundary collocation ; Stochastic arithmetic ; Interval arithmetic ; CADNA ; PROFIL ; Grating ; Rayleigh ansatz
• 刊名：Mathematics and Computers in Simulation
• 出版年：1999
• 出版时间：February, 1999
• 年：1999
• 卷：48
• 期：3
• 页码：307-317
• 全文大小：173 K

文摘

We investigate characteristic features of four different software packages by applying them to the numerical solution of a non-trivial physical problem in computer simulation, viz., scattering of waves from a sinusoidal boundary. The numerical method used is based on boundary collocation. This leads to highly ill-conditioned linear systems of equations, such that ensuing results may lose significant digits. The packages under consideration, each of which is based on a specific computer arithmetic, are the following: , , and .

We find that both and (using stochastic and interval arithmetic, respectively) provide an effortless validation of the numerical results obtained in computer simulation, whereby we get a reliable account of the limitations of the numerical methods.