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An Extension of Spectral Methods to Quasi-Periodic and Multiscale Problems

✍ Scribed by A. Wirth

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
385 KB
Volume
132
Category
Article
ISSN
0021-9991

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✦ Synopsis

To give a first idea of our method consider a (quasiperiodic) function of one variable such that in its Fourier For efficiently treating quasi-periodic and multiscale problems numerically, it is here proposed to change the number of space representation the only wavenumbers present are of the dimensions which is then multiplied by the number of different form k ϭ n ϩ m, where n and m are signed integers and (incommensurable or widely separated) scales occurring in the is irrational (the decomposition of k is thus unique).

problem. Then, all calculations are performed in this higher-Such a function has the following (generalized) Fourier dimensional space. In the higher-dimensional space the problem and CPU resources, when using the ''higher dimension'' method, is typically proportional to the ratio of scales. ᮊ 1997 Academic Press such that f (x) is recovered by restriction to the line y ϭ x of slope .

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