Pseudospectral Fourier reconstruction with the modified Inverse Polynomial Reconstruction Method

JOURNAL OF COMPUTATIONAL PHYSICS

卷:229

Article

Hrycak, Tomasz¹  Groechenig, Karlheinz¹ 

[1] Univ Vienna, Dept Math, A-1090 Vienna, Austria

关键词: IPRM;    Gibbs phenomenon;    Pseudospectral convergence;    Inverse methods;   

DOI  :  10.1016/j.jcp.2009.10.026

来源: Elsevier

【 摘 要 】

We generalize the Inverse Polynomial Reconstruction Method (IPRM) for mitigation of the Gibbs phenomenon by reconstructing a function from its m lowest Fourier coefficients as an algebraic polynomial of degree at most n - 1 (m >= n). We compute approximate Legendre coefficients of the function by solving a linear least squares problem. We show that if m >= n(2), the condition number of the problem does not exceed 2.39. Consequently, if m >= n(2), the convergence rate of the modified IPRM for an analytic function is root exponential on the whole interval of definition. Numerical stability and accuracy of the proposed algorithm are validated experimentally. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free