Runge-Walsh-wavelet approximation for the Helmholtz equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:235

Article

Freeden, W ; Schneider, F

关键词: Helmholtz equation;    scale continuous and discrete metaharmonic;    wavelets;    boundary-value problems;    Runge-Walsh approximation;    pyramid scheme;   

DOI  :  10.1006/jmaa.1999.6406

来源: Elsevier

【 摘 要 】

Metaharmonic wavelets are introduced for constructing the solution of the Helmholtz equation (reduced wave equation) corresponding to Dirichlet's or Neumann's boundary values on a closed surface Sigma in three-dimensional Euclidean space R-3. A consistent scale continuous and scale discrete wavelet approach leading to exact reconstruction formulas is considered in more detail. A scale discrete version of multiresolution is described for potential functions metaharmonic outside the closed surface and satisfying the radiation condition at infinity. Moreover, we discuss fully discrete wavelet representations of band-limited metaharmonic potentials. Finally, a decomposition and reconstruction (pyramid) scheme for economical numerical implementation is presented for Runge-wavelet approximation. (C) 1999 Academic Press.

【 授权许可】

Free