Pflaum C (2002)
Publication Type: Journal article, Report
Publication year: 2002
Publisher: Springer Verlag (Germany)
Book Volume: 69
Pages Range: 339-352
Journal Issue: 4
URI: https://www10.informatik.uni-erlangen.de/Publications/Papers/2002/Pflaum_Computing_Vol69Nr4.pdf
DOI: 10.1007/s00607-002-1464-y
In this paper, we present a new approach to construct robust multilevel algorithms for elliptic differential equations. The multilevel algorithms consist of multiplicative subspace corrections in spaces spanned by problem dependent generalized prewavelets. These generalized prewavelets are constructed by a local orthogonalization of hierarchical basis functions with respect to a so-called local coarse-grid space. Numerical results show that the local orthogonalization leads to a smaller constant in strengthened Cauchy-Schwarz inequality than the original hierarchical basis functions. This holds also for several equations with discontinuous coefficients. Thus, the corresponding multilevel algorithm is a fast and robust iterative solver.
APA:
Pflaum, C. (2002). Problem Dependent Generalized Prewavelets. Computing, 69(4), 339-352. https://dx.doi.org/10.1007/s00607-002-1464-y
MLA:
Pflaum, Christoph. "Problem Dependent Generalized Prewavelets." Computing 69.4 (2002): 339-352.
BibTeX: Download