250 IGPM250.pdf        March 2005
TITLE Adaptive Methods for Boundary Integral Equations - Complexity and Convergence Estimates
AUTHORS Wolfgang Dahmen, Helmut Harbrecht, Reinhold Schneider
ABSTRACT This paper is concerned with developing numerical techniques for the adaptive application of global operators of potential type in wavelet coordinates. This is a core ingredient for a new type of adaptive solvers that has so far been explored primarily for PDEs. We shall show how to realize asymptotically optimal complexity in the present context of global operators. "Asymptotically optimal" means here that any target accuracy can be achieved at a computational expense that stays proportional to the number of degrees of freedom (within the setting determined by an underlying wavelet basis) that would ideally be necessary for realizing that target accuracy if full knowledge about the unknown solution were given. The theoretical findings are supported and quantified by first numerical experiments.
KEYWORDS Boundary integral equations, adaptive wavelet scheme, best N-term approximation, compressible matrices, adaptive hp-quadrature, complexity and convergence estimates
DOI 10.1090/S0025-5718-07-01970-9
PUBLICATION Mathematics of computation
76(259), 1243-1274 (2007)