250	RWTH Publication No: 47244        2005        IGPM250.pdf
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)