805,973 research outputs found
Adaptive boundary element methods with convergence rates
This paper presents adaptive boundary element methods for positive, negative,
as well as zero order operator equations, together with proofs that they
converge at certain rates. The convergence rates are quasi-optimal in a certain
sense under mild assumptions that are analogous to what is typically assumed in
the theory of adaptive finite element methods. In particular, no
saturation-type assumption is used. The main ingredients of the proof that
constitute new findings are some results on a posteriori error estimates for
boundary element methods, and an inverse-type inequality involving boundary
integral operators on locally refined finite element spaces.Comment: 48 pages. A journal version. The previous version (v3) is a bit
lengthie
On a preconditioner for time domain boundary element methods
We propose a time stepping scheme for the space-time systems obtained from
Galerkin time-domain boundary element methods for the wave equation. Based on
extrapolation, the method proves stable, becomes exact for increasing degrees
of freedom and can be used either as a preconditioner, or as an efficient
standalone solver for scattering problems with smooth solutions. It also
significantly reduces the number of GMRES iterations for screen problems, with
less regularity, and we explore its limitations for enriched methods based on
non-polynomial approximation spaces.Comment: 15 pages, 16 figure
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