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Time plays an important role in medical and neuropsychological diagnosis and research. In the eld of Electro-and MagnetoEncephaloGraphy (EEG/MEG) source localization, a current distribution in the human brain is reconstructed noninvasively by means of measured elds outside the head. High resolution nite element modeling for the eld computation leads to a sparse, large scale, linear equation system with many di erent r i g h t hand sides to be solved. The presented solution process is based on a parallel algebraic multigrid method. It is shown that very short computation times can be achieved through the combination of the multigrid technique and the parallelization on distributed memory computers. A solver time comparison to a classical parallel Jacobi preconditioned conjugate gradient m e t h o d i s g i v en.

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The boundary element method (BEM) is of advantage in many applications including far-field computations in magnetostatics and solid mechanics as well as accurate computations of singularities. Since the numerical approximation is essentially reduced to the boundary of the domain under consideration, the mesh generation and handling is simpler than, for example, in a finite element discretization of the domain. In this paper, we discuss fast solution techniques for the linear systems of equations obtained by the BEM (BE-equations) utilizing the non-overlapping domain decomposition (DD). We study parallel algorithms for solving large scale Galerkin BE-equations approximating linear potential problems in plane, bounded domains with piecewise homogeneous material properties. We give an elementary spectral equivalence analysis of the BEM Schur complement that provides the tool for constructing and analysing appropriate preconditioners. Finally, we present numerical results obtained on a massively parallel machine using up to 128 processors, and we sketch further applications to elasticity problems and to the coupling of the finite element method (FEM) with the boundary element method. As shown theoretically and confirmed by the numerical experiments, the methods are of O(h −2 ) algebraic complex-

This paper analyzes the problem of deconvolution, especially for signals with peak-like structures. We present and analyze a so-called 'practical approach', which mainly consists of a wavelet shrinkage. It is shown that this practical approach is indeed a regularization procedure, and furthermore, it leads to a convergence rate that is superior to classical linear regularization theory. Our results are based on modeling signals and operators in Besov spaces, especially exploiting the fact that peaks have higher regularity in Besov spaces than in Sobolev spaces.