Olaf Steinbach

Bio: Olaf Steinbach is an academic researcher from Graz University of Technology. The author has contributed to research in topics: Boundary element method & Boundary value problem. The author has an hindex of 31, co-authored 184 publications receiving 3892 citations. Previous affiliations of Olaf Steinbach include University of Stuttgart.

Numerical Approximation Methods for Elliptic Boundary Value Problems. Finite and Boundary Elements

Abstract: Boundary Value Problems.- Function Spaces.- Variational Methods.- Variational Formulations of Boundary Value Problems.- Fundamental Solutions.- Boundary Integral Operators.- Boundary Integral Equations.- Approximation Methods.- Finite Elements.- Boundary Elements.- Finite Element Methods.- Boundary Element Methods.- Iterative Solution Methods.- Fast Boundary Element Methods.- Domain Decomposition Methods.

The Fast Solution of Boundary Integral Equations

Abstract: Boundary Integral Equations.- Boundary Element Methods.- Approximation of Boundary Element Matrices.- Implementation and Numerical Examples.

The construction of some efficient preconditioners in the boundary element method

Abstract: The discretization of first kind boundary integral equations leads in general to a dense system of linear equations, whose spectral condition number depends on the discretization used. Here we describe a general preconditioning technique based on a boundary integral operator of opposite order. The corresponding spectral equivalence inequalities are independent of the special discretization used, i.e., independent of the triangulations and of the trial functions. Since the proposed preconditioning form involves a (pseudo)inverse operator, one needs for its discretization only a stability condition for obtaining a spectrally equivalent approximation.

On the stability of the L 2 projection in H 1 (Ω)

Abstract: We prove the stability in H1(Ω) of the L2 projection onto a family of finite element spaces of conforming piecewise linear functions satisfying certain local mesh conditions. We give explicit formulae to check these conditions for a given finite element mesh in any number of spatial dimensions. In particular, stability of the L2 projection in H1(Ω) holds for locally quasiuniform geometrically refined meshes as long as the volume of neighboring elements does not change too drastically.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Solving Ordinary Differential Equations

Abstract: Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Regularization Of Inverse Problems

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