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- Timo Betcke, Heinrich Voss
- Future Generation Comp. Syst.
- 2004

This article discusses a projection method for nonlinear eigenvalue problems. The subspace of approximants is constructed by a Jacobi–Davidson type approach, and the arising eigenproblems of small dimension are solved by safeguarded iteration. The method is applied to a rational eigenvalue problem governing the vibrations of tube bundle immersed in an… (More)

- Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder, Françoise Tisseur
- ACM Trans. Math. Softw.
- 2013

We present a collection of 52 nonlinear eigenvalue problems in the form of a MATLAB toolbox. The collection contains problems from models of real-life applications as well as ones constructed specifically to have particular properties. A classification is given of polynomial eigenvalue problems according to their structural properties. Identifiers based on… (More)

- Timo Betcke, Lloyd N. Trefethen
- SIAM Review
- 2005

Fox, Henrici, and Moler made famous a " Method of Particular Solutions " for computing eigenvalues and eigenmodes of the Laplacian in planar regions such as polygons. We explain why their formulation of this method breaks down when applied to regions that are insufficiently simple and propose a modification that avoids these difficulties. The crucial… (More)

- Alex H. Barnett, Timo Betcke
- J. Comput. Physics
- 2008

The Method of Fundamental Solutions (MFS) is a popular tool to solve Laplace and Helmholtz boundary value problems. Its main drawback is that it often leads to ill-conditioned systems of equations. In this paper we investigate for the interior Helmholtz problem on analytic domains how the singularities (charge points) of the MFS basis functions have to be… (More)

Recently developed numerical methods make possible the high-accuracy computation of eigenmodes of the Laplacian for a variety of " drums " in two dimensions. A number of computed examples are presented together with a discussion of their implications concerning bound and continuum states, isospectrality, symmetry and degeneracy, eigenvalue avoidance,… (More)

Conclusions High-accuracy solution of the Helmholtz BVP requires that coefficients α remain O(1), which in turn requires that the MFS charge curve enclose no singularities in the analytic continuation of the solution. We prove this, with convergence rates, in the disc. We devise a singularity-adapted charge curve for general analytic domains, and show this… (More)

- Timo Betcke, Euan A. Spence
- SIAM J. Numerical Analysis
- 2011

Coercivity is an important concept for proving existence and uniqueness of solutions to variational problems in Hilbert spaces. But, while the existence of coercivity estimates is well known for many variational problems arising from partial differential equations, it is still an open problem in the context of boundary integral operators arising from… (More)

We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the L 2 condition numbers for these formulations, and also on the norms of the classical acoustic single-and double-layer potential operators. These… (More)

Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems , for… (More)

- Timo Betcke
- SIAM J. Matrix Analysis Applications
- 2008