Learn More
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)
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)
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 changes(More)
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)
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)
A powerful method for solving planar eigenvalue problems is the Method of Particular Solutions (MPS), which is also well known under the name “point matching method”. The implementation of this method usually depends on the solution of one of three types of linear algebra problems: singular value decomposition, generalized eigenvalue decomposition, or(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 L2 condition numbers for these formulations, and also on the norms of the classical acoustic singleand double-layer potential operators. These(More)
Many important partial differential equation problems in homogeneous media, such as those of acoustic or electromagnetic wave propagation, can be represented in the form of integral equations on the boundary of the domain of interest. In order to solve such problems, the boundary element method (BEM) can be applied. The advantage compared to(More)
We investigate the application of multifrequency electrical impedance tomography (MFEIT) to imaging the brain in stroke patients. The use of MFEIT could enable early diagnosis and thrombolysis of ischaemic stroke, and therefore improve the outcome of treatment. Recent advances in the imaging methodology suggest that the use of spectral constraints could(More)