Compound matrix method for eigenvalue problems in multiple connected domains

The method of fundamental solutions for Helmholtz eigenvalue problems in simply and multiply connected domains

In this paper a new boundary method for Helmholtz eigenproblems in simply and multiply connected domains is presented. The method is based on mathematically modelling the physical response of a system to external excitation over a range of frequencies. The response amplitudes are then used to determine the resonant frequencies. So, contrary to the traditional scheme, the method described does n...

Dynamic compound wavelet matrix method for multiphysics and multiscale problems.

The paper presents the dynamic compound wavelet method (dCWM) for modeling the time evolution of multiscale and/or multiphysics systems via an "active" coupling of different simulation methods applied at their characteristic spatial and temporal scales. Key to this "predictive" approach is the dynamic updating of information from the different methods in order to adaptively and accurately captu...

Some Unusual Matrix Eigenvalue Problems

We survey some unusual eigenvalue problems arising in different applications. We show that all these problems can be cast as problems of estimating quadratic forms. Numerical algorithms based on the well-known Gauss-type quadrature rules and Lanczos process are reviewed for computing these quadratic forms. These algorithms reference the matrix in question only through a matrix-vector product op...

Sign Wave Analysis in Matrix Eigenvalue Problems

The Jacobi-Davidson Method for Eigenvalue and Generalized Eigenvalue Problems

We consider variants of Davidson's method for the iterative computation of one or more eigenvalues and their corresponding eigenvectors of an n n matrix A. The original Davidson method 3], for real normal matrices A, may be viewed as an accelerated Gauss-Jacobi method, and the success of the method seems to depend quite heavily on diagonal dominance of A 3, 4, 17]. In the hope to enlarge the sc...