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Abstract. This paper presents new stability estimates for the scalar Helmholtz equation with a complex-valued Robin boundary condition as well as Dirichlet and Neumann boundary conditions. For each estimate, we state the explicit dependency of constants on the wave number. To deal with mixed boundary conditions, we impose geometrical constraints on the two-dimensional or threedimensional bounded domain.

Anasazi is a package within the Trilinos software project that provides a framework for the iterative, numerical solution of large-scale eigenvalue problems. Anasazi is written in ANSI C++ and exploits modern software paradigms to enable the research and development of eigensolver algorithms. Furthermore, Anasazi provides implementations for some of the most recent eigensolver methods. The purpose of our article is to describe the design and development of the Anasazi framework. A performance comparison of Anasazi and the popular FORTRAN 77 code ARPACK is given.

SUMMARY Frequency sweeps in structural dynamics, acoustics, and vibro‐acoustics require evaluating frequency response functions for a large number of frequencies. The brute force approach for performing these sweeps leads to the solution of a large number of large‐scale systems of equations. Several methods have been developed for alleviating this computational burden by approximating the frequency response functions. Among these, interpolatory model order reduction methods are perhaps the most successful. This paper reviews this family of approximation methods with particular attention to their applicability to specific classes of frequency response problems and their performance. It also includes novel aspects pertaining to the iterative solution of large‐scale systems of equations in the context of model order reduction and frequency sweeps. All reviewed computational methods are illustrated with realistic, large‐scale structural dynamic, acoustic, and vibro‐acoustic analyses in wide frequency bands. These highlight both the potential of these methods for reducing CPU time and their limitations. Copyright © 2012 John Wiley & Sons, Ltd.