Article

# Finite element calculation of wave propagation and excitation in periodic piezoelectric systems

01/2002;

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**ABSTRACT:**Surface acoustic wave filters are widely used for frequency filtering in telecommunications. These devices mainly consist of a piezoelectric substrate with periodically arranged electrodes on the surface. The periodic structure of the electrodes subdivides the frequency domain into stop-bands and pass-bands. This means only piezoelectric waves excited at frequencies belonging to the pass-band-region can pass the devices undamped. The goal of the presented work is the numerical calculation of so-called “dispersion diagrams”, the relation between excitation frequency and a complex propagation parameter. The latter describes damping factor and phase shift per electrode. The mathematical model is governed by two main issues, the underlying periodic structure and the indefinite coupled field problem due to piezoelectric material equations. Applying Bloch-Floquet theory for infinite periodic geometries yields a unit-cell problem with quasi-periodic boundary conditions. We present two formulations for a frequency-dependent eigenvalue problem describing the dispersion relation. Reducing the unit-cell problem only to unknowns on the periodic boundary results in a small-sized quadratic eigenvalue problem which is solved by QZ-methods. The second method leads to a large-scaled generalized non-hermitian eigenvalue problem which is solved by Arnoldi methods. The effect of periodic perturbations in the underlying geometry is confirmed by numerical experiments. Moreover, we present simulations of high frequency SAW- filter structures as used in TV-sets and mobile phones.12/2005: pages 74-98; - [Show abstract] [Hide abstract]

**ABSTRACT:**This is the first comprehensive monograph that features state-of-the-art multigrid methods for enhancing the modeling versatility, numerical robustness, and computational efficiency of one of the most popular classes of numerical electromagnetic field modeling methods: the method of finite elements. The focus of the publication is the development of robust preconditioners for the iterative solution of electromagnetic field boundary value problems (BVPs) discretized by means of finite methods. Specifically, the authors set forth their own successful attempts to utilize concepts from multigrid and multilevel methods for the effective preconditioning of matrices resulting from the approximation of electromagnetic BVPs using finite methods. Following the authors' careful explanations and step-by-step instruction, readers can duplicate the authors' results and take advantage of today's state-of-the-art multigrid/multilevel preconditioners for finite element-based iterative electromagnetic field solvers. Among the highlights of coverage are: Application of multigrid, multilevel, and hybrid multigrid/multilevel preconditioners to electromagnetic scattering and radiation problems Broadband, robust numerical modeling of passive microwave components and circuits Robust, finite element-based modal analysis of electromagnetic waveguides and cavities Application of Krylov subspace-based methodologies for reduced-order macromodeling of electromagnetic devices and systems Finite element modeling of electromagnetic waves in periodic structures The authors provide more than thirty detailed algorithms alongside pseudo-codes to assist readers with practical computer implementation. In addition, each chapter includes an applications section with helpful numerical examples that validate the authors' methodologies and demonstrate their computational efficiency and robustness. This groundbreaking book, with its coverage of an exciting new enabling computer-aided design technology, is an essential reference for computer programmers, designers, and engineers, as well as graduate students in engineering and applied physics.03/2006; , ISBN: 0471741108 - [Show abstract] [Hide abstract]

**ABSTRACT:**The characteristic of wave propagation in finite elastic solids is a major issue for surface acoustic wave (SAW) devices, which are designed based on accurate analysis. As a result, it is essential in engineering applications to analyze the SAW propagation in finite piezoelectric solids with the objective of revealing the influence of structural changes. As the finite element analysis of solids is already sophisticated, the problem of SAW analysis is reduced to the calculation of eigenvalues of extremely large linear equations that involves hundreds of thousands or even millions of degree of freedom because of the higher frequency. The operations of large scale matrices need high computing speed and large memory. In fact, these demands are beyond the capacity of widely available computing resources. For these reasons, we need to make use of computer clusters and parallel finite element method to improve the computing efficiency and expand applications. Based on our existing finite element program, the PARPACK package is used to compute eigenvalues in the specified range; the compressed sparse row (CSR) storage format is used to replace the Symmetric Skyline (SSK) storage method; the PETSc package is used to solve linear equations. The program is parallelized on a Linux cluster to utilize the computing power. The parallel FEM program with 3D elements is used to analyze the wave propagation in an actual SAW device model with interdigital transducers.01/2008;

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