Current technological challenges in materials science and high-tech device industry require the solution of boundary
value problems (BVPs) involving regions of various scales, e.g. multiple thin layers, fibre-reinforced composites, and
nano/micro pores. In most cases straightforward application of standard variational techniques to BVPs of practical
relevance necessarily leads to unsatisfactorily ill-conditioned analytical and/or numerical results. To remedy the
computational challenges associated with sub-sectional heterogeneities various sophisticated homogenization techniques
need to be employed. Homogenization refers to the systematic process of smoothing out the sub-structural
heterogeneities, leading to the determination of effective constitutive coefficients. Ordinarily, homogenization involves a
sophisticated averaging and asymptotic order analysis to obtain solutions. In the majority of the cases only zero-order
terms are constructed due to the complexity of the processes involved. In this paper we propose a constructive scheme
for obtaining homogenized solutions involving higher order terms, and thus, guaranteeing higher accuracy and greater
robustness of the numerical results. We present
KEYWORDS: Acoustics, Wave propagation, Fourier transforms, Transform theory, Solids, Modeling and simulation, Linear algebra, Signal processing, Velocity measurements, Analytical research
The modelling and simulation of periodic structures with defects define boundary value problems (BVPs) which
are conceptually and numerically difficult to solve. Innovative and problem-tailored analysis methods need to be
devised to solve defect problems efficiently and accurately. One possible attractive method is based on the ideas
related to the construction of Wannier functions. Wannier functions constitute a complete sequence of localised
orthogonal functions which are derived from associated periodic versions of defect problems. In this paper we
review general properties of Wannier functions from a linear algebra point of view, introduce an easy-to-use
symbolic notation for the diagonalisation of the governing equations and construct the Wannier functions for a
variety of phononic devices. Using certain distinguished properties inherent in the wavenumber-dependence of
the eigenvalues we prove the orthogonality and completeness of the Wannier functions in a conceptually novel
way.
For modelling molecular electronic and electrochemical boundary value problems (BVPs), we are faced with the solution of Schrodingers equation involving realistic models for potential energy functions. With the exception of a few canonical problems, there are currently no analytical methods available for obtaining closed-form solutions for the electron wavefunctions and their corresponding energy eigenvalues. One of the well-known techniques for obtaining approximate wavefunctions and energy states is the WKB approximation. The main drawbacks of the WKB method are the discontinuities at the so called turning points, where the total energy equals the potential energy and the restriction on exclusively solving for bound state solutions. To overcome these shortcomings, a novel accelerated numerical technique for solving time-independent Schrodingers equation is introduced, with applications to general potential functions. This method is based on the construction of an auxiliary BVP, which mimics significant features of the original BVP and possesses exact solutions. By construction, these solutions constitute a complete set of orthogonal problem-adapted analysing functions. This method provides numerical solutions with no discontinuities at the turning points.
KEYWORDS: Finite element methods, 3D applications, Microelectronics, Device simulation, Telecommunications, Electronic components, Medium wave, Acoustics, Signal processing, Computer simulations
The rapid growth of the telecommunication and microelectronic industry has been pushing the performance limit
of the passive and active electronic components and devices alike. Thereby, improved performance of the devices
has become a necessity for operating frequencies moving into the MW region. Examples are Surface Acoustic
Wave (SAW) and Bulk AcousticWave (BAW) Devices which are miniaturized microelectronic devices with a wide
range of applications in signal processing, forming and sensing. Computation of electroacoustic field distribution
in these structures needs to be accurate, efficient and rigorous. However, the amount of data required for preand
post-processing is immensely large, and the processing and handling of data are extremely time consuming.
In this paper we propose a conceptually novel method for significantly reducing the computational time and
thus enhancing efficiency by pre-calculating relevant data, storing, and subsequently retrieving them whenever
they are required for device analysis and simulation. We propose a method for symbolically and conveniently
calculating two- or three dimensional integrals over the surface of an arbitrary triangle or within the volume of
an arbitrary tetrahedral. The results we have obtained are universal in that their application is not limited to
microacoustic devices.
In this paper, a novel analysis technique for the performance evaluation of micro-acoustic devices has been
proposed. Whereas traditional techniques typically focus solely on the frequency domain characteristics, we
employ a Joint Time-Frequency Analysis (JTFA), which has been shown to provide a more complete characterisation
of overall device performance and underlying physical phenomena. Although an emphasis is placed
on a Flexural Plate Wave (FPW) device, the analysis technique presented is applicable to a wider range of
micro-acoustic devices including Surface Acoustic Wave (SAW) structures and Thin-Film Bulk Acoustic Wave
Resonators (TFBARs).
SAWdevices, and indeed general filters, are typically described by a frequency domain characteristic, whereby
the entire time domain information is discarded. This type of analysis assumes that the device has reached quasistationary
conditions. By employing JTFA, the device performance can simultaneously be studied as a function
of both time and frequency. This type of analysis is typically useful where spurious acoustic modes are generated
which may influence the overall filter characteristic.
We have investigated the functional properties of various JTFA kernels, including those appearing in the
Wigner-Ville, Choi-Williams and Page distributions. A known deficiency associated with JTFA is the appearance
of a number of spurious cross-terms in the computations. Whereas the cross-terms are relatively simple to
detect for "monochromatic" (single-component) signals, it is not a trivial task to minimise such artifacts for
"polychromatic" (multi-component) signals, which are typical in micro-acoustic devices. We propose novel
methods for reducing the cross-terms interference appearing in JTFA, thereby improving the performance of the
analysis technique.
To investigate the application of the proposed technique, the simulated time domain response of a FPW
device was investigated. The Finite Element Method (FEM) package ANSYS 8.0 was utilised to obtain the
impulse response of the FPW structure under a dynamic transient analysis. A comparison is also made with the
spectral domain Green's function to verify the FEM solution, where excellent agreement is obtained. Based on
the FEM solutions, the insertion loss characteristics is calculated which represents a commonly applied frequency
domain method of analysing micro-acoustic devices. A comparison has been made between the insertion loss
characteristics and the proposed approach, where it is clearly demonstrated that the problem-adapted technique
provides significantly more detailed information.
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