Article
On local nonreflecting boundary conditions for time dependent wave propagation
Chinese Annals of Mathematics (Impact Factor: 0.5). 01/2009; 30(5):589606. DOI: 10.1007/s1140100902035

Conference Paper: Dynamic analysis of CMUTs in different regimes of operation
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ABSTRACT: This paper reports on dynamic analysis of an immersed single capacitive micromachined ultrasonic transducer (CMUT) cell transmitting. A water loaded 24 μm circular silicon membrane of a transducer was modeled. The calculated collapse and snapback voltages were 80 V and 50 V, respectively. The resonance frequency, output pressure and nonlinearity of the CMUT in three regimes of operation were determined. These regimes were: a) the conventional regime in which the membrane does not make contact with the substrate, b) the collapsed regime in which the center of the membrane is in constant contact with the substrate, and c) the collapsesnapback regime in which the membrane intermittently makes contact with the substrate and releases. The average membrane displacement was compared as the CMUT was operated in these regimes. A displacement of 70 Å in the collapsed regime and 39 Å in conventional regime operation were predicted when a 5 V pulse was applied to the CMUT cell biased at 70 V. The CMUT showed a 2<sup>nd</sup> harmonic at 16 dB and 26 dB in conventional and collapsed regimes of operation, respectively. Collapsesnapback operation provided increased output pressure at the expense of a 3<sup>rd</sup> harmonic at 10 dB. Our simulations predicted that the average output pressure at the membrane could be 90 kPa/V with collapsesnapback operation compared to 4 kPa/V with conventional operation.Ultrasonics, 2003 IEEE Symposium on; 11/2003  [Show abstract] [Hide abstract]
ABSTRACT: Energy transmitted along a waveguide decays less rapidly than in an unbounded medium. In this paper we study the efficiency of a PML in a timedependent waveguide governed by the scalar wave equation. A straight forward application of a Neumann boundary condition can degrade accuracy in computations. To ensure accuracy, we propose extensions of the boundary condition to an auxiliary variable in the PML. We also present analysis proving stability of the constant coefficient PML, and energy estimates for the variable coefficients case. In the discrete setting, the modified boundary conditions are crucial in deriving discrete energy estimates analogous to the continuous energy estimates. Numerical stability and convergence of our numerical method follows. Finally we give a number of numerical examples, illustrating the stability of the layer and the high order accuracy of our proposed boundary conditions.Journal of Scientific Computing 12/2012; 53(3). · 1.71 Impact Factor 
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