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Sensitivity analysis of linear and nonlinear lithotripter models†

Published online by Cambridge University Press:  25 November 2010

BARBARA KALTENBACHER  and
SLOBODAN VELJOVIĆ
BARBARA KALTENBACHER
Affiliation:
Institute of Mathematics and Scientific Computing, University of Graz, Heinrichstr. 36, 8010 Graz, Austria email: barbara.kaltenbacher@uni-graz.at, slobodan.veljovic@uni-graz.at
SLOBODAN VELJOVIĆ
Affiliation:
Institute of Mathematics and Scientific Computing, University of Graz, Heinrichstr. 36, 8010 Graz, Austria email: barbara.kaltenbacher@uni-graz.at, slobodan.veljovic@uni-graz.at
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Abstract

In this paper, we perform a sensitivity analysis for shape optimization problems arising in models we suggest for a lithotripter. More precisely, we use two models based on high intensity ultrasound focusing by an acoustic lens, where through changing the shape of the lens we try to achieve a favourable focusing. The models are based on acoustic wave equations with piecewise constant coefficients, a linear and a nonlinear one, where for the nonlinear one we use the Westervelt equation. The sensitivity analysis is performed using an adjoint approach.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 22 , Issue 1 , February 2011 , pp. 21 - 43
Copyright
Copyright © Cambridge University Press 2010

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