


Abstract
Marcus Mohr, Fri, 12.0012.30

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Iterative Solution of the Piezoelectric Forward Problem
Marcus Mohr (Univ. ErlangenNürnberg)
Piezoelectric sensors and actuators can be found in a multitude of different
application areas like e.g. ultrasound devices for medical imaging and therapy
or surfaceacoustic wave filters in cell phones, force and to name just a few.
While the numerical simulation of such materials is of growing importance for
engineers, it suffers from two problems. On the one hand the material
parameters themselves (elastic stiffness constants, dielectric constants and
piezoelectric constants) can only be determined inadequately by experiments
alone. On the other hand the three groups of material parameters posses very
different orders of magnitude ∼10^{10}10^{+10}.
The design of piezoelectric components as well as the inverse problem of
parameter identification involve the subtask of solving the linear stationary
(forward) piezoelectric problem, i.e. the determination of material behaviour
for given parameters. Discretisation of this problem leads to a linear system
with a symmetric, but indefinite matrix with either real or complex (e.g. in
the case of lossy materials) entries.
In this talk we consider the iterative solution of such linear systems by
the Generalised Minimal Residual method (GMRES) preconditioned by different
ILU and block diagonal preconditioners and compare the performance to a Schur
complement based approach.




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