21st GAMM-Seminar Leipzig on
Robust Fast Solvers

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
Phone: +49.341.9959.752, Fax: +49.341.9959.999

  21st GAMM-Seminar
January, 26th-28th, 2005
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  Abstract Marcus Mohr, Fri, 12.00-12.30 Previous Contents Next  
  Iterative Solution of the Piezoelectric Forward Problem
Marcus Mohr (Univ. Erlangen-Nürnberg)

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 surface-acoustic 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 sub-task 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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Last updated:
28.01.2005 Impressum
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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