21st GAMM-Seminar Leipzig on
Robust Fast Solvers

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
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  21st GAMM-Seminar
January, 26th-28th, 2005
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  Abstract Andreas Wiegmann, Thu, 17.50-18.20 Previous Contents Next  
  Fast Structural Topology Design
Andreas Wiegmann (ITWM Kaiserslautern)

We describe an algorithmic approach for the topology design of elastic structures. At the core, our approach relies on three distinct ideas. Given a design, we apply the Explicit Jump Immersed Interface (finite difference) Method for rapidly computing the stresses for a given design shape by embedding this design in a rectangle. The equations are extended to the full rectangle, and the second order accurate solution to the Lamé equations is found via BiCGStab in a somewhat similar fashion to earlier capacitance matric methods. This means that the Schur complement for the jumps in the solution and it's derivatives on the domain boundary is solved, effectively reducing the dimension of the problem by one. The needed inversion of the Lamé equations on the rectangle is done with a new FFT-based direct elastostatic solver. We then use a narrow band level set method to perturb this shape with velocities based on the stresses and progress towards an improved design. Criteria are provided for advancing the shape in an appropriate direction, and to correct the evolving shape when given constraints are violated.

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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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