Plenary and Semi-Plenary Lectures
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| Title: |
| A Multilevel Partition of Unity Method and its Application in Computational Mechanics |
| Lecturer: |
| Michael Griebel |
| Abstract: |
The partition of unity method (PUM) is a meshfree generalization of the finite element method. It is based on points only and does not require the existence of a valid mesh. The PUM can be employed in an h-version, a p-version and an hp-version. Furthermore, the PUM supports the use of problem-dependent approximation spaces (i.e. there is a PUM q-version) and it can be interpreted as a variational multi-scale method. The freedom in the meshfree construction of the PUM shape functions makes the design of efficient multilevel solution techniques for the sparse linear systems arising from a PUM-Galerkin discretization somewhat more involved than for the FEM.
In this talk, we present a number of examples of the multilevel PUM in computational mechanics (e.g. thermal and elastic problems, magnetic multiparticle problems) which demonstrate the approximation properties as well as the computational efficiency of or multilevel PUM.
This is joint work with Alex Schweitzer. |
 Michael Griebel received his Ph.D. in 1989 at the Technical University Munich, Germany, in computer science. Currently, he is a full professor of Mathematics and Director of the Institute of Numerical Simulation at the University of Bonn, Germany. He is a member of GAMM, SIAM and DMV. Michael is the managing editor for "Numerische Mathematik (Springer)", and serves on the editorial boards of the "SIAM Journal of Scientific Computing", the journal "Computational Methods in Applied Mathematics". Furthermore, he is an editor of the Springer book series "Lecture Notes in Computational Science and Engineering" and "Texts in Computational Science and Engineering". |
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