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NOTE: Different day/time/location
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Joint Computer Science and
Aerospace Engineering Colloquium

October 13, 1995
2:00 - 3:00 pm
Eaton Conference Room
AE 1-25

Domain Decomposition and Multigrid Algorithms for Elliptic Problems on
Unstructured Meshes

Professor Tony F. Chan
Department of Mathematics
UCLA

We summarize some recent works of ours on the design and analysis of
multigrid and overlapping domain decomposition algorithms for solving
elliptic boundary value problems on unstructured meshes in two and three
dimensions. Unstructured meshes have become very popular recently in
scientific computing, primarily because of their flexibility in adapting
efficiently to complex geometries and rapid changes in the solution field.
However, many traditional solvers have to be modified so that their
efficiency will not be adversely affected by the lack of structure.

In this talk, we describe a class ofalgorithms which are based on the
construction of a coarse grid hierarchy, and the associated standard finite
element interpolation operators, from the given fine grid. We generate the
coarse grids by recursively computing maximal independent sets of the
boundary points and the interior points of a fine mesh and then
triangulating these points. We develop a theory which shows that our
additive domain decomposition and multilevel algorithms have the same
optimal convergence rate as the usual algorithms for structured meshes.
Very general meshes and subdomains are allowed: neither the fine mesh nor
the coarse mesh need to be quasi-uniform, the subdomains can be of
arbitrary shapes and sizes, and the coarse mesh need not be nested to, or
cover the same physical domain as the fine mesh. In particular, the theory
predicts that interpolation between the fine and coarse mesh on the Neumann
part of the fine grid boundary must be chosen carefully and we will discuss
several possibilities. Some numerical results for 2D problems will be
presented to demonstrate both the theory and the algorithms.

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http://www.cs.colorado.edu/95-96/colloq/schedule.html