TITLE:

FORMULATION OF A TARGET-MATRIX PARADIGM FOR MESH OPTIMIZATION

DATE:

Friday, April 4th, 2008

TIME:

3:30 PM

LOCATION:

GMCS 214

SPEAKER:

Patrick M. Knupp, Optimization and Uncertainty Estimation Department, Sandia National Laboratories

ABSTRACT:

PDE simulations generally require a mesh on which the physical domain is discretized. The mesh can have a strong impact on solution accuracy & efficiency if not constructed properly. Methods to address this issue include solution-adaptive meshes, smoothing & swapping, and mesh optimization. An extension of Direct optimization (Castillo & others) will be described in this talk.

A Target-Matrix paradigm (TMP) for improving mesh quality by node repositioning via optimization is formulated in which target matrices describe the desired Jacobian matrix at mesh sample points. Attention is devoted to basic definitions & properties of mesh-based matrices, local & non-local quality metrics, and objective functions based on the power-mean. New local metrics are proposed that satisfy seven important requirements for a properly formulated mesh quality metric. Numerical experiments illustrate the theoretical properties and indicate the potential of this paradigm.

HOST:

Jose Castillo

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