OOptimization Techniques for Mesh Warping and Nonlinear Elasticity

Suzanne Shontz

Department of Computer Science and Engineering
Penn State University

This talk will address two recent moving mesh problems from my research in the areas of mesh warping and nonlinear elasticity.

In the first part of my talk, I will describe a mesh warping problem of interest. The process of warping a mesh from a source to a target domain can potentially drastically alter the quality of the mesh from step to step. One problem that can occur is element reversal, which is when an element changes its orientation. We consider an algorithm called FEMWARP for warping tetrahedral finite element meshes that computes the warping using the finite element method itself. Our main concern is when this algorithm reverses elements. We analyze the causes for this undesirable behavior and propose techniques to make the method more robust against reversals. Among the methods includes combining FEMWARP with an optimization-based untangler. We will also demonstrate the applicability of FEMWARP to cardiology.

n the second part of my talk, I will propose a solution procedure for the finite element discretization of a hyperelastic solid with large boundary deformation. Mesh tangling is again an issue for straightforward algorithms. Our algorithm first untangles the mesh and then uses a constrained Newton-type method to avoid further tangling. Our computational results indicate significant improvements over the straightforward Newton-continuation procedure.

Part of this talk represents joint work with S. Vavasis of the University of Waterloo.