Abstract ? O?Brien (0915462) This research project focuses on numerical and geometric methods for physically realistic simulation of objects and materials whose shapes are grossly deforming or changing. These methods use several techniques for dynamic mesh generation, wherein unstructured tetrahedral volume meshes and triangular surface meshes evolve or change through time to accommodate the movement of a highly deformable material. This research is leading to unprecedented simulation capabilities to evolve the meshes used for numerical techniques such as finite element methods and finite volume methods, while maintaining high-quality tetrahedra and triangles. These new algorithms will enable the simulation of phenomena that could not previously be modeled well because of the difficulty of simulating materials whose shapes change radically, such as body tissues during surgery or ballistics undergoing high-speed impacts. The technical contributions of this research fall into two classes. The first contribution is numerical methods that use dynamic mesh generation to bring better accuracy to simulations of elastoplastic solids and viscous fluids undergoing plastic flow, cutting, and fracture. The simulation and dynamic mesher are being coupled so that they locally conserve mass, energy, and momentum as a mesh evolves, and so that the refinement and anisotropy of the mesh are tailored to the physical problem. The second contribution is extensions of dynamic geometry algorithms developed by the researchers that more accurately model surface evolution, that enable a finer surface resolution than volume resolution, and that easily handle topological changes and self-collisions.
