My work involves developing validated numerical methods (Multiscale FEM) to understand and simulate the evolution of field discontinuities (displacement, curvature, related distributions in other field theories).  Mathematically this translates to restructuring the field into “coarse” and  “fine’’ scales  and enriching the fine scale field with discontinuous shape functions (step functions).  Physically, this manifests as crack/damage evolution in materials based on experimentally determined criteria. Concepts are drawn from continuum/fracture mechanics, theory of distributions, numerical methods and scientific computing techniques.