We are interested in computational methods to solve for problems related to shells and 3-d solids. In particular, questions related to computational methods that can handle singularities in geometric and mechanical fields in solids. Further I am interested in questions related to rigorous understanding of convergence etc. for numerical methods applicable for such systems.
Computational methods to handle singularities: Both point and interfacial singularities play a central role in mechanics. We try to extend methods like FEM to model such singularities and obtain solutions under presence of singularities
Mechanics of singularities: FEM based methods to track movement and interaction of singularities
Topological constraints: Computational methods for defect in different topologies like sphere, torus etc.