My area of work, in particular, is the generalization of substructuring methods with Waveform Relaxation method, formally named as the Dirichlet-Neumann Waveform Relaxation (DNWR) and the Neumann-Neumann Waveform Relaxation (NNWR), for time dependent problems. Currently, we have shown superlinear convergence behavior of the above mentioned methods for the Heat equation, and finite step convergence for We are continuing our works with the Wave equation. A practical implementation of these methods has been formulated in pipeline fashion to enhance performance in parallel computer.
Currently I am focusing on applying Domain Decomposition to Hamilton-Jacobi type equations.