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Partial Differential Equations

Hoang Viet Ha's research in Computational Mathematics concentrates on efficient numerical methods for problems with multiple scales and stochastic partial differential equations. In particular, he has been using sparse finite element methods to reduce complexity in solving high dimensional problems arising in these fields. For multiscale problems, together with his collaborator he has developed an algorithm that reduces significantly the complexity of solving periodic multiscale problems. He hopes to extend the method to non-periodic problems. For stochastic partial differential equations, he has been developing methods that achieve the same complexity as for a single deterministic partial differential equation.

Hoang Viet Ha's research in Partial Differential Equations is mainly on periodic and random homogenization, and on bounding the effective coefficients. He is also interested in partial differential equations with a forcing term driven by white noise. He also maintains an interest on free boundary value problems, especially those that can be solved exactly by conformal mapping methods.