Title: Immersed Finite Element Methods for Interface Problems Basic idea, Development, Analysis, and Applications Abstract: Simulating a multi-scale/multi-physics phenomenon often involves a domain consisting of different materials. This often leads to the so-called interface problems of partial differential equations. Classical finite elements methods can solve interface problems satisfactorily if the mesh is aligned with interfaces; otherwise the

Title: Effective models of flow in highly heterogeneous fractured/vuggy porous media   Abstract:  The presence of vugs and fractures in porous media can significantly affect pressure and flow behavior of a fluid. In this talk, I will present the effective models of flow in a porous medium including multi-scale fractures and  several vuggs of various

Title: Semidefinite relaxation of the clustering problem and first-order methods for their solution Abstract: I will discuss a novel relaxation approach for the graph clustering problem. Although intractable in worst-case, much recent research has established that clusters can be recovered if the underlying network or data is well-behaved. In particular, I will provide conditions on