Phase-Field Free Energy and Boundary Force for Molecular Solvation Abstract: We discuss a phase-filed variational model for the solvation of charged molecules with implicit solvent. The solvation free-energy functional of all phase fields consists of the surface energy, solute excluded volume and solute-solvent van der Waals dispersion energy, and electrostatic free energy. The last part

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

Title: New augmented Lagrangian method for a curvature dependent segmentation model Abstract: Augmented Lagrangian methods (ALMs) have proved to be successful for the minimization of curvature dependent functionals in image processing. However, those ALM based algorithms often suffer from choosing appropriate penalty parameters in the numerical implementation. In this talk, we will discuss our recent