The Sequential Regularization Method and Its Applications

Many mathematical models arising in Science and Engineering lead to computationally challenging problems involving differential equations with constraints. Examples include constrained mechanical systems, incompressible fluid flows, oil reservoir simulation, microstructures of liquid crystals and molecular dynamics. The direct discretization of such models is typically fraught with difficulties. We thus need to reformulate the original problem to obtain a better behaved problem before discretization. In this talk, I will use an example to introduce the concept of such equations and various reformulation methods. I will then discuss a particular family of such methods, the sequential regularization method (SRM). Advantages of the SRM over usual methods will be highlighted. I will provide examples of the application of the SRM to the incompressible Navier-Stokes equations, the miscible displacement in porous media in reservoir simulation and large mechanical chain problems. Other applications of the SRM and parallel implementation issues will be briefly mentioned.

Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).