Efficient Solvers for Some Partial Differential Equations in Physics

Dr. Yunrong Zhu
Idaho State University
Department of Mathematics

Many sciences and engineering phenomenas can be modeled by some linear/nonlinear partial differential  equations (PDEs).  Since the experimental techniques are quite limited and the analytic solutions of these problems are difficult to obtain if not impossible, numerical simulation to such problems in complex geometric domains is a primary method of scientific investigation. A significant problem is to design accurate and efficient numerical algorithms for these PDEs. 
In this talk, I will first give an overview of the numerical PDE. I will discuss the numerical discretizations of some model equations in physics (for example, the Poisson’s equation and Maxwell’s equations). The discretization of these PDEs results in large, space and extremely ill conditioned linear systems. Then I will discuss the efficient multilevel iterative solvers for these linear system, which allow us to solve the systems with the computer operations proportional to the number of unknowns.