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.