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Design, Analysis and Application of Optimal PDE Solvers

Jinchao Xu
Department of Mathematics, Penn State University


A number of recent results, including special discretization schemes,adaptive methods and multilevel iterative methods for the resultingalgebraic systems, will be presented in this talk for variouspartial differential equations (PDEs). With a careful and combineduse of qualitative properties of PDEs, the underlying functionalspaces and their discretizations, many different kinds of equationswill be treated with similar techniques. After an introduction tosome practically efficient methods such as the algebraic multigridmethod for the Poisson equations, it will be shown how morecomplicated systems such as linear elasticity equations, electro-magnetic equations, porous media, Stokes equations and more generalnewtoninan-nonnewtonian models can be reduced to the solution of asequence of Poisson equation and its simple variants. Theefficiency of these algorithms will be illustrated by theoreticalanalysis, numerical examples and engineering applications.

Thursday, March 15, 2007
11:00AM AP&M 2402