Dr. Jeff Ovall speaks on numerical analysis and PDEs
Date: 3:30pm PST February 18, 2015 Location: JR Howard 254
JR Howard 254
Dr. Jeff Ovall, Maseeh Associate Professor of Mathematics at PSU, will discuss his work in numerically estimating solutions to PDEs.
Eigenvalue problems for differential operators naturally arise in analysis of the response of structures to vibrations. Except for a few very operators (e.g. the Laplacian) on very special domains (line segments, rectangles, triangles, circles and their sectors, etc.), eigenvalues and eigenvectors must be approximated numerically using discretization schemes which transform the problem into a linear algebraic eigenvalue problem. Our discussion will focus on the Laplace eigenvalue problem for bounded domains in one and two dimensions, and we will highlight some key results having natural analogues in linear algebra. By carefully considering examples where things are explicitly known, we will gain intuition about the potential challenges of providing efficient and accurate approximations for more realistic problems. We will introduce both finite difference and finite element discretization schemes and compare their relative merits. If time permits, we will consider the extension of these ideas to other types of elliptic differential operators.