In this talk, first, we will give an introduction to the Difference Potentials Method (DPM).
DPM is a framework for developing efficient, high-order accurate numerical methods for the solution of interior
or exterior boundary value problems (BVPs) on arbitrary domains. DPM can be viewed as a discrete analog to
the method of generalized Calderón potentials and Calderón boundary equations with projections in the theory
of partial differential equations. Designing numerical methods with high-order accuracy for problems with interfaces
(for example, models for composite materials or fluids, etc.), as well as models in irregular domains is crucial
to many physical and biological applications. We will discuss recently developed efficient numerical schemes based
on the idea of the Difference Potentials for elliptic and parabolic interface/composite domain problems.
Numerical experiments to illustrate high-order accuracy and the robustness of the developed methods will be
presented as well.
This colloquium will be held in
7800 York Road,
Room 320 at 4:00 p.m., with light refreshments served before the talk, at