Title: Finding Efficient and Accurate Ways to Solve Interface Problems
Presented by: Cameron Campbell, Stacy Porten-Willson, Chuan Li
Abstract: Interface problems are a large class of problems that study the change of a physical
quantity in Physics, Biology, Engineering or Materials, such as heat or electrostatic
potential, as it propagates across a material interface. Due to the irregularly shaped
interface, solutions to interface problems can only be found numerically. However,
for the very same reason, classical numerical methods cannot deliver accurate estimations,
or may fail entirely. A new numerical method is necessary for solving interface problems
efficiently and accurately. In this project, we present our recent study of a well-tuned
matched Alternative Direction Interface (ADI) method for solving two-dimensional interface
problems with the most general of physical interface jump conditions. We also plan
to present our recent improvements on the efficiency, accuracy, and stability of the
proposed method.