Abstract

Interface problems are ubiquitous in fields such as fluid mechanics, materials science, and biophysics. Traditional finite element and finite volume methods often rely on an interface-fitted mesh, which can be both difficult and expensive to generate with high quality. In this presentation, I will introduce a kernel-free boundary integral method, which serves as a finite difference analogue to the boundary integral approach, for accurately and efficiently solving partial differential equation (PDE) interface problems. This method reformulates boundary and volume integrals as simpler interface problems, which are then solved using a corrected finite difference scheme on an unfitted Cartesian grid. The use of a correction function near the interface significantly simplifies the computation of correction terms, enabling the development of high-order schemes with minimal additional effort. Numerical examples will be presented to demonstrate the accuracy and efficiency of the method.

 

WebEx Link: https://nationaltaiwanuniversity-ksz.my.webex.com/nationaltaiwanuniversity-ksz.my/j.php?MTID=m89b9e6a7886581e4fd915f44aa0ccd9c

Meeting number (access code): 2516 918 5737

Meeting password: EymyZCaT833

 

Organizer: Te-Sheng Lin (NYCU)