Applied and Computational Math Seminar: Computational analysis of problems on domains with small holes

Speaker: Ana Maria Soane, United States Naval Academy
Title: Computational analysis of problems on domains with small holes

Abstract: The modeling challenges arising when the problem domain has small holes in it are considered through a representative membrane problem. We propose a numerical method which combines analytic knowledge of the solution singularities with finite element approximation of its smooth components. This allows us to perform the finite element modeling on a "filled in" domain without discs, thus obviating the need to use curvilinear elements or implement any special meshing. Theoretical and numerical results are provided to establish the efficacy and robustness of the method, both in the the energy norm and in extracting a representative quantity of interest. The method converges both with respect to the size of the holes and the mesh discretization parameter, and provides a more accurate alternative to using the asymptotic limit. This is joint work with Ivo Babuska (UT Austin) and Manil Suri (UMBC). 

Time: Friday, September 7, 2018, 1:30-2:30pm

Place: Exploratory Hall, Room 4106