Hunter La Croix
University of Notre Dame
12:30 PM
154 Hurley Hall
Least-Squares Series Solution to PDEs in First Passage Time Problems
In this talk, we will discuss how series solution methods, which has terms that already solve an underlying PDE and coefficients that fit to boundary data, have potential to solve many of the PDEs that are of interest in 2-dimensional first passage time problems, including mean first passage and reaction times, splitting, diffusion, shielding and capacitance problems. Problems on smooth geometries without abrupt switches in boundary conditions can generally be solved with exponential convergence with stability thanks to an Arnoldi orthogonalization algorithm. Root-exponential convergence for problems on sharper geometries and/or changes in boundary conditions from Dirichlet/Neumann/Robin can be recovered thanks to a Lightning solver approach. The different methods are explained and benchmarked against existing methods commonly used in FPT application.
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(This seminar is reserved for ACMS Graduate students and Postdocs only)