Doghonay Arjmand: Solving elliptic PDEs in R^d

Abstract:

Solving elliptic problems in infinite domains often requires a truncation of the infinite domain and posing artificial boundary conditions on the boundary of the truncated computational geometry. These artificial boundary conditions pollute the solution inside a bounded domain of interests, the effect of which may be reduced by enlarging the computational domain. On the other hand, solving partial differential equations (PDEs) over very large domains is prohibitively expensive from a computational point of view and much more efficient methodologies are needed. A modelling strategy based on exponentially regularized elliptic problem was previously developed and analysed for periodic problems. In this work, we extend the analysis with no structural assumption on the coefficient while accurately approximating the solution of the elliptic PDE in a bounded domain of interest. In particular, the analysis here uncovers an interesting property of the right-hand side in the Fourier domain for the method to perform well for problems beyond periodicity.This is joint work with PhD student Filip Marttala.