Boundary integral methods are attractive for solving homogeneous elliptic

partial differential equations on complicated geometries, since they can

offer accurate solutions with a computational cost that is linear or close

to linear in the number of discretization points on the boundary of the

domain. However, these numerical methods are not straightforward to apply to

time-dependent equations, which often arise in science and engineering. We

address this problem with an integral equation-based solver for the

advection-diffusion equation on moving and deforming geometries in two space

dimensions. In this method, an adaptive high-order accurate time-stepping

scheme based on semi-implicit spectral deferred correction is applied. One

time-step then involves solving a sequence of non-homogeneous modified

Helmholtz equations, a method known as elliptic marching. Our solution

methodology utilizes several recently developed methods, including special

purpose quadrature, a function extension technique and a spectral Ewald

method for the modified Helmholtz kernel. Special care is also taken to

handle the time-dependent geometries. The numerical method is tested through

several numerical examples to demonstrate robustness, flexibility and

accuracy.

# An integral equation method for the advection-diffusion equation on time-dependent domains in the plane

Event time:

Wednesday, January 25, 2023 - 1:00pm

Location:

AKW 200

Speaker:

Fredrik Fryklund

Speaker affiliation:

NYU

Event description: