45 citations · 68 across the 6 of their papers we have counts for
6 papers
A Fast Integral Equation Method for the Two-Dimensional Navier-Stokes Equations
Ludvig af Klinteberg, Travis Askham, Mary Catherine Kropinski
The integral equation approach to partial differential equations (PDEs) provides significant advantages in the numerical solution of the incompressible Navier-Stokes equations. In…
An integral equation based numerical method for the forced heat equation on complex domains
Fredrik Fryklund, Mary Catherine A. Kropinski, Anna-Karin Tornberg
Integral equation based numerical methods are directly applicable to homogeneous elliptic PDEs, and offer the ability to solve these with high accuracy and speed on complex domains…
Integral equation methods for the Yukawa-Beltrami equation on the sphere
Nilima Nigam, Mary-Catherine Kropinski, Bryan Quaife
An integral equation method for solving the Yukawa-Beltrami equation on a multiply-connected sub-manifold of the unit sphere is presented. A fundamental solution for the Yukawa-Bel…
Fast integral equation methods for the Laplace-Beltrami equation on the sphere
Mary Catherine A. Kropinski, Nilima Nigam
Integral equation methods for solving the Laplace-Beltrami equation on the unit sphere in the presence of multiple "islands" are presented. The surface of the sphere is first mappe…
Fast integral equation methods for the heat equation and the modified Helmholtz equation in two dimensions
Mary-Catherine Kropinski, Bryan Quaife
We present an efficient integral equation approach to solve the heat equation, $u_t (\x) - Δu(\x) = F(\x,t)$, in a two-dimensional, multiply connected domain, and with Dirichlet bo…
Fast integral equation methods for the modified Helmholtz equation
Mary-Catherine Kropinski, Bryan Quaife
We present a collection of integral equation methods for the solution to the two-dimensional, modified Helmholtz equation, $u(\x) - α^2 Δu(\x) = 0$, in bounded or unbounded multipl…