1 citations · 3 across the 7 of their papers we have counts for
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Numerical Optimal Transport from 1D to 2D using a Non-local Monge-Ampère Equation
Matthew A. Cassini, Brittany Froese Hamfeldt
We consider the numerical solution of the optimal transport problem between densities that are supported on sets of unequal dimension. Recent work by McCann and Pass reformulates t…
Domain Decomposition Methods for the Monge-Ampère equation
Yassine Boubendir, Jake Brusca, Brittany Froese Hamfeldt +1
We introduce a new overlapping Domain Decomposition Method (DDM) to solve the fully nonlinear Monge-Ampère equation. While DDMs have been extensively studied for linear problems, t…
A Convergent Quadrature Based Method For The Monge-Ampère Equation
Jake Brusca, Brittany Froese Hamfeldt
We introduce an integral representation of the Monge-Ampère equation, which leads to a new finite difference method based upon numerical quadrature. The resulting scheme is monoton…
On the Reduction in Accuracy of Finite Difference Schemes on Manifolds without Boundary
Brittany Froese Hamfeldt, Axel G. R. Turnquist
We investigate error bounds for numerical solutions of divergence structure linear elliptic PDEs on compact manifolds without boundary. Our focus is on a class of monotone finite d…
A Convergent Numerical Method for the Reflector Antenna Problem via Optimal Transport on the Sphere
Brittany Froese Hamfeldt, Axel G R Turnquist
We consider a PDE approach to numerically solving the reflector antenna problem by solving an Optimal Transport problem on the unit sphere with cost function $c(x,y) = -2\log \left…
A Convergent Finite Difference Method for Optimal Transport on the Sphere
Brittany Froese Hamfeldt, Axel G. R. Turnquist
We introduce a convergent finite difference method for solving the optimal transportation problem on the sphere. The method applies to both the traditional squared geodesic cost (a…