2 citations · 5 across the 12 of their papers we have counts for
12 papers
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 strong comparison principle for the generalized Dirichlet problem for Monge-Ampere
Brittany Froese Hamfeldt
We prove a strong form of the comparison principle for the elliptic Monge-Ampere equation, with a Dirichlet boundary condition interpreted in the viscosity sense. This comparison p…
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…
Convergent Finite Difference Methods for Fully Nonlinear Elliptic Equations in Three Dimensions
Brittany Froese Hamfeldt, Jacob Lesniewski
We introduce a generalized finite difference method for solving a large range of fully nonlinear elliptic partial differential equations in three dimensions. Methods are based on C…
A convergence framework for optimal transport on the sphere
Brittany Froese Hamfeldt, Axel G. R. Turnquist
We consider a PDE approach to numerically solving the optimal transportation problem on the sphere. We focus on both the traditional squared geodesic cost and a logarithmic cost, w…
A convergent finite difference method for computing minimal Lagrangian graphs
Brittany Froese Hamfeldt, Jacob Lesniewski
We consider the numerical construction of minimal Lagrangian graphs, which is related to recent applications in materials science, molecular engineering, and theoretical physics. I…
Convergence framework for the second boundary value problem for the Monge-Ampère equation
Brittany Froese Hamfeldt
It is well known that the quadratic-cost optimal transportation problem is formally equivalent to the second boundary value problem for the Monge-Ampère equation. Viscosity solutio…
Higher-order Adaptive Finite Difference Methods for Fully Nonlinear Elliptic Equations
Brittany D. Froese, Tiago Salvador
We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by…