109 citations · 522 across the 51 of their papers we have counts for
18 papers · 1 filter
Improved accuracy of monotone finite difference schemes on point clouds and regular grids
Chris Finlay, Adam Oberman
Finite difference schemes are the method of choice for solving nonlinear, degenerate elliptic PDEs, because the Barles-Sougandis convergence framework [Barles and Sougandidis, Asym…
Computing the quasiconvex envelope using a nonlocal line solver
Bilal Abbasi, Adam M. Oberman
Recently in a series of articles, Barron, Goebel, and Jensen \cite{barron2012functions} \cite{barron2012quasiconvex} \cite{barron2013quasiconvex} \cite{barron2013uniqueness} have s…
Finite difference methods for fractional Laplacians
Yanghong Huang, Adam Oberman
The fractional Laplacian is the prototypical non-local elliptic operator. While analytical theory has been advanced and understood for some time, there remain many ope…
Numerical methods for motion of level sets by affine curvature
Adam M. Oberman, Tiago Salvador
We study numerical methods for the nonlinear partial differential equation that governs the motion of level sets by affine curvature. We show that standard finite difference scheme…
An efficient linear programming method for Optimal Transportation
Adam M. Oberman, Yuanlong Ruan
An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discre…
Numerical Methods for the 2-Hessian Elliptic Partial Differential Equation
Brittany D. Froese, Adam M. Oberman, Tiago Salvador
The elliptic 2-Hessian equation is a fully nonlinear partial differential equation (PDE) that is related to intrinsic curvature for three dimensional manifolds. We introduce two nu…
Adaptive finite difference methods for nonlinear elliptic and parabolic partial differential equations with free boundaries
Adam M. Oberman, Ian Zwiers
Monotone finite difference methods provide stable convergent discretizations of a class of degenerate elliptic and parabolic Partial Differential Equations (PDEs). These methods ar…
Numerical methods for matching for teams and Wasserstein barycenters
Guillaume Carlier, Adam Oberman, Edouard Oudet
Equilibrium multi-population matching (matching for teams) is a problem from mathematical economics which is related to multi-marginal optimal transport. A special but important ca…
Filtered schemes for Hamilton-Jacobi equations: a simple construction of convergent accurate difference schemes
Adam M. Oberman, Tiago Salvador
We build a simple and general class of finite difference schemes for first order Hamilton-Jacobi (HJ) Partial Differential Equations. These filtered schemes are convergent to the u…
A multigrid scheme for 3D Monge-Ampère equations
Jun Liu, Brittany D. Froese, Adam M. Oberman +1
The elliptic Monge-Ampère equation is a fully nonlinear partial differential equation which has been the focus of increasing attention from the scientific computing community. Fast…
Numerical Methods for the Fractional Laplacian: a Finite Difference-quadrature Approach
Yanghong Huang, Adam Oberman
The fractional Laplacian is a non-local operator which depends on the parameter and recovers the usual Laplacian as . A numerical method for the fractional…
Numerical solution of the Optimal Transportation problem using the Monge-Ampere equation
Jean-David Benamou, Brittany D. Froese, Adam M. Oberman
A numerical method for the solution of the elliptic Monge-Ampere Partial Differential Equation, with boundary conditions corresponding to the Optimal Transportation (OT) problem is…
A viscosity solution approach to the Monge-Ampere formulation of the Optimal Transportation Problem
Jean-David Benamou, Brittany D. Froese, Adam M. Oberman
In this work we present a numerical method for the Optimal Mass Transportation problem. Optimal Mass Transportation (OT) is an active research field in mathematics.It has recently…
Convergent filtered schemes for the Monge-Ampère partial differential equation
Brittany D. Froese, Adam M. Oberman
The theory of viscosity solutions has been effective for representing and approximating weak solutions to fully nonlinear Partial Differential Equations (PDEs) such as the elliptic…
A numerical method for variational problems with convexity constraints
Adam M. Oberman
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interfa…
Finite difference methods for the Infinity Laplace and p-Laplace equations
Adam M. Oberman
We build convergent discretizations and semi-implicit solvers for the Infinity Laplacian and the game theoretical -Laplacian. The discretizations simplify and generalize earlier…
Fast finite difference solvers for singular solutions of the elliptic Monge-Ampère equation
Brittany D. Froese, Adam M. Oberman
The elliptic Monge-Ampere equation is a fully nonlinear Partial Differential Equation which originated in geometric surface theory, and has been applied in dynamic meteorology, ela…
Convergent finite difference solvers for viscosity solutions of the elliptic Monge-Ampère equation in dimensions two and higher
Brittany D. Froese, Adam M. Oberman
The elliptic Monge-Ampère equation is a fully nonlinear Partial Differential Equation that originated in geometric surface theory and has been applied in dynamic meteorology, elast…