High-order Filtered Schemes for the Hamilton-Jacobi Continuum Limit of Nondominated Sorting

A Hamilton-Jacobi Equation for the Continuum Limit of Nondominated Sorting

105 points 106 points Application: Polynuclear growth Random model for layer by layer growth [1] 1. Initially a flat crystal in contact with supersaturated vapor. 2. At a random later time, a supercritical nucleus forms, and spreads laterally via attachment of particles at the perimeter. 3. New layers are randomly nucleated upon existing layers. 4. When islands within the same layer collide, th...

A direct verification argument for the Hamilton-Jacobi equation continuum limit of nondominated sorting

Nondominated sorting is a combinatorial algorithm that sorts points in Euclidean space into layers according to a partial order. It was recently shown that nondominated sorting of random points has a Hamilton-Jacobi equation continuum limit. The original proof, given in [1], relies on a continuum variational problem. In this paper, we give a new proof using a direct verification argument that c...

High-Order Central WENO Schemes for Multidimensional Hamilton-Jacobi Equations

We present new thirdand fifth-order Godunov-type central schemes for approximating solutions of the Hamilton–Jacobi (HJ) equation in an arbitrary number of space dimensions. These are the first central schemes for approximating solutions of the HJ equations with an order of accuracy that is greater than two. In two space dimensions we present two versions for the third-order scheme: one scheme ...

High-Order Central WENO Schemes for 1D Hamilton-Jacobi Equations

Fifth-Order Weighted Power-ENO Schemes for Hamilton-Jacobi Equations

We design a class of Weighted Power-ENO (Essentially Non-Oscillatory) schemes to approximate the viscosity solutions of Hamilton-Jacobi (HJ) equations. The essential idea of the Power-ENO scheme is to use a class of extended limiters to replace the minmod type limiters in the classical third-order ENO schemes so as to improve resolution near kinks where the solution has discontinuous gradients....