FLIP: A method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions
Journal of Computational Physics
Numerical grid generation: foundations and applications
Numerical grid generation: foundations and applications
Equidistribution schemes, poisson generators, and adaptive grids
Applied Mathematics and Computation
Computer Methods in Applied Mechanics and Engineering
Adaptive grid generation from harmonic maps on Reimannian manifolds
Journal of Computational Physics
FLIP MHD: a particle-cell method for magnetohydrodynamics
Journal of Computational Physics
A numerical method for suspension flow
Journal of Computational Physics
An adaptive grid with directional control
Journal of Computational Physics
A simple adaptive grid method in two dimensions
SIAM Journal on Scientific Computing
Moving mesh partial differential equations (MMPDES) based on the equidistribution principle
SIAM Journal on Numerical Analysis
Structured adaptive grid generation
Applied Mathematics and Computation - Special issue on differential equations and computational simulations I
Solution adaptive direct variational grids for fluid flow calculations
Journal of Computational and Applied Mathematics
Jacobian-Weighted Elliptic Grid Generation
SIAM Journal on Scientific Computing
Moving mesh methods with upwinding schemes for time-dependent PDEs
Journal of Computational Physics
Numerical solution of the quasilinear Poisson equation in a nonuniform triangle mesh
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
An Adaptive Grid Method and Its Application to Steady Euler Flow Calculations
SIAM Journal on Scientific Computing
An r-adaptive finite element method based upon moving mesh PDEs
Journal of Computational Physics
A multilevel iterative field solver for implicit, kinetic, plasma simulation
Journal of Computational Physics
A multgrid Newton-Krylov method for multimaterial equilibrium radiation diffusion
Journal of Computational Physics
A Study of Monitor Functions for Two-Dimensional Adaptive Mesh Generation
SIAM Journal on Scientific Computing
A Multigrid Preconditioned Newton--Krylov Method
SIAM Journal on Scientific Computing
An implicit energy-conservative 2D Fokker-Planck algorithm: II. Jacobian-free Newton—Krylov solver
Journal of Computational Physics
On Newton-Krylov multigrid methods for the imcompressible Navier-Stokes equations
Journal of Computational Physics
Variational mesh adaptation: isotropy and equidistribution
Journal of Computational Physics
An implicit, nonlinear reduced resistive MHD solver
Journal of Computational Physics
A Multigrid-Preconditioned Newton--Krylov Method for the Incompressible Navier--Stokes Equations
SIAM Journal on Scientific Computing
A 2D high-ß Hall MHD implicit nonlinear solver
Journal of Computational Physics
Journal of Computational Physics
r-Adaptive mesh generation for shell finite element analysis
Journal of Computational Physics
A fully implicit, nonlinear adaptive grid strategy
Journal of Computational Physics
The Monge-Ampère equation: Various forms and numerical solution
Journal of Computational Physics
Robust, multidimensional mesh-motion based on Monge-Kantorovich equidistribution
Journal of Computational Physics
Fast finite difference solvers for singular solutions of the elliptic Monge-Ampère equation
Journal of Computational Physics
Optimal mass transport for higher dimensional adaptive grid generation
Journal of Computational Physics
Generalized Monge-Kantorovich Optimization for Grid Generation and Adaptation in $L_{p}$
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
Quadratic Finite Element Approximations of the Monge-Ampère Equation
Journal of Scientific Computing
Numerical solution of the Optimal Transportation problem using the Monge-Ampère equation
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Hi-index | 31.48 |
A new cell-area equidistribution method for two-dimensional grid adaptation, based on Monge-Kantorovich optimization (or Monge-Kantorovich optimal transport), is presented. The method is based on a rigorous variational principle, in which the L"2 norm of the grid displacement is minimized, constrained locally to produce a prescribed positive-definite cell volume distribution. The procedure involves solving the Monge-Ampere equation: A single, nonlinear, elliptic scalar equation with no free parameters, and with proved existence and uniqueness theorems. We show that, for sufficiently small grid displacement, this method also minimizes the mean grid-cell distortion, measured by the trace of the metric tensor. We solve the Monge-Ampere equation numerically with a Jacobian-Free Newton-Krylov method. The ellipticity property of the Monge-Ampere equation allows multigrid preconditioning techniques to be used effectively, delivering a scalable algorithm under grid refinement. Several challenging test cases demonstrate that this method produces optimal grids in which the constraint is satisfied numerically to truncation error. We also compare this method to the well known deformation method [G. Liao, D. Anderson, Appl. Anal. 44 (1992) 285]. We show that the new method achieves the desired equidistributed grid using comparable computational time, but with considerably better grid quality than the deformation method.