The fluid dynamic approach to equidistribution methods for grid adaptation

DOI10.1016/j.cpc.2010.10.010zbMath1217.65184OpenAlexW1975544169MaRDI QIDQ537003

Gian Luca Delzanno, John M. Finn

Publication date: 31 May 2011

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2010.10.010

zbMATH Keywords

numerical examplesequidistributionMonge-Ampère equationNewton-Krylovmultigrid preconditioningmoving meshesMonge-Kantorovich optimizationadaptive grid generationfluid dynamic formulationgrid tanglingimage morphing

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Preconditioners for iterative methods (65F08) Parabolic Monge-Ampère equations (35K96)

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Uniform convergence analysis of finite difference approximations for advection–reaction–diffusion problem on adaptive grids ⋮ A new hybrid adaptive mesh algorithm based on Voronoi tessellations and equi-distribution principle: algorithms and numerical experiments ⋮ Numerical solution of Monge-Kantorovich equations via a dynamic formulation ⋮ Robust, multidimensional mesh-motion based on Monge-Kantorovich equidistribution ⋮ Adaptive isogeometric analysis using optimal transport and their fast solvers

Cites Work

• Unnamed Item
• Unnamed Item
• Robust, multidimensional mesh-motion based on Monge-Kantorovich equidistribution
• A survey of dynamically-adaptive grids in the numerical solution of partial differential equations
• Cost-effectiveness of fully implicit moving mesh adaptation: a practical investigation in 1D
• On a partial differential equation involving the Jacobian determinant
• An optimal robust equidistribution method for two-dimensional grid adaptation based on Monge-Kantorovich optimization
• Equidistribution schemes, Poisson generators, and adaptive grids
• Adaptive grid generation
• Adaptive zoning for singular problems in two dimensions
• Grid generation via deformation
• The geometry of optimal transportation
• Variational grid adaptation based on the minimization of local truncation error: Time-inde\-pend\-ent problems.
• Formes-volume sur les variétés à bord
• \(r\)-adaptive mesh generation for shell finite element analysis
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• Optimal mass transport for registration and warping
• Moving Mesh Generation Using the Parabolic Monge–Ampère Equation
• Mathematical and Numerical Analysis of a Robust and Efficient Grid Deformation Method in the Finite Element Context
• A new approach to grid generation
• Differential equations methods for the Monge-Kantorovich mass transfer problem
• An Adaptive Grid Method and Its Application to Steady Euler Flow Calculations
• Numerical grid generator based on Moser's deformation method
• Moving Mesh Partial Differential Equations (MMPDES) Based on the Equidistribution Principle
• Minimizing Flows for the Monge--Kantorovich Problem
• Least squares and approximate equidistribution in multidimensions
• The Monge–Kantorovitch mass transfer and its computational fluid mechanics formulation
• A moving grid finite‐element method using grid deformation
• Analysis and computation of adaptive moving grids by deformation
• Generalized Monge–Kantorovich Optimization for Grid Generation and Adaptation in $L_{p}$
• On the Volume Elements on a Manifold
• Mixed \(L^2\)-Wasserstein optimal mapping between prescribed density functions