Optimal-Transport--Based Mesh Adaptivity on the Plane and Sphere Using Finite Elements
From MaRDI portal
Publication:4637678
DOI10.1137/16M1109515zbMath1448.65143arXiv1612.08077OpenAlexW2963607619WikidataQ129904595 ScholiaQ129904595MaRDI QIDQ4637678
Andrew T. T. McRae, Chris J. Budd, Colin John Cotter
Publication date: 25 April 2018
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1612.08077
Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Parabolic Monge-Ampère equations (35K96) Monge-Ampère equations (35J96) PDEs on manifolds (35R01)
Related Items (17)
A convergent finite difference method for optimal transport on the sphere ⋮ Conservation with moving meshes over orography ⋮ A convergence framework for optimal transport on the sphere ⋮ Sliced optimal transport on the sphere ⋮ Adaptive mesh methods on compact manifolds via optimal transport and optimal information transport ⋮ Computing Weak Distance between the 2-Sphere and Its Nonsmooth Approximations ⋮ A fast dynamic smooth adaptive meshing scheme with applications to compressible flow ⋮ Numerical homogenization by an adaptive Fourier spectral method on non-uniform grids using optimal transport ⋮ Registration-based model reduction of parameterized PDEs with spatio-parameter adaptivity ⋮ Numerical methods for fully nonlinear and related PDEs. Abstracts from the workshop held June 27 -- July 3, 2021 (hybrid meeting) ⋮ An Adaptive Moving Mesh Method for Forced Curve Shortening Flow ⋮ A surface moving mesh method based on equidistribution and alignment ⋮ Well balanced residual distribution for the ALE spherical shallow water equations on moving adaptive meshes ⋮ The scaling and skewness of optimally transported meshes on the sphere ⋮ Unnamed Item ⋮ A Diffusion-Driven Characteristic Mapping Method for Particle Management ⋮ Multi-scale hydro-morphodynamic modelling using mesh movement methods
Uses Software
Cites Work
- Unnamed Item
- Numerical solution of the optimal transportation problem using the Monge-Ampère equation
- Fast three dimensional r-adaptive mesh redistribution
- Modelling atmospheric flows with adaptive moving meshes
- Optimal mass transport for higher dimensional adaptive grid generation
- Adaptive moving mesh methods
- Robust, multidimensional mesh-motion based on Monge-Kantorovich equidistribution
- Fast finite difference solvers for singular solutions of the elliptic Monge-Ampère equation
- The geometry of r-adaptive meshes generated using optimal transport methods
- Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampère type equation
- An augmented Lagrangian approach to the numerical solution of the Dirichlet problem for the elliptic Monge-Ampère equation in two dimensions
- Quadratic mixed finite element approximations of the Monge-Ampère equation in 2D
- An optimal robust equidistribution method for two-dimensional grid adaptation based on Monge-Kantorovich optimization
- Efficient implementation of essentially nonoscillatory shock-capturing schemes
- On the numerical solution of the equation \(\frac{\partial ^ 2z\partial ^ 2z}{\partial x^ 2\partial y^ 2}-(\frac{\partial ^ 2z}{\partial x\partial y})^ 2=f\) and its discretizations. I
- An all-scale anelastic model for geophysical flows: dynamic grid deformation.
- Convergence analysis of finite difference approximations on equidistributed grids to a singularly perturbed boundary value problem
- Numerical solution of the Monge--Ampère equation by a Newton's algorithm
- The scaling and skewness of optimally transported meshes on the sphere
- Finite element methods for fully nonlinear second order PDEs based on a discrete Hessian with applications to the Monge-Ampère equation
- Numerical methods for fully nonlinear elliptic equations of the Monge-Ampère type
- Monge-Ampère based moving mesh methods for numerical weather prediction, with applications to the Eady problem
- A (dis)continuous finite element model for generalized 2D vorticity dynamics
- Composing Scalable Nonlinear Algebraic Solvers
- Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements
- A Parallel Edge Orientation Algorithm for Quadrilateral Meshes
- Finite element approximations of the three dimensional Monge-Ampère equation
- A Finite Element Method for Nonlinear Elliptic Problems
- Preconditioning discretizations of systems of partial differential equations
- 𝒞⁰ penalty methods for the fully nonlinear Monge-Ampère equation
- A Finite Element Method for Second Order Nonvariational Elliptic Problems
- Convergent Finite Difference Solvers for Viscosity Solutions of the Elliptic Monge–Ampère Equation in Dimensions Two and Higher
- An Algorithm for the Optimization of Finite Element Integration Loops
- Moving Mesh Generation Using the Parabolic Monge–Ampère Equation
- Firedrake
- Mixed Finite Element Methods for the Fully Nonlinear Monge–Ampère Equation Based on the Vanishing Moment Method
- Two Numerical Methods for the elliptic Monge-Ampère equation
- On Convex Functions and the Finite Element Method
- Adaptivity with moving grids
- Polar factorization and monotone rearrangement of vector‐valued functions
- TSFC: A Structure-Preserving Form Compiler
- Towards mesh adaptivity for geophysical turbulence: continuous mapping approach
- Generalized Monge–Kantorovich Optimization for Grid Generation and Adaptation in $L_{p}$
- Parabolic Monge–Ampère methods for blow-up problems in several spatial dimensions
- Unified form language
- Polar factorization of maps on Riemannian manifolds
This page was built for publication: Optimal-Transport--Based Mesh Adaptivity on the Plane and Sphere Using Finite Elements
