A Generalized Newton Method for Homogenization of Hamilton--Jacobi Equations

DOI10.1137/16M1058613zbMath1354.65129MaRDI QIDQ2833534

Simone Cacace, Fabio Camilli

Publication date: 18 November 2016

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

homogenizationHamilton-Jacobi equationsNewton-like methodseffective Hamiltoniandislocation dynamicsnumerical testmean field gamesinconsistent nonlinear systems

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Newton-type methods (49M15) Existence theories for optimal control problems involving partial differential equations (49J20) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Hamilton-Jacobi equations (35F21)

Related Items (12)

Asymptotics for small nonlinear price impact: A PDE approach to the multidimensional case ⋮ Error analysis of the high order scheme for homogenization of Hamilton-Jacobi equation ⋮ Two numerical approaches to stationary mean-field games ⋮ A Simple Explicit Operator-Splitting Method for Effective Hamiltonians ⋮ On the Variational Formulation of Some Stationary Second-Order Mean Field Games Systems ⋮ An eikonal equation with vanishing Lagrangian arising in global optimization ⋮ Proximal Methods for Stationary Mean Field Games with Local Couplings ⋮ One-dimensional forward-forward mean-field games ⋮ A mean field games approach to cluster analysis ⋮ A policy iteration method for mean field games ⋮ The Hessian Riemannian flow and Newton’s method for effective Hamiltonians and Mather measures ⋮ An ergodic problem for Mean Field Games: qualitative properties and numerical simulations

Cites Work

• Unnamed Item
• Unnamed Item
• A posteriori error estimates for the effective Hamiltonian of dislocation dynamics
• Mean field games
• Homogenization of some particle systems with two-body interactions and of the dislocation dynamics
• A numerical study for the homogenisation of one-dimensional models describing the motion of dislocations
• Some new PDE methods for weak KAM theory
• Multi-population mean field games systems with Neumann boundary conditions
• An approximation scheme for the effective Hamiltonian and applications
• A Newton-Raphson method for the solution of systems of equations
• Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, Frenkel-Kontorova models and homogenization of Hamilton-Jacobi equations
• A numerical method for Mean Field Games on networks
• HOMOGENIZATION OF FIRST-ORDER EQUATIONS WITH u/∊-PERIODIC HAMILTONIAN: RATE OF CONVERGENCE AS ∊ → 0 AND NUMERICAL METHODS
• A New Approximation for Effective Hamiltonians for Homogenization of a class of Hamilton–Jacobi Equations
• A stochastic analogue of Aubry-Mather theory*
• HOMOGENIZATION OF HAMILTON–JACOBI EQUATIONS: NUMERICAL METHODS
• Homogenization of Metric Hamilton–Jacobi Equations
• Rates of convergence in periodic homogenization of fully nonlinear uniformly elliptic PDEs
• One-Sided Difference Approximations for Nonlinear Conservation Laws
• Computing the Effective Hamiltonian Using a Variational Approach
• Computing the Effective Hamiltonian in the Majda--Souganidis Model of Turbulent Premixed Flames
• Aubry Sets for Weakly Coupled Systems of Hamilton--Jacobi Equations
• Mean Field Games: Numerical Methods

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