Artificial Viscosity Joint Spacetime Multigrid Method for Hamilton–Jacobi–Bellman and Kolmogorov–Fokker–Planck System Arising from Mean Field Games

In this paper, we study numerical solutions for the Hamilton-Jacobi-Bellman (HJB) and Kolmogorov–Fokker–Planck (KFP) equations arising from mean field games. In order to solve the nonlinear discretized systems efficiently, we propose a multigrid method. Our proposed multigrid method is developed on...

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Veröffentlicht in:Journal of scientific computing Jg. 88; H. 1; S. 10
Hauptverfasser: Chen, Yangang, Wan, Justin W. L.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.07.2021
Springer Nature B.V
Schlagworte:
Algorithms
Anisotropy
Approximation
Coarsening
Computational Mathematics and Numerical Analysis
Discretization
Fourier analysis
Games
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Multigrid methods
Nonlinear systems
Partial differential equations
Smartphones
Spacetime
Theoretical
Viscosity
Hamilton–Jacobi–Bellman equation
Kolmogorov–Fokker–Planck equation
Multigrid methods
Full approximation scheme
Artificial viscosity
Mean field games
Spacetime methods
ISSN:0885-7474, 1573-7691
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Zusammenfassung:In this paper, we study numerical solutions for the Hamilton-Jacobi-Bellman (HJB) and Kolmogorov–Fokker–Planck (KFP) equations arising from mean field games. In order to solve the nonlinear discretized systems efficiently, we propose a multigrid method. Our proposed multigrid method is developed on the joint spacetime and is a full approximation scheme (FAS). We consider hybrid full-semi coarsening and kernel preserving biased restriction to address the anisotropy in time and convections in space. The main novelty of this paper is that we propose adding artificial viscosity to the direct discretization coarse grid operators, such that the coarse grid error estimations are more accurate. We use Fourier analysis to illustrate the efficiency of our proposed multigrid method. Numerical experiments show that the convergence rate of the proposed multigrid method is mesh-independent and faster than the existing methods in the literature.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-021-01520-0