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- W4380136706 abstract "We introduce two hybridizable discontinuous Galerkin (HDG) methods for numerically solving the Monge-Ampere equation. The first HDG method is devised to solve the nonlinear elliptic Monge-Ampere equation by using Newton's method. The second HDG method is devised to solve a sequence of the Poisson equation until convergence to a fixed-point solution of the Monge-Ampere equation is reached. Numerical examples are presented to demonstrate the convergence and accuracy of the HDG methods. Furthermore, the HDG methods are applied to r-adaptive mesh generation by redistributing a given scalar density function via the optimal transport theory. This r-adaptivity methodology leads to the Monge-Ampere equation with a nonlinear Neumann boundary condition arising from the optimal transport of the density function to conform the resulting high-order mesh to the boundary. Hence, we extend the HDG methods to treat the nonlinear Neumann boundary condition. Numerical experiments are presented to illustrate the generation of r-adaptive high-order meshes on planar and curved domains." @default.
- W4380136706 created "2023-06-10" @default.
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- W4380136706 date "2023-06-08" @default.
- W4380136706 modified "2023-09-25" @default.
- W4380136706 title "Hybridizable discontinuous Galerkin methods for the Monge-Ampere equation" @default.
- W4380136706 doi "https://doi.org/10.48550/arxiv.2306.05296" @default.
- W4380136706 hasPublicationYear "2023" @default.
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