The Experts below are selected from a list of 52563 Experts worldwide ranked by ideXlab platform
Romain Teyssier - One of the best experts on this subject based on the ideXlab platform.
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a simple multigrid scheme for solving the Poisson Equation with arbitrary domain boundaries
Journal of Computational Physics, 2011Co-Authors: Thomas Guillet, Romain TeyssierAbstract:We present a new multigrid scheme for solving the Poisson Equation with Dirichlet boundary conditions on a Cartesian grid with irregular domain boundaries. This scheme was developed in the context of the Adaptive Mesh Refinement (AMR) schemes based on a graded-octree data structure. The Poisson Equation is solved on a level-by-level basis, using a ''one-way interface'' scheme in which boundary conditions are interpolated from the previous coarser level solution. Such a scheme is particularly well suited for self-gravitating astrophysical flows requiring an adaptive time stepping strategy. By constructing a multigrid hierarchy covering the active cells of each AMR level, we have designed a memory-efficient algorithm that can benefit fully from the multigrid acceleration. We present a simple method for capturing the boundary conditions across the multigrid hierarchy, based on a second-order accurate reconstruction of the boundaries of the multigrid levels. In case of very complex boundaries, small scale features become smaller than the discretization cell size of coarse multigrid levels and convergence problems arise. We propose a simple solution to address these issues. Using our scheme, the convergence rate usually depends on the grid size for complex grids, but good linear convergence is maintained. The proposed method was successfully implemented on distributed memory architectures in the RAMSES code, for which we present and discuss convergence and accuracy properties as well as timing performances.
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a simple multigrid scheme for solving the Poisson Equation with arbitrary domain boundaries
Journal of Computational Physics, 2011Co-Authors: Thomas Guillet, Romain TeyssierAbstract:We present a new multigrid scheme for solving the Poisson Equation with Dirichlet boundary conditions on a Cartesian grid with irregular domain boundaries. This scheme was developed in the context of the Adaptive Mesh Refinement (AMR) schemes based on a graded-octree data structure. The Poisson Equation is solved on a level-by-level basis, using a ''one-way interface'' scheme in which boundary conditions are interpolated from the previous coarser level solution. Such a scheme is particularly well suited for self-gravitating astrophysical flows requiring an adaptive time stepping strategy. By constructing a multigrid hierarchy covering the active cells of each AMR level, we have designed a memory-efficient algorithm that can benefit fully from the multigrid acceleration. We present a simple method for capturing the boundary conditions across the multigrid hierarchy, based on a second-order accurate reconstruction of the boundaries of the multigrid levels. In case of very complex boundaries, small scale features become smaller than the discretization cell size of coarse multigrid levels and convergence problems arise. We propose a simple solution to address these issues. Using our scheme, the convergence rate usually depends on the grid size for complex grids, but good linear convergence is maintained. The proposed method was successfully implemented on distributed memory architectures in the RAMSES code, for which we present and discuss convergence and accuracy properties as well as timing performances.
Thomas Guillet - One of the best experts on this subject based on the ideXlab platform.
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a simple multigrid scheme for solving the Poisson Equation with arbitrary domain boundaries
Journal of Computational Physics, 2011Co-Authors: Thomas Guillet, Romain TeyssierAbstract:We present a new multigrid scheme for solving the Poisson Equation with Dirichlet boundary conditions on a Cartesian grid with irregular domain boundaries. This scheme was developed in the context of the Adaptive Mesh Refinement (AMR) schemes based on a graded-octree data structure. The Poisson Equation is solved on a level-by-level basis, using a ''one-way interface'' scheme in which boundary conditions are interpolated from the previous coarser level solution. Such a scheme is particularly well suited for self-gravitating astrophysical flows requiring an adaptive time stepping strategy. By constructing a multigrid hierarchy covering the active cells of each AMR level, we have designed a memory-efficient algorithm that can benefit fully from the multigrid acceleration. We present a simple method for capturing the boundary conditions across the multigrid hierarchy, based on a second-order accurate reconstruction of the boundaries of the multigrid levels. In case of very complex boundaries, small scale features become smaller than the discretization cell size of coarse multigrid levels and convergence problems arise. We propose a simple solution to address these issues. Using our scheme, the convergence rate usually depends on the grid size for complex grids, but good linear convergence is maintained. The proposed method was successfully implemented on distributed memory architectures in the RAMSES code, for which we present and discuss convergence and accuracy properties as well as timing performances.
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a simple multigrid scheme for solving the Poisson Equation with arbitrary domain boundaries
Journal of Computational Physics, 2011Co-Authors: Thomas Guillet, Romain TeyssierAbstract:We present a new multigrid scheme for solving the Poisson Equation with Dirichlet boundary conditions on a Cartesian grid with irregular domain boundaries. This scheme was developed in the context of the Adaptive Mesh Refinement (AMR) schemes based on a graded-octree data structure. The Poisson Equation is solved on a level-by-level basis, using a ''one-way interface'' scheme in which boundary conditions are interpolated from the previous coarser level solution. Such a scheme is particularly well suited for self-gravitating astrophysical flows requiring an adaptive time stepping strategy. By constructing a multigrid hierarchy covering the active cells of each AMR level, we have designed a memory-efficient algorithm that can benefit fully from the multigrid acceleration. We present a simple method for capturing the boundary conditions across the multigrid hierarchy, based on a second-order accurate reconstruction of the boundaries of the multigrid levels. In case of very complex boundaries, small scale features become smaller than the discretization cell size of coarse multigrid levels and convergence problems arise. We propose a simple solution to address these issues. Using our scheme, the convergence rate usually depends on the grid size for complex grids, but good linear convergence is maintained. The proposed method was successfully implemented on distributed memory architectures in the RAMSES code, for which we present and discuss convergence and accuracy properties as well as timing performances.
Delphine Salort - One of the best experts on this subject based on the ideXlab platform.
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transport Equations with unbounded force fields and application to the vlasov Poisson Equation
Mathematical Models and Methods in Applied Sciences, 2009Co-Authors: Delphine SalortAbstract:The aim of this paper is to give new dispersive tools for certain kinetic Equations. As an application, we study the three-dimensional Vlasov–Poisson Equation for initial data having strictly less than six moments in where the nonlinear term E is a priori unbounded. We prove via new dispersive effects that in fact the force field E is smooth in space at the cost of a localization in a ball and an averaging in time. We deduce new conditions to bound the density ρ in L∞ and to have existence and uniqueness of global weak solutions of the Vlasov–Poisson Equation with bounded density for initial data strictly less than six moments in . The proof is based on a new approach which consists in establishing a priori dispersion estimates (moment effects) on the one hand for linear transport Equations with unbounded force fields and on the other hand along the trajectories of the Vlasov–Poisson Equation.
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Transport Equations with rough force fields and applications to Vlasov-Poisson Equation.
2008Co-Authors: Delphine SalortAbstract:In this article, we study the three dimensional Vlasov-Poisson Equation. We give new conditions on the initial data using low moments to control the force field and density. In particular, we introduce a new approach which consists in establishing moments effects for linear transport Equations with rough force fields.
Aixia Qian - One of the best experts on this subject based on the ideXlab platform.
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ground state solution for a schrodinger Poisson Equation with critical growth
Nonlinear Analysis-real World Applications, 2018Co-Authors: Jingmei Liu, Aixia QianAbstract:Abstract In this paper, we consider the following nonlinear Schrodinger–PoissonEquation − △ u + V ( x ) u + K ( x ) ϕ u = μ a ( x ) | u | q − 1 u + | u | 4 u , in R 3 , − △ ϕ = K ( x ) u 2 , in R 3 , where μ is a positive parameter. Under certain assumptions on V ( x ) , K ( x ) and a ( x ) , we prove that for every μ > 0 and q ∈ ( 2 , 5 ) , the Schrodinger–Poisson Equation with critical growth has at least a positive ground state solution by variational method.
Xiaofei Zhao - One of the best experts on this subject based on the ideXlab platform.
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Multiscale Particle-in-Cell methods and comparisons for the long-time two-dimensional Vlasov-Poisson Equation with strong magnetic field
Computer Physics Communications, 2018Co-Authors: Nicolas Crouseilles, Sever Hirstoaga, Xiaofei ZhaoAbstract:We applied different kinds of multiscale methods to numerically study the long-time Vlasov-Poisson Equation with a strong magnetic field. The multiscale methods include an asymptotic preserving Runge-Kutta scheme, an exponential time differencing scheme, stroboscopic averaging method and a uniformly accurate two-scale formulation. We briefly review these methods and then adapt them to solve the Vlasov-Poisson Equation under a Particle-in-Cell discretization. Extensive numerical experiments are conducted to investigate and compare the accuracy, efficiency, and long-time behavior of all the methods. The methods with the best performance under different parameter regimes are identified.
