Boundary Treatment and Multigrid Preconditioning for Semi-Lagrangian Schemes Applied to Hamilton–Jacobi–Bellman Equations
作者: Christoph ReisingerJulen Rotaetxe Arto
作者单位: 1University of Oxford
刊名: Journal of Scientific Computing, 2017, Vol.72 (1), pp.198-230
来源数据库: Springer Journal
DOI: 10.1007/s10915-016-0351-1
关键词: Fully non-linear PDEsMonotone approximation schemesWide stencilsSemi-Lagrangian schemesMultigrid65M0665M1265M5549L2593E20
英文摘要: We analyse two practical aspects that arise in the numerical solution of Hamilton–Jacobi–Bellman equations by a particular class of monotone approximation schemes known as semi-Lagrangian schemes. These schemes make use of a wide stencil to achieve convergence and result in discretization matrices that are less sparse and less local than those coming from standard finite difference schemes. This leads to computational difficulties not encountered there. In particular, we consider the overstepping of the domain boundary and analyse the accuracy and stability of stencil truncation. This truncation imposes a stricter CFL condition for explicit schemes in the vicinity of boundaries than in the interior, such that implicit schemes become attractive. We then study the use of geometric,...
原始语种摘要: We analyse two practical aspects that arise in the numerical solution of Hamilton–Jacobi–Bellman equations by a particular class of monotone approximation schemes known as semi-Lagrangian schemes. These schemes make use of a wide stencil to achieve convergence and result in discretization matrices that are less sparse and less local than those coming from standard finite difference schemes. This leads to computational difficulties not encountered there. In particular, we consider the overstepping of the domain boundary and analyse the accuracy and stability of stencil truncation. This truncation imposes a stricter CFL condition for explicit schemes in the vicinity of boundaries than in the interior, such that implicit schemes become attractive. We then study the use of geometric,...
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影响因子:1.71 (2012)

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关键词翻译
关键词翻译
  • stencil 模板
  • truncation 
  • algebraic 代数的
  • computational 计算的
  • geometric 凡何
  • benchmark 基准点
  • Lagrangian 拉格朗日算符
  • numerically 数字上
  • approximation 近似
  • achieve 达到