In this paper,we propose a novel Local Macroscopic Conservative(LoMaC)low rank tensor method with discontinuous Galerkin(DG)discretization for the physical and phase spaces for simulating the Vlasov-Poisson(VP)system....In this paper,we propose a novel Local Macroscopic Conservative(LoMaC)low rank tensor method with discontinuous Galerkin(DG)discretization for the physical and phase spaces for simulating the Vlasov-Poisson(VP)system.The LoMaC property refers to the exact local conservation of macroscopic mass,momentum,and energy at the discrete level.The recently developed LoMaC low rank tensor algorithm(arXiv:2207.00518)simultaneously evolves the macroscopic conservation laws of mass,momentum,and energy using the kinetic flux vector splitting;then the LoMaC property is realized by projecting the low rank kinetic solution onto a subspace that shares the same macroscopic observables.This paper is a generalization of our previous work,but with DG discretization to take advantage of its compactness and flexibility in handling boundary conditions and its superior accuracy in the long term.The algorithm is developed in a similar fashion as that for a finite difference scheme,by observing that the DG method can be viewed equivalently in a nodal fashion.With the nodal DG method,assuming a tensorized computational grid,one will be able to(i)derive differentiation matrices for different nodal points based on a DG upwind discretization of transport terms,and(ii)define a weighted inner product space based on the nodal DG grid points.The algorithm can be extended to the high dimensional problems by hierarchical Tucker(HT)decomposition of solution tensors and a corresponding conservative projection algorithm.In a similar spirit,the algorithm can be extended to DG methods on nodal points of an unstructured mesh,or to other types of discretization,e.g.,the spectral method in velocity direction.Extensive numerical results are performed to showcase the efficacy of the method.展开更多
Agile manufacturing is an important manufacturing philosophy to develop advanced manufacturing enterprises to improve competivity. The evaluation of Agile Manufacturing Enterprises (AME) is one of the key activities i...Agile manufacturing is an important manufacturing philosophy to develop advanced manufacturing enterprises to improve competivity. The evaluation of Agile Manufacturing Enterprises (AME) is one of the key activities in implementing agile manufacturing. This paper proposes a method for evaluating AME, establishes a basic feature model of AME based on the feature tree and discusses the hierarchical decomposition algorithm based on the model with an example.展开更多
Sparse grids have become a versatile tool for a vast range of applications reaching from interpolation and numerical quadrature to data-driven problems and uncertainty quantification.We review four selected real-world...Sparse grids have become a versatile tool for a vast range of applications reaching from interpolation and numerical quadrature to data-driven problems and uncertainty quantification.We review four selected real-world applications of sparse grids:financial product pricing with the Black-Scholes model,interactive explo-ration of simulation data with sparse-grid-based surrogate models,analysis of simu-lation data through sparse grid data mining methods,and stability investigations of plasma turbulence simulations.展开更多
基金supported by the NSF(Grant Nos.the NSF-DMS-1818924 and 2111253)the Air Force Office of Scientific Research FA9550-22-1-0390 and Department of Energy DE-SC0023164+1 种基金supported by the NSF(Grant Nos.NSF-DMS-1830838 and NSF-DMS-2111383)the Air Force Office of Scientific Research FA9550-22-1-0390.
文摘In this paper,we propose a novel Local Macroscopic Conservative(LoMaC)low rank tensor method with discontinuous Galerkin(DG)discretization for the physical and phase spaces for simulating the Vlasov-Poisson(VP)system.The LoMaC property refers to the exact local conservation of macroscopic mass,momentum,and energy at the discrete level.The recently developed LoMaC low rank tensor algorithm(arXiv:2207.00518)simultaneously evolves the macroscopic conservation laws of mass,momentum,and energy using the kinetic flux vector splitting;then the LoMaC property is realized by projecting the low rank kinetic solution onto a subspace that shares the same macroscopic observables.This paper is a generalization of our previous work,but with DG discretization to take advantage of its compactness and flexibility in handling boundary conditions and its superior accuracy in the long term.The algorithm is developed in a similar fashion as that for a finite difference scheme,by observing that the DG method can be viewed equivalently in a nodal fashion.With the nodal DG method,assuming a tensorized computational grid,one will be able to(i)derive differentiation matrices for different nodal points based on a DG upwind discretization of transport terms,and(ii)define a weighted inner product space based on the nodal DG grid points.The algorithm can be extended to the high dimensional problems by hierarchical Tucker(HT)decomposition of solution tensors and a corresponding conservative projection algorithm.In a similar spirit,the algorithm can be extended to DG methods on nodal points of an unstructured mesh,or to other types of discretization,e.g.,the spectral method in velocity direction.Extensive numerical results are performed to showcase the efficacy of the method.
文摘Agile manufacturing is an important manufacturing philosophy to develop advanced manufacturing enterprises to improve competivity. The evaluation of Agile Manufacturing Enterprises (AME) is one of the key activities in implementing agile manufacturing. This paper proposes a method for evaluating AME, establishes a basic feature model of AME based on the feature tree and discusses the hierarchical decomposition algorithm based on the model with an example.
文摘Sparse grids have become a versatile tool for a vast range of applications reaching from interpolation and numerical quadrature to data-driven problems and uncertainty quantification.We review four selected real-world applications of sparse grids:financial product pricing with the Black-Scholes model,interactive explo-ration of simulation data with sparse-grid-based surrogate models,analysis of simu-lation data through sparse grid data mining methods,and stability investigations of plasma turbulence simulations.
