In this paper,we consider the positive semi-definite space tensor cone constrained convex program,its structure and *** study defining functions,defining sequences and polyhedral outer approximations for this positive...
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In this paper,we consider the positive semi-definite space tensor cone constrained convex program,its structure and *** study defining functions,defining sequences and polyhedral outer approximations for this positive semidefinite space tensor cone,give an error bound for the polyhedral outer approximation approach,and thus establish convergence of three polyhedral outer approximation algorithms for solving this *** then study some other approaches for solving this structured convex *** include the conic linear programming approach,the nonsmooth convex program approach and the bi-level program *** numerical examples are presented.
In the rarefied gas dynamics,the direct simulation Monte Carlo(DSMC)method is one of the most popular numerical *** performs satisfactorily in simulating hypersonic flows surrounding re-entry vehicles and micro-/***,t...
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In the rarefied gas dynamics,the direct simulation Monte Carlo(DSMC)method is one of the most popular numerical *** performs satisfactorily in simulating hypersonic flows surrounding re-entry vehicles and micro-/***,the computational cost is expensive,especially whenε→*** for flows in the near-continuum regime,pure
We propose an efficient and reliable technique to calculate highly localized Whispering Gallery Modes (WGMs) inside an oblate spheroidal cavity. The idea is to first separate variables in spheroidal coordinates and th...
We propose an efficient and reliable technique to calculate highly localized Whispering Gallery Modes (WGMs) inside an oblate spheroidal cavity. The idea is to first separate variables in spheroidal coordinates and then to deal with two ODEs, related to the angular and radial coordinates solved using high order finite difference schemes. It turns out that, due to solution structure, the efficiency of the calculation is greatly enhanced by using variable stepsizes to better reflect the behaviour of the evaluated functions. We illustrate the approach by numerical experiments.
作者：
Wei RenHong LiuShi JinJ C Wu Center for Aerodynamics
School of Aeronautics and Astronautics Shanghai Jiao Tong University Shanghai 200240 China Department of Mathematics
Institute of Natural Sciences and MOE Key Lab in Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai China 200240 and Department of Mathematics University of Wisconsin Madison WI 53706 USA
In the rarefied gas dynamics, the DSMC method is one of the most popular numerical tools. It performs satisfactorily in simulating hypersonic flows surrounding re-entry vehicles and micro-/nano- flows. However, the co...
In the rarefied gas dynamics, the DSMC method is one of the most popular numerical tools. It performs satisfactorily in simulating hypersonic flows surrounding re-entry vehicles and micro-/nano- flows. However, the computational cost is expensive, especially when Kn → 0. Even for flows in the near-continuum regime, pure DSMC simulations require a number of computational efforts for most cases. Albeit several DSMC/NS hybrid methods are proposed to deal with this, those methods still suffer from the boundary treatment, which may cause nonphysical solutions. Filbet and Jin [1] proposed a framework of new numerical methods of Boltzmann equation, called asymptotic preserving schemes, whose computational costs are affordable as Kn → 0. Recently, Ren et al. [2] realized the AP schemes with Monte Carlo methods (AP-DSMC), which have better performance than counterpart methods. In this paper, AP-DSMC is applied in simulating nonequilibrium hypersonic flows. Several numerical results are computed and analyzed to study the efficiency and capability of capturing complicated flow characteristics.
The local one-dimensional multisymplectic scheme(LOD-MS)is developed for the three-dimensional(3D)Gross-Pitaevskii(GP)equation in Bose-Einstein *** idea is originated from the advantages of multisymplectic integrators...
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The local one-dimensional multisymplectic scheme(LOD-MS)is developed for the three-dimensional(3D)Gross-Pitaevskii(GP)equation in Bose-Einstein *** idea is originated from the advantages of multisymplectic integrators and from the cheap computational cost of the local one-dimensional(LOD)*** 3D GP equation is split into three linear LOD Schrodinger equations and an exactly solvable nonlinear Hamiltonian *** three linear LOD Schrodinger equations are multisymplectic which can be approximated by multisymplectic integrator(MI).The conservative properties of the proposed scheme are *** is ***,the scheme preserves the discrete local energy conservation laws and global energy conservation law if the wave function is variable *** is impossible for conventional MIs in nonlinear Hamiltonian *** numerical results show that the LOD-MS can simulate the original problems very *** are consistent with the numerical analysis.
A new system is generated from a multi-linear form of a （2＋1）- dimensional Volterra system. Though the system is only partially integrable and needs additional conditions to possess two-soliton solutions, its （1＋...
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A new system is generated from a multi-linear form of a （2＋1）- dimensional Volterra system. Though the system is only partially integrable and needs additional conditions to possess two-soliton solutions, its （1＋1）- dimensional reduction gives an integrable equation which has been studied via reduction skills. Here, we give this （1＋1）-dimensional reduction a simple bilinear form, from which a Backlund transformation is derived and the corresponding nonlinear superposition formula is built.
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