基于N-S(Navier-Stokes)方程,进行了航行船舶辐射问题的数值模拟,包括强制垂荡和强制纵摇的模拟,计算了船舶垂荡和纵摇的附加质量和阻尼。数值模拟中,控制方程—RANS(Reynolds Averaged Navier-Stokes)方程和连续性方程使用有限体积法离...基于N-S(Navier-Stokes)方程,进行了航行船舶辐射问题的数值模拟,包括强制垂荡和强制纵摇的模拟,计算了船舶垂荡和纵摇的附加质量和阻尼。数值模拟中,控制方程—RANS(Reynolds Averaged Navier-Stokes)方程和连续性方程使用有限体积法离散,非线性自由面采用VOF方法处理。文中给出了以不同航速前进的船舶强制垂荡和纵摇的力与力矩,以及船舶垂荡和纵摇的附加质量系数和阻尼系数,并与DUT(Delft University of Technology)的试验数据进行了比较,二者吻合良好。展开更多
In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for the Schrödinger equation in 3-dimensional. We numerically implement the coefficie...In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for the Schrödinger equation in 3-dimensional. We numerically implement the coefficients of the explicit formulas. In this work, Lipschitz type stability is established near the edge of the domain with giving estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neuman map.展开更多
In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for a hyperbolic differential equation in 3-dimensional. We show that the Dirichlet-Neumann op...In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for a hyperbolic differential equation in 3-dimensional. We show that the Dirichlet-Neumann operators corresponding to a potential radial have the same properties for hyperbolic differential equations as for elliptic differential equations. We numerically implement the coefficients of the explicit formulas. Moreover, a Lipschitz type stability is established near the edge of the domain by an estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neumann map in the inverse problem for a hyperbolic differential equation.展开更多
A stabilized and convergent finite element formulation for the generalized Stokes problem is proposed and a posteriori analysis is performed to produce an error indicator. On this basis adaptive numerical method for s...A stabilized and convergent finite element formulation for the generalized Stokes problem is proposed and a posteriori analysis is performed to produce an error indicator. On this basis adaptive numerical method for solying the problem is developed . Numerical calculations are performed to confirm the reliability and effectiveness of the method.展开更多
In this note we show that on any compact subdomain of a K?hler manifold that admits sufficiently many global holomorphic functions, the products of harmonic functions form a complete set. This gives a positive answer ...In this note we show that on any compact subdomain of a K?hler manifold that admits sufficiently many global holomorphic functions, the products of harmonic functions form a complete set. This gives a positive answer to the linearized anisotropic Calderón problem on a class of complex manifolds that includes compact subdomains of Stein manifolds and sufficiently small subdomains of K?hler manifolds. Some of these manifolds do not admit limiting Carleman weights, and thus cannot be treated by standard methods for the Calderón problem in higher dimensions. The argument is based on constructing Morse holomorphic functions with approximately prescribed critical points. This extends earlier results from the case of Riemann surfaces to higher dimensional complex manifolds.展开更多
In this paper, we prove that an into isometry form S（l（n）^∞） to S（E）, which under some conditions, can be extended to be a linear isometry defined on the whole space. Therefore we improve the results of [Ding, ...In this paper, we prove that an into isometry form S（l（n）^∞） to S（E）, which under some conditions, can be extended to be a linear isometry defined on the whole space. Therefore we improve the results of [Ding, G. G.： The isometric extension of an into mapping from the unit sphere S（l（2）^∞） to S（Lμ^1）. Acta Mathematica Sinica, English Series, 22（6）, 1721-1724 （2006）].展开更多
文摘基于N-S(Navier-Stokes)方程,进行了航行船舶辐射问题的数值模拟,包括强制垂荡和强制纵摇的模拟,计算了船舶垂荡和纵摇的附加质量和阻尼。数值模拟中,控制方程—RANS(Reynolds Averaged Navier-Stokes)方程和连续性方程使用有限体积法离散,非线性自由面采用VOF方法处理。文中给出了以不同航速前进的船舶强制垂荡和纵摇的力与力矩,以及船舶垂荡和纵摇的附加质量系数和阻尼系数,并与DUT(Delft University of Technology)的试验数据进行了比较,二者吻合良好。
文摘In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for the Schrödinger equation in 3-dimensional. We numerically implement the coefficients of the explicit formulas. In this work, Lipschitz type stability is established near the edge of the domain with giving estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neuman map.
文摘In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for a hyperbolic differential equation in 3-dimensional. We show that the Dirichlet-Neumann operators corresponding to a potential radial have the same properties for hyperbolic differential equations as for elliptic differential equations. We numerically implement the coefficients of the explicit formulas. Moreover, a Lipschitz type stability is established near the edge of the domain by an estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neumann map in the inverse problem for a hyperbolic differential equation.
文摘A stabilized and convergent finite element formulation for the generalized Stokes problem is proposed and a posteriori analysis is performed to produce an error indicator. On this basis adaptive numerical method for solying the problem is developed . Numerical calculations are performed to confirm the reliability and effectiveness of the method.
基金partially supported by ERC Consolidator Grant IPFLOW(Grant No.725967)supported by the Academy of Finland(Finnish Centre of Excellence in Inverse Problems Research(Grant Nos.284715 and 309963))+2 种基金by the European Research Council under FP7/2007-2013 ERC StG(Grant No.307023)Horizon 2020 ERC CoG(Grant No.770924)partially supported by Australian Research Council(Grant Nos.DP190103302 and DP190103451)
文摘In this note we show that on any compact subdomain of a K?hler manifold that admits sufficiently many global holomorphic functions, the products of harmonic functions form a complete set. This gives a positive answer to the linearized anisotropic Calderón problem on a class of complex manifolds that includes compact subdomains of Stein manifolds and sufficiently small subdomains of K?hler manifolds. Some of these manifolds do not admit limiting Carleman weights, and thus cannot be treated by standard methods for the Calderón problem in higher dimensions. The argument is based on constructing Morse holomorphic functions with approximately prescribed critical points. This extends earlier results from the case of Riemann surfaces to higher dimensional complex manifolds.
基金Supported by National Natural Science Foundation of China (Grant No. 10871101)the Doctoral Pr0grame Foundation of Institution of Higher Education (Grant No. 20060055010)
文摘In this paper, we prove that an into isometry form S（l（n）^∞） to S（E）, which under some conditions, can be extended to be a linear isometry defined on the whole space. Therefore we improve the results of [Ding, G. G.： The isometric extension of an into mapping from the unit sphere S（l（2）^∞） to S（Lμ^1）. Acta Mathematica Sinica, English Series, 22（6）, 1721-1724 （2006）].
