具有特殊非齐次项波动方程的处理方法

针对一维非齐次波动方程,介绍了当其自由项具有几种特殊形式时的特殊解法,并举例说明.     

A cell functional minimization scheme for parabolic problem

We are interested in a robust and accurate finite volume scheme for 2-D parabolic problems derived from the cell functional minimization approach. The scheme has a local stencil, is locally conservative, treats discontinuity rigorously and leads to a symmetric positive definite linear system. Since the scheme has both cell centered unknowns and cell edge unknowns, the computational cost is an issue and a parallel algorithm is then suggested based on nonoverlapping domain decomposition approach. The interface condition is of the Dirichlet–Robin type and has a parameter λ. By choosing this parameter properly, the convergence of the iteration process could be sped up. Numerical results for linear and nonlinear problems demonstrate the good performance of the cell functional minimization scheme and its parallel version on distorted meshes.     

Numerical simulation of inductive method for determining spatial distribution of critical current density

The inductive method for measuring the critical current density j_C in a high-temperature superconducting (HTS) thin film has been investigated numerically. In order to simulate the method, a non-axisymmetric numerical code has been developed for analyzing the time evolution of the shielding current density. In the code, the governing equation of the shielding current density is spatially discretized with the finite element method and the resulting first-order ordinary differential system is solved by using the 5th-order Runge–Kutta method with an adaptive step-size control algorithm. By using the code, the threshold current I_T is evaluated for various positions of a coil. The results of computations show that, near a film edge, the accuracy of the estimating formula for j_C is remarkably degraded. Moreover, even the proportional relationship between j_C and I_T will be lost there. Hence, the critical current density near a film edge cannot be estimated by using the inductive method.     

使用广义粗网有限差分方法加速中子输运特征线方法

提出广义粗网有限差分方法(GCMFD),可以使用三维任意几何形状的粗网格来加速中子输运特征线方法(MOC),同时给出确定广义粗网有限差分方法中宽度因子的方法.将广义粗网有限差分方法应用到三维特征线方法程序TCM中,若干基准题的验证表明,广义粗网有限差分方法可以使用任意形状粗网格来加速特征线方法,使用自动调整宽度因子的方法后,广义粗网格有限差分方法可以得到较好的加速效果.     

基于伴随方程法的材料热传导系数反演方法

建立利用材料内部温度场的测量结果反演材料热传导系数随时间和空间位置变化函数的伴随方程法,参考迭代正则化的思想在优化过程中给目标函数设置停止准则.对典型算例计算表明,方法在测量噪声较小情况下能得出较为合理的反演结果.但在有测量噪声的情况下,反演结果与真值在边界x=0和L处存在着一定偏差.当测量噪声较大时,反演结果与真值的偏差较为明显,且初值选取会对反演结果有相当大的影响.     

A Low Order Nonconforming Mixed Finite Element Method for Non-Stationary Incompressible Magnetohydrodynamics System

A low order nonconforming mixed finite element method (FEM) is established for the fully coupled non-stationary incompressible magnetohydrodynamics (MHD) problem in a bounded domain in 3D. The lowest order finite elements on tetrahedra or hexahedra are chosen to approximate the pressure, the velocity field and the magnetic field, in which the hydrodynamic unknowns are approximated by inf-sup stable finite element pairs and the magnetic field by $H^1(\Omega)$-conforming finite elements, respectively. The existence and uniqueness of the approximate solutions are shown. Optimal order error estimates of $L^2(H^1)$-norm for the velocity field, $L^2(L^2)$-norm for the pressure and the broken $L^2(H^1)$-norm for the magnetic field are derived.     

线性互补问题基于模同步块多重分裂方法的收敛性

通过利用不动点迭代来研究线性互补问题,根据基模同步多重分裂迭代方法将其线性互补问题的系数矩阵是点的形式推广到块H+的形式,并且分析了当系数矩阵是块矩阵时线性互补问题解的收敛情况。