In the finite element method, one of the restrictions on the approximating functions is relaxed . 在有限单元方法中,放开了定近似函数的限制。
When adding an entropy function as regularizing term to the lagrangian function , we obtain a smooth approximate function for m ( x ) , which turns out to be the exponential penalty function 当将熵函数作为正则项加到拉格朗日函数上,我们得到了逐点逼近于m ( x )的光滑函数。经证明,该函数即为指数罚函数。
By constructing approximate functions and using prior estimate and conversion of variable , it is proved that the inverse problem has weak solution for given initial value , boundary value and the oil output 通过变量和函数变换,作逼近函数和估计等方法,证明了对给定的初边值和石油产量,此反问题存在弱解。
Ph linearization method is employed to solve a nonlinear reynolds equation for a steady state and micro - scale flow field , and the approximate function expressions of gas dynamic pressure and velocity in the spiral groove are obtained 摘要应用ph线性化方法、迭代法,近似求解了螺旋槽内稳态微尺度流动场的非线性雷诺方程,求得了气体动压和速度分布的解析解。
2 . for the problem with size , stress and displacement constraints , the stress constraint is transformed into movable lower bounds of sizes , the displacement constraint is transformed into an approximate function which explicitly includes design variables by using mohr integral theory . a mathematical programming model of the optimization problem is set up . the dual programming of the model is approached into a quadratic programming model 2 .对于尺寸、应力和位移约束的问题,将应力约束化为动态下限,用单位虚荷载方法将位移约束近似显式化,构造优化问题的数学规划模型,将其对偶规划处理为二次规划问题,采用lemke算法进行求解,得到满足尺寸、应力和位移约束条件的截面最优解。