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本文采用不规则网格的差分方法,对平面油水模型进行了数值模拟,并用IMPES方法计算了两个实例。例1的计算结果与精确解吻合良好,比Pedrosa的局部加密网格法使用的网格数少而且计算更简便。例2为矩形网格难以计算的问题,应用本文方法也得出了较好的结果。这表明本文的不规则网格差分方法是可靠而简便的,它可以有效地应用于复杂外边界和复杂地层结构的油藏模拟问题。 相似文献
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雷光耀 《应用数学和力学(英文版)》1992,13(2):199-204
From the formulas of the conjugate gradient, a similarity between a symmetric positive definite (SPD) matrix A and a tridiagonal matrix B is obtained. The elements of the matrix B are determinedby the parameters of the conjugate gradient. The computation of eigenvalues of A is then reduced to the case of the tridiagonal matrix B. The approximation of extreme eigenvalues of A can be obtained as a by-product in the computation of the conjugate gradient ifa computational cost of O(s) arithmetic operations is added, where s is the number of iterations This computational cost is negligible compared with the conjugate gradient. If the matrix A is not SPD, the approximation of the condition number of A can be obtained from the computation of the conjugate gradient on A~T A. Numerical results show that this is a convenient and highly efficient method for computing extreme eigenvalues and the condition number of nonsingular matrices. 相似文献
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本文从共轭梯度法的公式推导出对称正定阵A与三对角阵B的相似关系,B的元素由共轭梯度法的迭代参数确定.因此,对称正定阵的条件数计算可以化成三对角阵条件数的计算,并且可以在共轭梯度法的计算中顺带完成.它只需增加O(s)次的计算量,s为迭代次数.这与共轭梯度法的计算量相比是可以忽略的.当A为非对称正定阵时,只要A非奇异,即可用共轭梯度法计算ATA的特征极值和条件数,从而得出A的条件数.对不同算例的计算表明,这是一种快速有效的简便方法. 相似文献
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