| 1. | The precise integration method of differential equation was presented by using 2 algorithm , its numerical precision was also analyzed
运用指数矩阵的2 ~ n类算法，构造了微分方程的精细积分算法，并分析了计算精度。 |
| 2. | The results show that , when the number of grid in numerical region is fewer , the numerical precision in iso - volumetric grid is higher than that in iso - spacing grid
结果表明，当网格节点数较少时，等体积网格比等距网格具有更高的计算精度。 |
| 3. | The impaction of numerical precision on the accuracy of simulated flow field is checked . curving level of throat wall arc mesh is compared to see the effect on flow loss
并比较了数值精度对流场模拟精度的影响和喉道壁面网格的圆弧度处理对流动损失的影响。 |
| 4. | Numerical results all indicate that the two axisymmetric finite elements exhibit better numerical precision , excellent performance at the nearly incompressible limit and distortions of the element geometry , and element performances are improved after optimization . the layout of this thesis is follows
具体表现是：对畸变网格有很好的适应性；计算可靠，不发生poissonlocking现象；对双线性等参元的粗网格精度有很好的改善。 |
| 5. | The concept of row ( column ) transposed matrix and row ( column ) symmetric matrix is given , their basic property is studied , and the formula for full rank factorization and orthogonal diagonal factorization of row ( column ) symmetric matrix are presented , which can reduce dramatically the amount of calculation and save the cpu time and memory without loss of any numerical precision
摘要提出了行（列）转置矩阵与行（列）对称矩阵的概念，研究了其性质，给出了行（列）对称矩阵的满秩分解和正交时角分解公式，极大地减少了行（列）对称矩阵的满秩分解和正交对角分解的计算量与存储量，且没有降低数值精度。 |
| 6. | Through the research in this thesis , following conclusion can be drew : on the condition of nearly incompressible limit , the n - s equations can be recovered by the lb method ' s models with 2 - order numerical precision ; computational efficiency in simulating flow fields can be improved effectively by perfection of the lb method ' s theory ; development of parallel computation can contribute to the simulation of large - scale flow field with complex geometry
通过本文的研究，可得出如下结论： lb方法的模型在接近不可压缩的条件下能够以二阶精度逼近n - s方程； lb方法理论的完善能够有效地提高流场模拟的计算效率；并行计算的发展有利于lb方法模拟大尺度的复杂流场。 |
| 7. | The astringency , error and stability of the numerical method are researched . zero matrix method , constant matrix method , and jacobian matrix method are constructed in order to improve numerical precision and efficiency . the steps for calculating matrix exponential function using pade approach method are given out
研究了所提西安理工大学博士学位论文数值计算方法的误差、稳定性、收敛性等数学性质，在计算精度和计算效率两方面提出了一些改进措施，构造了零矩阵法、常数矩阵法、雅可比矩阵法等计算格式，给出了利川pade逼近计算矩阵指数函数的求解步骤。 |
| 8. | Due to the difference of material characters and mechanics performance between concrete structures and soils , it is necessary to pay great attention to model the interface element , simulate the soil behavior and the optimization of the finite elements to satisfy the numerical precision and the compatibility relation of the whole project
由于结构与土的材料特性，受力性能等方面的差异，为了满足有限元计算精度和效率的要求，合理的反映结构与土体之间的位移协调，需要在结构与土体之间设置恰当的接触面单元，正确的模拟土的本构关系，并尽可能地简化结构的数值模型。 |
