区域分解

• On the base of mathematical domain decomposition method ( ddm ) , this paper investigates systematically the quasi - static problems based on laplace equation , the transmission problems in waveguide based helmholtz equation and the three - dimensional scattering and radiation problems based on maxwell equations . the theoretical system is built for the further exploration of ddm in electromagnetic problems
  本文在区域分解法已有的数学基础上，从基于laplace方程的准静态问题，到基于helmholtz方程的波导传输问题以及基于maxwell方程的三维散射辐射问题，系统地探讨了该方法在电磁领域中的应用，为进一步扩展应用研究建立了理论体系。
• The method is also tested by finite volume scheme and partitioning algorithm of euler equation in parallel computing in fluid dynamics . the testing results demonstrate that the suggested method in this method is of practical and scientific significance in parallel computing in fluid dynamics
  本文还结合euler方程的有限体积格式和区域分解算法对文中的算法在流体力学并行计算中进行了进一步的验证，从数值计算结果可以看出，本文提出的算法能够很好地应用于计算流体力学并行计算，具有一定的科学应用价值。
• Considering the seepage of linear and the seepage of non - linear in the karst area are always coexisting , the model of linear seepage and non - linear seepage is put forward firstly on the basis of domain decomposition method . the movement of groundwater in an ideal model is simulated with this method , and the program of dar - nondar . for is compiled . then these results are applied to zhongliang water resources and power engineering , the leakage quantity of karst water is calculated
  考虑到岩溶区渗流往往都是线性流与非线性流并存，首次提出了基于区域分解法理论的线性?非线性渗流模型，利用该方法模拟出理想模型中的水流运动，并编制了计算程序dar - nondar . for ，然后将该成果应用于中梁水利水电工程中，预测出库区岩溶水渗漏量。
• This technique combines the edge - based finite - element method with physical optics ( po ) and physical theory of diffraction ( ptd ) . the hybrid technique is applied to compute the scattering fields from the electrically large bodies with cracks and cavities on their surfaces . it is also used to analyze the scattering characteristics of microstrip antennas residing in a cavity mounted on metal objects with finite sizes
  本文采用edge - basedfem为基本方法，结合物理光学法( po ) 、物理绕射理论( ptd ) 、边界积分方程( bi ) 、区域分解技术( ddm )和完全匹配层( pml )吸收边界条件等求解方法构成的混合方法，对电磁散射和辐射问题进行了研究，主要包括以下内容：提出了一种edge - basedfem与物理光学方法和物理绕射理论相结合的混合方法? fem po - ptd方法，并将该混合方法应用于带有腔体或槽缝的电大尺寸导体目标的电磁散射特性分析和位于有限导体目标上的背腔式微带贴片天线的电磁散射特性分析。
• The calculation of the position of the shocks for the domain decomposition of the hyperbolic approximation is discussed . it is the matching stable problem for the different schemes in the different domains with different mesh size . after tracing the position of the shocks , the artificial compression method are applied to eliminate the smearing effect and to raise the resolution of the schemes . in the boundaries of each regions , the universal connected matching stable schemes are inserted in so as to make the schemes between different regions matching stable each other . at last , some numerical examples are presented
  讨论在激波计算中的区域分解法，即在不同区域中应用不同网格及格式的耦合稳定性问题.先定出激波位置，再在激波附近小范围内，用低阶格式及人工压缩方法以消除弥散效应.在激波区域外，应用高精度格式，减少了过超振荡现象，提高了分辨率.在各区域交界应用全能稳定联接格式，解决了格式的耦合稳定问题.最后举出数值计算实例，计算结果与理论分析符合
• The novel three - dimensional finite - difference approximations of mur ' s absorbing boundary conditions are also presented in frequency - domain . then the ddm based on fdfd is investigated in the applications of three - dimensional electromagnetics problems . and it is used to analyze the leaky wave antenna based on image nonradiative dielectric ( nrd ) guide
  最后，阐述了maxwell方程组和划分区域的despres传输条件的频域差分格式建立，在截断边界上构造了三维频域mur条件的差分近似，探讨了基于频域有限差分的区域分解法在三维电磁问题中的应用实现，并将该算法用于分析一种基于nrd波导结构的漏波天线。
• In chapter 4 , we present some new techniques in designing finite difference domain decomposition algorithm for the heat equation . the basic procedure is to define the finite difference schemes at the interface grid points with smaller time step by explicit schemes , and the prior error estimates for the numerical solutions are obtained
  在第四章，我们发展了一些新技术，在子区域的边界处采用小时间步长古典显式格式求解，构造了新的区域分解算法，得到了差分解的先验误差估计。
• Aiming at efficient analyses of electromagnetic characteristics of electrically large complex cavities , some hybrid techniques are developed based on eb - fem , including ipo / fem , extended ipo , improved ipo / fem , ddm / fem - bie , ddm / fem - po - ptd , fem / ibc , and fem / pml . the following contributions have been made in this dissertation : a novel hybrid approach is proposed in which iterative physical optics ( ipo ) subdomain - splicing technique is combined with eb - fem , the mathematical model of the proposed ipo / fem is established by some approximate methods
  本文以eb - fem为基础，以电大尺寸复杂腔体的电磁特性为分析对象，对eb - fem与迭代物理光学法( ipo ) 、区域分解法( ddm ) 、阻抗边界条件( ibc ) 、完全匹配层( pml )和mur吸收边界条件的结合算法以及具有非完纯导体边界的ipo理论模型进行了研究。