论文部分内容阅读
提出比例边界等几何方法(scaled boundary isogeometric analysis,SBIGA),并用以求解波导本征值问题.在比例边界等几何坐标变换的基础上,利用加权余量法将控制偏微分方程进行离散处理,半弱化为关于边界控制点变量的二阶常微分方程,即TE波或TM波波导的比例边界等几何分析的频域方程以及波导动刚度方程,同时利用连分式求解波导动刚度矩阵.通过引入辅助变量进一步得出波导本征方程.该方法只需在求解域的边界上进行等几何离散,使问题降低一维,计算工作量大为节约,并且由于边界的等几何离散,使得解的精度更高,进一步节省求解自由度.以矩形和L形波导的本征问题分析为例,通过与解析解和其他数值方法比较,结果表明该方法具有精度高、计算工作量小的优点.
A scaled boundary isogeometric analysis (SBIGA) is proposed and used to solve the eigenvalue problem of waveguide. On the basis of geometric coordinate transformation such as proportional boundary, the control partial differential equations are discretized using halftones Weakening into the second-order ordinary differential equation about the boundary control point variable, that is, the frequency domain equation of the geometrical analysis such as the proportional boundary of the TE wave or the TM wave guide and the wave equation of the wave guide stiffness and using the continuous fraction to solve the waveguide dynamic stiffness matrix, The auxiliary variables further derive the eigen-wave equation of the waveguide. The method only needs to be geometrically discretized on the boundary of the domain to be solved, so that the problem is reduced by one dimension and the computational workload is greatly saved. Moreover, due to the geometric dispersion of the boundary, And further save the freedom of solution.With the analysis of the intrinsic problems of rectangular and L-shaped waveguides as an example, the results show that this method has the advantages of high precision and small computational load by comparison with analytical solutions and other numerical methods.