静电问题中的尺寸维渐近波形估计

Size dimensional asymptotic waveform evaluation in electrostatic problem

渐近波形估计 (AWE)方法是数值计算中一种非常有效的外推方法。这种方法已经获得广泛的应用。但用尺寸作变量时 ,AWE方法会遇到尺寸求导的问题。该文采用固定网格数 ,引入尺寸伸缩系数的方法 ,把AWE方法推广到了尺寸维。微带贴片静电电容的计算实例表明该方法是可行的。

The method of asymptotic waveform evaluation (AWE) is a very efficient extrapolation method in numerical computation. The frequency, dielectric constant or angle is taken as variables of the AWE method. In optimization design, however, the size of a structure is usually an important parameter. When the size is taken as the variable of AWE method, the derivatives with respect to the size has to be considered. By fixing the mesh shape and introducing a size variable coefficient, the AWE method is extended into size dimension. As an example, the capacitance of a microstrip patch is calculated. The numerical results show that the method is feasible and is extremely powerful when only small part of the whole structure changes. The presented method can be also extended into dynamic problems. The combination of this method with the conventional AWE method may increase the dimensions of AWE method.