论文标题
GBEM：3-D电容提取的Galerkin边界元素方法
GBEM: Galerkin Boundary Element Method for 3-D Capacitance Extraction
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
For modern IC design, electromagnetic coupling among interconnect wires plays an increasingly important role in signoff analysis. The requirement of fast and accurate capacitance extraction is becoming more and more urgent.The critical step of extracting capacitance among interconnect wires is solving electric field. However, due to the high computational complexity, solving electric field is extreme timing-consuming. To improve computational efficiency, we propose a Galerkin boundary element method (GBEM) to extract capacitance. The advantage of this method is that it can greatly reduce the number of boundary elements on the premise of ensuring that the error is small enough. As a consequence, the matrix order of the discretization equation will also decrease. The experiments in this paper have proved this advantage of our algorithm. Moreover, we have took advantage of some mathematical theorems in this paper. Our attempt shows that there will be more connections between the capacitance extraction and some mathematical conception so that we can use more mathematical tools to solve the problems of capacitance extraction.
