标题： 通过随机有限差分实现高效的FRW转换以处理非分层电介质 显示英文标题

标题： Efficient FRW Transitions via Stochastic Finite Differences for Handling Non-Stratified Dielectrics

摘要： 基于浮动随机游走（FRW）的电容提取精度仅在递归FRW转换根据周围介质无偏采样时成立。 先进的技术配置，具有复杂的非分层介质，对现有近似介质为分层或八分之一模式的FRW转换方案的准确性构成了挑战。 在本工作中，我们提出了一种名为MicroWalk的算法，能够在保持高效率的同时，实现任意介质的准确FRW转换。 它被证明是无偏的，并且等价于使用有限差分法求解的转换概率，但成本低几个数量级（802$\times$倍更快）。 开发了一个增强的三维电容求解器，采用混合策略处理复杂介质，结合MicroWalk与第一个转换立方体的特殊处理以及分层立方体的解析算法。 在真实结构上的实验表明，我们的求解器在保持高效率的同时，相较于现有的FRW求解器具有显著的准确性优势。 显示英文摘要

摘要： The accuracy of floating-random-walk (FRW) based capacitance extraction stands only when the recursive FRW transitions are sampled unbiasedly according to surrounding dielectrics. Advanced technology profiles, featuring complicated non-stratified dielectrics, challenge the accuracy of existing FRW transition schemes that approximate dielectrics with stratified or eight-octant patterns. In this work, we propose an algorithm named MicroWalk, enabling accurate FRW transitions for arbitrary dielectrics while keeping high efficiency. It is provably unbiased and equivalent to using transition probabilities solved by finite difference method, but at orders of magnitude lower cost (802$\times$ faster). An enhanced 3-D capacitance solver is developed with a hybrid strategy for complicated dielectrics, combining MicroWalk with the special treatment for the first transition cube and the analytical algorithm for stratified cubes. Experiments on real-world structures show that our solver achieves a significant accuracy advantage over existing FRW solvers, while preserving high efficiency.