While research work on fast integral equation solver has resulted in several algorithms of similar linear equation solving performance, it has been well observed that the convergence of capacitance versus discretization is rather slow due to the most commonly used first-order collocation or Galerkin methods. This paper reports a new high-order scheme, Quadrature-evaluated Method of Moments Solver (QMMS), that uses high-order weighting and Gaussian quadrature to optimally handle the singularities at the edges and corners. For practical interconnect extraction problems, singularities at edges are analytically known and the corresponding Gaussian nodes allocation affords a near optimal discretization scheme. The new formulation avoids the special position-dependent quadrature rules, and surprisingly, provides a well-behaved matrix that converges rapidly without any pre-conditioning. Combining the high-order scheme with a kernel-independent fast solver yields an efficient algorithm for 3-D capacitance extraction.
在快速积分方程求解器的研究工作中,产生了几种具有类似线性方程求解性能的算法,但人们已经很好地观察到,由于最常用的一阶配置或Galerkin,电容与离散化的收敛相当慢方法。本文报告了一种新的高阶方案,即矩值求和法(QMMS)的正交求值方法,该方法使用高阶加权和高斯求积法来最佳地处理边缘和拐角处的奇点。对于实际的互连提取问题,在边缘处的奇点已被解析已知,并且相应的高斯节点分配提供了接近最佳的离散化方案。新的公式避免了特殊的位置相关的正交规则,令人惊讶的是,它提供了行为良好的矩阵,无需进行任何预处理即可快速收敛。将高阶方案与独立于内核的快速求解器结合起来,可以得到一种高效的3-D电容提取算法。 P>
机译:RWCap:浮动随机游走求解器,用于超大规模集成互连的3D电容提取
机译:使用带有棱镜元素的双离散几何方法提取3D IC互连电容
机译:利用矩的多分辨率方法对高速数字电路中互连的三维电容进行有效求解
机译:用于3D电容提取的矩量求解器的奇异处理正交求值方法
机译:基于边界元法的电容提取有效数值方法
机译:基于完美匹配层和光谱元素方法的3D量子传输解算器用于半导体纳米器件的仿真
机译:基于核独立分层方法和几何矩的3-d电容提取算法
机译:复杂三维(三维)几何电容提取的快速多极算法