VoxCap：FFT加速和Tucker-Enhanced体素化结构电容提取模拟器
VoxCap: FFT-Accelerated and Tucker-Enhanced Capacitance Extraction Simulator for Voxelized Structures
摘要：
VoxCap是一种快速傅里叶变换（FFT）加速和塔克增强的积分方程模拟器，用于体素化结构的电容提取。VoxCap解决导体和电介质表面的表面积分方程（SIE），具有三个关键属性，使得VoxCap对于体素化结构的电容提取具有高度的CPU和存储器效率：（i）VoxCap利用FFT在由于SIE的离散化而产生的线性方程组的迭代求解期间加速矩阵向量乘法。(ii)在迭代求解过程中，VoxCap使用了一个高效的预处理器，大大减少了迭代次数。(iii)VoxCap采用Tucker分解来压缩块Toeplitz和循环张量，需要模拟器中最大的内存。通过这样做，它将这些张量的内存需求从数百GB减少到几兆字节，并且对于非常大规模的问题，获得Toeplitz张量所需的CPU时间从数十分钟（甚至数小时）减少到几秒钟。VoxCap能够在台式计算机上精确计算任意形状和大规模体素化结构的电容。
英文摘要：
VoxCap, a fast Fourier transform (FFT)-accelerated and Tucker-enhanced integral equation simulator for capacitance extraction of voxelized structures, is proposed. The VoxCap solves the surface integral equations (SIEs) for conductor and dielectric surfaces with three key attributes that make the VoxCap highly CPU and memory efficient for the capacitance extraction of the voxelized structures: (i) VoxCap exploits the FFTs for accelerating the matrix-vector multiplications during the iterative solution of linear system of equations arising due to the discretization of SIEs. (ii) During the iterative solution, VoxCap uses a highly effective and memory-efficient preconditioner that reduces the number of iterations significantly. (iii) VoxCap employs Tucker decompositions to compress the block Toeplitz and circulant tensors, requiring the largest memory in the simulator. By doing so, it reduces the memory requirement of these tensors from hundreds of gigabytes to a few megabytes and the CPU time required to obtain Toeplitz tensors from tens of minutes (even hours) to a few seconds for very large scale problems. VoxCap is capable of accurately computing capacitance of arbitrarily shaped and large-scale voxelized structures on a desktop computer.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
