FastCap: a multipole accelerated 3-D capacitance extraction program. A fast algorithm for computing the capacitance of a complicated three-dimensional geometry of ideal conductors in a uniform dielectric is described and its performance in the capacitance extractor FastCap is examined. The algorithm is an acceleration of the boundary-element technique for solving the integral equation associated with the multiconductor capacitance extraction problem. The authors present a generalized conjugate residual iterative algorithm with a multipole approximation to compute the iterates. This combination reduces the complexity so that accurate multiconductor capacitance calculations grow nearly as nm, where m is the number of conductors. Performance comparisons on integrated circuit bus crossing problems show that for problems with as few as 12 conductors the multipole accelerated boundary element method can be nearly 500 times faster than Gaussian-elimination-based algorithms, and five to ten times faster than the iterative method alone, depending on required accuracy.

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  1. Ding, Lingyun; Huang, Jingfang; Marzuola, Jeremy L.; Tang, Zhuochao: Quadrature by two expansions: evaluating Laplace layer potentials using complex polynomial and plane wave expansions (2021)
  2. Malik, Rahila; Alam, Mehboob; Muhammad, Shah; Hussain, Rashida; Ali, Asghar; Akram, Namra; Duraihem, Faisal Zaid; Haq, Anwar Ul: Statistically inspired multi-shift Arnoldi projection for on-chip interconnects (2021)
  3. Huang, S.; Liu, Y. J.: A new fast direct solver for the boundary element method (2017)
  4. Deng, Yani; Ye, Wenjing; Gray, L. J.: Complexity and accuracy of the grid-based direct-volume integration BEM for quasilinear problems (2015)
  5. Yokota, Rio; Bardhan, Jaydeep P.; Knepley, Matthew G.; Barba, L. A.; Hamada, Tsuyoshi: Biomolecular electrostatics using a fast multipole BEM on up to 512 GPUs and a billion unknowns (2011)
  6. Zhang, Bo; Huang, Jingfang; Pitsianis, Nikos P.; Sun, Xiaobai: A Fourier-series-based kernel-independent fast multipole method (2011)
  7. Coulaud, O.; Fortin, P.; Roman, J.: High performance BLAS formulation of the adaptive fast multipole method (2010)
  8. Greengard, Leslie; Gueyffier, Denis; Martinsson, Per-Gunnar; Rokhlin, Vladimir: Fast direct solvers for integral equations in complex three-dimensional domains (2009)
  9. Sumant, Prasad S.; Aluru, Narayana R.; Cangellaris, Andreas C.: A methodology for fast finite element modeling of electrostatically actuated MEMS (2009)
  10. Coulaud, O.; Fortin, P.; Roman, J.: High performance BLAS formulation of the multipole-to-local operator in the fast multipole method (2008)
  11. He, Xuefei; Lim, Kian Meng; Lim, Siak Piang: A fast elastostatic solver based on fast Fourier transform on multipoles (FFTM) (2008)
  12. Lim, Kian Meng; He, Xuefei; Lim, Siak Piang: Fast Fourier transform on multipoles (FFTM) algorithm for Laplace equation with direct and indirect boundary element method (2008)
  13. Chen, Hui; Mukherjee, Subrata: Charge distribution on thin conducting nanotubes-reduced 3-D model (2006)
  14. Lei, Ting; Yao, Zhenhan; Wang, Haitao; Wang, Pengbo: A parallel fast multipole BEM and its applications to large-scale analysis of 3-D fiber-reinforced composites (2006)
  15. Yu, T.; Cai, W.: FIFA-fast interpolation and filtering algorithm for calculating dyadic Green’s function in the electromagnetic scattering of multi-layered structures. (2006)
  16. Bao, Zhongping; Mukherjee, Subrata: Electrostatic BEM for MEMS with thin beams (2005)
  17. Buchau, André; Hafla, Wolfgang; Groh, Friedemann; Rucker, Wolfgang M.: Fast multipole method based solution of electrostatic and magnetostatic field problems (2005) ioport
  18. Zhou, Dian; Li, Rui-Ming: Design and verification of high-speed VLSI physical design (2005) ioport
  19. Masters, Nathan; Ye, Wenjing: Fast BEM solution for coupled 3D electrostatic and linear elastic problems (2004)
  20. Ong, E. T.; Lee, K. H.; Lim, K. M.: A fast algorithm for three-dimensional electrostatics analysis: fast Fourier transform on multipoles (FFTM) (2004)

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