FFTSVD: A Fast Multiscale Boundary-Element Method Solver Suitable for Bio-MEMS and Biomolecule Simulation. This paper presents a fast boundary-element method (BEM) algorithm that is well suited for solving electrostatics problems that arise in traditional and bio-microelectromechanical systems (bio-MEMS) design. The algorithm, FFTSVD, is Green’s-function-independent for low-frequency kernels and efficient for inhomogeneous problems. FFTSVD is a multiscale algorithm that decomposes the problem domain using an octree and uses sampling to calculate low-rank approximations to dominant source distributions and responses. Long-range interactions at each length scale are computed using the FFT. Computational results illustrate that the FFTSVD algorithm performs better than precorrected-FFT (pFFT)-style algorithms or the multipole-style algorithms in FastCap.

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  1. Bardhan, Jaydeep P.; Knepley, Matthew G.; Brune, Peter: Nonlocal electrostatics in spherical geometries using eigenfunction expansions of boundary-integral operators (2015)
  2. Geng, Weihua; Krasny, Robert: A treecode-accelerated boundary integral Poisson-Boltzmann solver for electrostatics of solvated biomolecules (2013)
  3. Li, Chuan; Li, Lin; Petukh, Marharyta; Alexov, Emil: Progress in developing Poisson-Boltzmann equation solvers (2013)
  4. An, Xiang; Lü, Zhi-Qing: Fast analysis of electrically large electromagnetic scattering/radiation problems using the adaptive cross approximation with FFT (2011)
  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. Greengard, Leslie; Gueyffier, Denis; Martinsson, Per-Gunnar; Rokhlin, Vladimir: Fast direct solvers for integral equations in complex three-dimensional domains (2009)
  7. Of, G.; Kaltenbacher, M.; Steinbach, O.: Fast multipole boundary element method for electrostatic field computations (2009)
  8. Lu, B.Z.; Zhou, Y.C.; Holst, M.J.; McCammon, J.A.: Recent progress in numerical methods for the Poisson-Boltzmann equation in biophysical applications (2008)
  9. Lu, Benzhuo; Cheng, Xiaolin; McCammon, J.Andrew: “New-version-fast-multipole-method” accelerated electrostatic calculations in biomolecular systems (2007)
  10. Altman, Michael D.; Bardhan, Jaydeep P.; Tidor, Bruce; White, Jacob K.: FFTSVD: A fast multiscale boundary-element method solver suitable for bio-MEMS and biomolecule simulation. (2006)