Fast multipole method for 3-D Poisson-Boltzmann equation in layered electrolyte-dielectric media

[1]  Masatake Mori,et al.  Double Exponential Formulas for Numerical Integration , 1973 .

[2]  Leslie Greengard,et al.  A fast algorithm for particle simulations , 1987 .

[3]  H. Berendsen,et al.  The electric potential of a macromolecule in a solvent: A fundamental approach , 1991 .

[4]  H. H. Clercx,et al.  An alternative expression for the addition theorems of spherical wave solutions of the Helmholtz equation , 1993 .

[5]  L. Greengard,et al.  A new version of the Fast Multipole Method for the Laplace equation in three dimensions , 1997, Acta Numerica.

[6]  W. Hackbusch A Sparse Matrix Arithmetic Based on $\Cal H$-Matrices. Part I: Introduction to ${\Cal H}$-Matrices , 1999, Computing.

[7]  B. Roux,et al.  Implicit solvent models. , 1999, Biophysical chemistry.

[8]  L. Greengard,et al.  A new version of the fast multipole method for screened Coulomb interactions in three dimensions , 2002 .

[9]  Steffen Börm,et al.  Data-sparse Approximation by Adaptive ℋ2-Matrices , 2002, Computing.

[10]  Mark A Olson,et al.  An efficient hybrid explicit/implicit solvent method for biomolecular simulations , 2004, J. Comput. Chem..

[11]  D. Zorin,et al.  A kernel-independent adaptive fast multipole algorithm in two and three dimensions , 2004 .

[12]  Shivkumar Chandrasekaran,et al.  A Fast ULV Decomposition Solver for Hierarchically Semiseparable Representations , 2006, SIAM J. Matrix Anal. Appl..

[13]  Benzhuo Lu,et al.  RecentProgress in NumericalMethods forthePoisson- Boltzmann Equation in Biophysical Applications , 2008 .

[14]  Peijun Li,et al.  A Cartesian treecode for screened coulomb interactions , 2009, J. Comput. Phys..

[15]  Bo Zhang,et al.  FMM-Yukawa: An adaptive fast multipole method for screened Coulomb interactions , 2009, Comput. Phys. Commun..

[16]  Jianlin Xia,et al.  Fast algorithms for hierarchically semiseparable matrices , 2010, Numer. Linear Algebra Appl..

[17]  Peng Wang,et al.  Implementing molecular dynamics on hybrid high performance computers - short range forces , 2011, Comput. Phys. Commun..

[18]  Wei Cai,et al.  A parallel fast algorithm for computing the Helmholtz integral operator in 3-D layered media , 2012, J. Comput. Phys..

[19]  Wei Cai,et al.  Accuracy and efficiency in computing electrostatic potential for an ion channel model in layered dielectric/electrolyte media , 2014, J. Comput. Phys..

[20]  W. Cai,et al.  Investigating the Selectivity of KcsA Channel by an Image Charge Solvation Method (ICSM) in Molecular Dynamics Simulations , 2015, 1510.04579.

[21]  Thomas Sterling,et al.  DASHMM: Dynamic Adaptive System for Hierarchical Multipole Methods , 2016 .

[22]  Krzysztof A. Michalski,et al.  Efficient computation of Sommerfeld integral tails – methods and algorithms , 2016 .

[23]  M. Praprotnik,et al.  Open-Boundary Molecular Dynamics of a DNA Molecule in a Hybrid Explicit/Implicit Salt Solution. , 2018, Biophysical journal.

[24]  Fast Multipole Method For 3-D Helmholtz Equation in Layered Media , 2019, SIAM J. Sci. Comput..

[25]  Wei Cai,et al.  An O(Nlog⁡N) hierarchical random compression method for kernel matrices by sampling partial matrix entries , 2019, J. Comput. Phys..

[26]  Wei Cai,et al.  Fast Multipole Method For 3-D Helmholtz Equation in Layered Media , 2019, SIAM J. Sci. Comput..

[27]  Wenzhong Zhang,et al.  Exponential Convergence for Multipole and Local Expansions and Their Translations for Sources in Layered Media: Two-Dimensional Acoustic Wave , 2020, SIAM J. Numer. Anal..

[28]  Bo Wang,et al.  Fast multipole method for 3-D Laplace equation in layered media , 2019, Computer Physics Communications.