Introduction to the Fast Multipole Method

Victor Anisimov is an Application Performance Engineer at the Argonne Leadership Computing Facility. He holds a Ph.D. degree in Physical Chemistry from the Institute of Chemical Physics of the Russian Academy of Sciences (1997), which was followed by 5 years of computational chemistry software development with Fujitsu, where his team developed the linear scaling semi-empirical quantum chemistry code LocalSCF that expanded the limits of the approximate electronic structure theory to millions of atoms. He performed postdoctoral work at the University of Maryland at Baltimore (2003-2008), and at the University of Texas at Houston (2008-2011), improving molecular dynamics methods and contributing to the CHARMM code. In the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign (2011-2019), Dr. Anisimov held the position of Senior Research Scientist, conducted application support for petascale resource allocation teams on the Blue Waters supercomputer, optimized various application codes, and improved the performance and scaling profiles of coupled cluster singles and doubles electronic structure method in NWChem code. Dr. Anisimov works on the faithful representation of long-range electrostatic interactions in large-scale molecular simulations, near-neighbor communication algorithms, and linear-scaling methods. He specializes in performance optimization and fidelity improvements of electronic structure and soft matter simulation application codes on exascale platforms.

This book introduces the reader to the theory and methodology of quantum-mechanical modeling of chemical and biological systems. Given the immense complexity of such systems, there is a constant search for new methods.

1. Legendre Polynomials 2. Associated Legendre Functions 3. Spherical Harmonics 4. Angular Momentum 5. Wigner Matrix 6. Clebsch-Gordan Coefficients 7. Recurrence Relations for Wigner Matrix 8. Solid Harmonics 9. Electrostatic Force 10. Scaling of Solid Harmonics 11. Scaling of Multipole Translations 12. Fast Multipole Method 13. Multipole Translations along the z-Axis 14. Rotation of Coordinate System 15. Rotation-Based Multipole Translations 16. Periodic Boundary Condition