Description
Introduction to the Fast Multipole Method introduces the reader to the theory and computer implementation of the Fast Multipole Method. It covers the topics of Laplace’s equation, spherical harmonics, angular momentum, the Wigner matrix, the addition theorem for solid harmonics, and lattice sums for periodic boundary conditions, along with providing a complete, self-contained explanation of the math of the method, so that anyone having an undergraduate grasp of calculus should be able to follow the material presented. The authors derive the Fast Multipole Method from first principles and systematically construct the theory connecting all the parts.
Key Features
- Introduces each topic from first principles
- Derives every equation presented, and explains each step in its derivation
- Builds the necessary theory in order to understand, develop, and use the method
- Describes the conversion from theory to computer implementation
- Guides through code optimization and parallelization
Table of Contents
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
