Introduction to the fast multipole method : topics in computational biophysics, theory, and implementation
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書誌事項
Introduction to the fast multipole method : topics in computational biophysics, theory, and implementation
CRC Press, Taylor & Francis Group, c2020
- : hardback
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注記
Includes bibliographical references (p.441) and index
収録内容
- Legendre polynomials
- Associated Legendre functions
- Spherical harmonics
- Angular momentum
- Wigner matrix
- Clebsch-Gordan coefficients
- Recurrence relations for Wigner matrix
- Solid harmonics
- Electrostatic force
- Scaling of solid harmonics
- Scaling of multipole translations
- Fast multipole method
- Multipole translations along the z-axis
- Rotation of coordinate system
- Rotation-based multipole translations
- Periodic boundary condition
内容説明・目次
内容説明
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
目次
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
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