Spherical Helmholtz Translation and Rotation

Python implementations of translation and rotation theorems for spherical solutions of the Helmholtz equation in three dimensions. This is heavily based on the book “Fast Multipole Methods for the Helmholtz Equation in Three Dimensions”, by N. A. Gumerov and R. Duraiswami, Elsevier 2005.

• Documentattion: https://spherical-helmholtz-translation-and-rotation.readthedocs.io/en/latest/

• Source code and issue tracker: https://github.com/AppliedAcousticsChalmers/Spherical-Helmholtz-Translation-and-Rotation

Contents:

• Bases
• Expansions
• Transforms
• Examples
  • Simple Rotations of Surface Expansion
    • Original field
    • First rotation
    • Second rotation
    • Final rotated field
    • Reexpansion
    • Reevaluated expansion
  • Simple Translation of a Monopole
    • Original Field
    • Translated field
    • Reexpanded field
    • Reevalulated field

Indices and tables

• Index

• Module Index

• Search Page