Solving the Christoffel equation: Phase and group velocities

• DOI: 10.1016/j.cpc.2016.06.014
• Publication Date: 2016-06-27T14:02:03Z
• Authors: Jan W. Jaeken; Stefaan Cottenier
• Keywords: Christoffel symbols

Abstract We provide christoffel , a Python tool for calculating direction-dependent phase velocities, polarization vectors, group velocities, power flow angles and enhancement factors based on the stiffness tensor of a solid. It is built in a modular way to allow for efficient and flexible calculations, and the freedom to select and combine results as desired. All derivatives are calculated analytically, which circumvents possible numerical sampling problems. GNUPlot scripts are provided for convenient visualization. Program summary Program title: Christoffel Catalogue identifier: AFAT_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AFAT_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 2631 No. of bytes in distributed program, including test data, etc.: 14958 Distribution format: tar.gz Programming language: Python. Computer: Workstations. Operating system: Linux/UNIX/Windows/MacOS. Classification: 7.8. External routines: NumPy Nature of problem: Calculating acoustic phase and group velocities in homogeneous solids Solution method: Solving the Christoffel equation eigenvalue problem by diagonalization; calculating group velocities and enhancement factors analytically as derivatives. Running time: Seconds/minutes