Solving the Christoffel equation: Phase and group velocities

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 summaryProgram title: ChristoffelCatalogue identifier: AFAT_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFAT_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 2631No. of bytes in distributed program, including test data, etc.: 14958Distribution format: tar.gzProgramming language: Python.Computer: Workstations.Operating system: Linux/UNIX/Windows/MacOS.Classification: 7.8.External routines: NumPyNature of problem: Calculating acoustic phase and group velocities in homogeneous solidsSolution method:Solving the Christoffel equation eigenvalue problem by diagonalization; calculating group velocities and enhancement factors analytically as derivatives.Running time:Seconds/minutes