r4.02.01 Finite elements in acoustics

Summary:

This document describes in stationary linear acoustics at low frequency in a bounded environment the equations used, the variational formulations that result from them as well as the corresponding translation into isoparametric finite elements using a usual formulation with an unknown \(p\) (sound pressure). This document corresponds to PHENOMENE =” ACOUSTIQUE “.

• 1. Introduction
• 2. Equations and boundary conditions of the problem
  • 2.1. Boundary equations and conditions
• 3. Pressure formulation
  • 3.1. Mathematical expression of the problem
  • 3.2. Finite element discretization
• 4. Commands specific to acoustic modeling
  • 4.1. Definition of the characteristics of propagation media
  • 4.2. Boundary conditions
  • 4.3. Calculation of elementary matrices
  • 4.4. Calculation of the elementary source vector
  • 4.5. Calculating the solution
  • 4.6. Post-treatments
• 5. Conclusion
• 6. Bibliography