Numerical Simulation of Wave Propagation

Wave equations are hyperbolic partial differential equations (PDEs) which describe the propagation of various types of waves, such as acoustic, elastic, and electromagnetic waves. In order to solve PDEs, the finite element method (FEM) can be used. After a brief introduction to the mathematical method used by FEM to evaluate the solution in nodes, where the polynomial curve that interpolates the differential equation has to be solved, we will describe the methodology used to solve the wave propagation problem described by the Helmholtz’s equation. The wave propagation problem is analyzed by following specific steps: construction of the geometry to study, application of the boundary conditions, and meshing of the domain to be solved. The same procedure is used to simulate the behavior of piezoelectric transducers and the problem of wave propagation in medium with defects. Finally, the procedure followed for the simulation of acoustic problems using a specific software, i.e., COMSOL Multiphysics, is illustrated.