## Illustrating wave propagation phenomena

In this page, I am showing some numerical simulations that I completed, mainly during my thesis. These numerical experiments have been performed with the software Montjoie.

### Didactic example for solving 2-D Helmholtz equation with finite element method

 The use of finite element methods is demonstrated for 2-D Helmholtz equation. The mesh and solution are generated with the pdetool package of Matlab. High-order curved elements are also experimented to show their efficiency.

### Eigenvalues for domains presenting a singularity

 Benchmark for computing eigenvalues in domains that contain corners or singular edges. Nedelec's edge elements of the first kind are used in conjunction with hexahedral mesh with a local refinement.

### Scattering by an aircraft at 750Mhz

 A plane wave is scattered by an aircraft. This time-domain simulation is performed with Discontinuous Galerkin method on hexahedral meshes, and with a local time-stepping strategy.

### Scattering by an aircraft at 900Mhz

 The same experiment as the previous one is conducted for an higher frequency. It can be observed that the mesh seems a bit too coarse for this frequency.

### Scattering by a satellite

 A plane wave is scattered by a satellite (GENEC). The used local time stepping strategy is quite efficient on this case because of the presence of very small elements (thin slots, solar panels with a small thickness).

### Resonance phenomena for a finite-length slot.

 A wave is propagating through a finite-length slot. For some given frequencies, some resonances appear and the transmission coefficient is higher.

### Propagation of a pulse through a slot

 Propagation of a wave through a slot inside a wall. The time source is a Ricker.

### Source point in a cobra cavity

 A wave is propagating inside a cobra cavity. The right side of the cavity is open (numerically a first-order absorbing boundary condition is set).

### Random media in a waveguide

 Propagation of waves inside a waveguide, that is characterized by a media with slow random variations. The physical index random variation is less than 3%.

### Random media in a big waveguide.

 This case is the same as the previous one, but for a larger waveguide (500 wavelegnths). The solution is represented by splitting the waveguide in several slices.

### Benchmark of a selective optical filter

 Studying an optical band-pass filter. This filter is highly selective, and this sensitivity is favorable to high-order element methods.

### Scattering of a plane wave by a thin wire

 Electromagnetic waves are scattered by a thin wire. Several models are available (Holland's model, fictitious domain model)
 Propagation of an acoustic wave in presence of a flow. Solving Linearized Euler equations with Discontinuous Galerkin method with hexahedral mesh.
 Propagation of an acoustic wave inside a piano-shaped cavity.
 Propagation of an acoustic wave inside the lungs.