Immersive Boundary Conditions

Immersive Boundary Conditions dynamically link wave propagation on two or more domains. By applying a time- and space-variant boundary condition, the wave propagation on a finite-size physical or numerical domain can be made equal to the wave propagation on a larger, desired medium that extends the finite domain.

The required boundary condition can be derived by comparing representations for the wavefield on the finite domain to representations for the wavefield on the desired extended medium. Since the boundary condition depends on the desired wavefield at the boundary itself, it must be obtained by exploiting causality and computed recursively. To this end, a mathematically-closed recording surface is introduced a small distance away from the boundaries, so that the desired wavefield can be predicted by extrapolation from this surface ahead of time. 

Note that, crucially, this extrapolation can be done with Green's functions computed for a medium that differs from the true medium inside the recording surface. Therefore, it is not necessary to characterize the medium inside the recording surface. Only the medium between the recording surface and the boundary needs to match the true medium when computing the extrapolation Green's functions. 

We use immersive boundary conditions in a wide range of applications including local wavefield recomputation, hybrid modeling, seismic data processing, absorbing boundary conditions and to link physical and numerical modeling in the Centre for Immersive Wave Experimentation