Compressive Wave Computation

This paper considers large-scale simulations of wave propagation phenomena. We argue that it is possible to accurately compute a wavefield by decomposing it onto a largely incomplete set of eigenfunctions of the Helmholtz operator, chosen at random, and that this provides a natural way of parallelizing wave simulations for memory-intensive applications. Where a standard eigenfunction expansion in general fails to be accurate if a single term is missing, a sparsity-promoting 1 minimization problem can vastly enhance the quality of synthesis of a wavefield from low-dimensional spectral information. This phenomenon may be seen as “compressive sampling in the Helmholtz domain”, and has recently been observed to have a bearing on the performance of data extrapolation techniques in seismic imaging [41]. This paper shows that 1-Helmholtz recovery also makes sense for wave computation, and identifies a regime in which it is provably effective: the one-dimensional wave equation with co...

• Type: Journal
• Year: 2011
• Where: FOCM
• Authors: Laurent Demanet, Gabriel Peyré
• Keywords: Extrapolation Techniques, FOCM 2011, Formal Methods, Minimization Problem, Wave Propagation Phenomena