Efficient computation of extended surface sources

Abstract

Source extension is a reformulation of inverse problems in wave propagation, that at least in some cases leads to computationally tractable iterative solution methods. The core subproblem in all source extension methods is the solution of a linear inverse problem for a source (right hand side in a system of wave equations) through minimization of data error in the least squares sense with soft imposition of physical constraints on the source via an additive quadratic penalty. For an acoustic formulation for sources supported on a surface, with a soft contraint enforcing concentration at a point, a variant of the time reversal method from photoacoustic tomography provides an approximate solution. This approximate inverse can be used to precondition Krylov space iteration for rapid convergence to the solution of the core subproblem in this setting. Numerical examples illustrate the effectiveness of this preconditioner.