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We propose domain decomposition preconditioners for the solution of anintegral equation formulation of forward and inverse acoustic scatteringproblems with point scatterers. We study both forward and inverse problems andpropose preconditioning techniques to accelerate the iterative solvers. For theforward scattering problem, we extend the domain decomposition basedpreconditioning techniques presented for partial differential equations in {\em"A restricted additive Schwarz preconditioner for general sparse linearsystems", SIAM Journal on Scientific Computing, 21 (1999), pp. 792--797}, tointegral equations. We combine this domain decomposition preconditioner with alow-rank correction, which is easy to construct, forming a new preconditioner.For the inverse scattering problem, we use the forward problem preconditioneras a building block for constructing a preconditioner for the Gauss-NewtonHessian. We present numerical results that demonstrate the performance of bothpreconditioning strategies.

A domain decomposition preconditioning for the integral equation formulation of the inverse scattering problem