Abstract
A Quasi-Newton method for reconstructing the constitutive parameters of three-dimensional (3D) penetrable scatterers from scattered field measurements is presented. This method is adapted for handling large-scale electromagnetic problems while keeping the memory requirement and the time flexibility as low as possible. The forward scattering problem is solved by applying the finite-element tearing and interconnecting full-dual-primal (FETI-FDP2) method which shares the same spirit as the domain decomposition methods for finite element methods. The idea is to split the computational domain into smaller non-overlapping sub-domains in order to simultaneously solve local sub-problems. Various strategies are proposed in order to efficiently couple the inversion algorithm with the FETI-FDP2 method: a separation into permanent and non-permanent subdomains is performed, iterative solvers are favorized for resolving the interface problem and a marching-on-in-anything initial guess selection further accelerates the process. The computational burden is also reduced by applying the adjoint state vector methodology. Finally, the inversion algorithm is confronted to measurements extracted from the 3D Fresnel database.
Highlights
Quantitative inverse scattering algorithms attempt to estimate from scattering experiments the physical parameters and features of an unknown target
Our aim is not just to plug the Finite-Element Tearing and Interconnecting (FETI)-FDP2 method to replace the Finite Element Method (FEM) method, but it is to show how a Domain Decomposition Finite Element method can be efficiently combined with an iterative optimization algorithm and to point out the different strategies that we have followed in order to limit the computational burden and reduce the memory storage
In order to quantitatively appraise the effectiveness of the implementation strategy, we compare the results obtained with the FETI-FDP2 approach with the ones that are retrieved when combining the inversion algorithm with a classical FEM method
Summary
Quantitative inverse scattering algorithms attempt to estimate from scattering experiments the physical parameters and features (position, form, size and complex permittivity) of an unknown target. Unlike qualitative methods, quantitative ones solve the exact non-linear electromagnetic inverse problem, which requires the solution of a system of coupled equations For this aim, either a global optimization procedure is applied [1, 2] or a local one [3, 4, 5], into which the forward solver plays a key role. We can point out a Broyden-Fletcher-Goldfarb-Shanno (BFGS) Quasi-Newton optimization algorithm with line search [4] [40], which distinguishes itself through an approximation of the Hessian matrix in the Newton correction step with a matrix that does not involve the explicit computation of second order derivatives Even if it requires additional storage, this BFGS scheme is known for presenting a faster convergence rate than the conjugate-gradient methods which can be seen as memory-less BFGS methods [41, 42]. G0(r; r ) is the classical 3D free-space scalar Green function
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