Efficient combination of a 3D Quasi-Newton inversion algorithm and a vector dual-primal finite element tearing and interconnecting method

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.

MRI-based electric properties tomography with a quasi-Newton approach

“…In the adjoint problem, there are a large number of virtual receivers N r , maybe as many as the number of elements in the MRI image. Computationally speaking, it is worthless to compute (27) for each virtual receiver r r separately and sum them up afterwards. Instead, we gather all the contributions as expressed in (26) to obtain the right-hand-side for a given transmitter r s .…”

“…This enables us to reduce the number of unknowns and thus render less ill-posed this inverse problem. Finally, we employ a quasi-Newton minimization algorithm to recover the quantitative permittivity and conductivity distribution maps [27].…”