  The motivation of this work is the detection of cerebrovascular accidents by
microwave tomographic imaging. This requires the solution of an inverse problem
relying on a minimization algorithm (for example, gradient-based), where
successive iterations consist in repeated solutions of a direct problem. The
reconstruction algorithm is extremely computationally intensive and makes use
of efficient parallel algorithms and high-performance computing. The
feasibility of this type of imaging is conditioned on one hand by an accurate
reconstruction of the material properties of the propagation medium and on the
other hand by a considerable reduction in simulation time. Fulfilling these two
requirements will enable a very rapid and accurate diagnosis. From the
mathematical and numerical point of view, this means solving Maxwell's
equations in time-harmonic regime by appropriate domain decomposition methods,
which are naturally adapted to parallel architectures.
