Matrix times vector multiplication based on Floquet-Bloch decomposition in the context of large antenna arrays. Application to finite-element partitionings

The calculation of the electromagnetic field scattered from large antenna arrays is of prime interest in many aerospace applications. Unfortunately, large antenna arrays bring out major difficulties, such as complex composite design or mutual coupling between elements in the near field. The goal of this communication is to present a general method for computing matrix times vector multiplication in this context. The Floquet-Bloch decomposition is used to highlight the Toeplitz-related matrices associated with such arrays. We describe an application of this approach to the finite-element solution of iterative substructuring algorithms. The computational complexity and the memory requirements are significantly reduced. Numerical results are detailed showing the efficiency of our approach.