Abstract
In this paper, we describe a matrix-free iterative algorithm based on the GMRES method for solving electromagnetic scattering problems expressed in an integral formulation. Integral methods are an interesting alternative to differential equation solvers for this problem class since they do not require absorbing boundary conditions and they mesh only the surface of the radiating object giving rise to dense and smaller linear systems of equations. However, in realistic applications the discretized systems can be very large and for some integral formulations, like the popular Electric Field Integral Equation, they become ill-conditioned when the frequency increases. This means that iterative Krylov solvers have to be combined with fast methods for the matrix-vector products and robust preconditioning to be affordable in terms of CPU time. In this work we describe a matrix-free two-grid preconditioner for the GMRES solver combined with the Fast Multipole Method. The preconditioner is an algebraic two-grid cycle built on top of a sparse approximate inverse that is used as smoother, while the grid transfer operators are defined using spectral information of the preconditioned matrix. Experiments on a set of linear systems arising from real radar cross section calculation in industry illustrate the potential of the proposed approach for solving large-scale problems in electromagnetism.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
