A Multilevel Numerical Approach with Application in Time-Domain Electromagnetics (Communications in Computational Physics, 2018)
An algebraic multilevel method is proposed for efficiently simulating linearwave propagation using higher-order numerical schemes. This method is used inconjunction with the Finite Volume Time Domain (FVTD) technique for the numericalsolution of the time-domain Maxwell's equations in electromagnetic scatteringproblems. In the multilevel method the solution is cycled through spatial operatorsof varying orders of accuracy, while maintaining highest-order accuracy at coarser approximationlevels through the use of the relative truncation error as a forcing function.Higher-order spatial accuracy can be enforced using the multilevel method at afraction of the computational cost incurred in a conventional higher-order implementation.The multilevel method is targeted towards electromagnetic scattering problemsat large electrical sizes which usually require long simulation times due to the use ofvery fine meshes dictated by point-per-wavelength requirements to accurately modelwave propagation over long distances.