A comparison of time‐domain hybrid solvers for complex scattering problems

Abstract

SUMMARYIn this paper the accuracy, efficiency and stability of two hybrid solvers are compared to FDTD in several complex scattering cases. The explicit hybrid solver, FD-FV, combines an unstructured FVTD solver with FDTD, and the explicit-implicit solver, FD-FE, combines an unstructured FETD solver with FDTD.The results show that the two hybrid solvers are much more efficient than FDTD for complex objects where a Cartesian grid is not able to capture the geometry properly. Furthermore, they show that the FD-FE solver is a better choice than the FD-FV solver. Mainly because it is stable as long as the time step satisfies the CFL condition in the FDTD region, while the FD-FV solver may suffer from late time instabilities. But the FD-FE solver is also more efficient since the iterative method used to solve the matrixvector system arising in FETD converges fast and the FVTD solver is heavily penalized by having to take shorter time steps to satisfy its CFL condition.

Tailoring unstructured meshes for use with a 3D time domain co‐volume algorithm for computational electromagnetics

“…However, parallelization of the approach will be necessary before the method can be applied to more challenging applications. In addition, when this has been accomplished, the performance of the method can then be compared with that of the powerful current generation of hybrid finite difference time domain/FETD methods [28][29][30][31].…”

A parallel implicit/explicit hybrid time domain method for computational electromagnetics

“…In Equation (19), M I J is the standard finite element mass matrix, D denotes the boundary of region D andF ne is a normal boundary flux. A Galerkin variational formulation of Equation (13), leads to the implicit equation system…”

“…The corresponding boundary conditions are imposed in a weak sense, through the integral of the normal boundary flux,F ne , in Equation (19). The value ofF ne that should be employed is determined using a process of characteristic decomposition [8,21].…”

A new technique for accurate and stable modeling of arbitrarily oriented thin wires in the fdtd method

“…An approach to avoid staircasing that has gained popularity lately is to use unstructured grids near curved objects, but revert to Cartesian grids as quickly as possible for the rest of the computational domain. We have developed a stable hybrid solver, which combines FDTD with an FETD solver [9].…”

“…This is due to the fact that FETD is based on a volume integral formulation. For wire segments close to a grid interface special care must be taken since the interpolation cylinder may include hexahedral, tetrahedral as well pyramidal elements, where the pyramidal elements are used to connect the tetrahedral and hexahedral elements [9]. Thus, to model wires running through or close to the grid interface is only a bookkeeping problem but poses no fundamental difficulties.…”