Hp -Vector Finite Element Method for the Full-Wave Analysis of Waveguides with No Spurious Modes

Mixed Spectral-Element Method for the Waveguide Problem With Bloch Periodic Boundary Conditions

“…In order to obtain accurate solutions, from Table 1, we can see that COMSOL requires more 34.96 times DOFs and 7.758 times CPU time than the MSEM. Also, we can see that our schemes (24) and (25) have nearly the same accuracy which indicates that (24) is equivalent to (25). In fact, using the algorithm (24), we can arrive at the reference value k 10,h i,z by only taking N = 6.…”

“…In short, our both MSEM schemes not only have the favorable inheritance, but also reduce the computational costs by using (27) to remove part of the degrees of freedom. Note that we still use (24) and (25) to express the waveguide eigenvalue problems which have been imposed the BPBC (7) and the PBC (15), respectively.…”

“…In addition, spurious modes in numerical methods are often mixed with physical modes of a waveguide problem. In [25], a novel variational formulation with the Nédélec element and the Gauss' law was developed to eliminate all the spurious modes. The mixed finite element methods (MFEM), which is composed of the curl-conforming basis functions and the Gauss' law, was also employed to suppress the spurious modes [26,27].…”

Multigrid Finite Element Methods for Electromagnetic Field Modeling (Zhu, Y. and Cangellaris, A.; 2006) [Reviews and Abstracts]

“…This reviewer recently had occasions to (independently) review much of the published literature on this topic, and the discussion in Chapter 9. is an excellent summary of this. (One approach not mentioned in this chapter is the use of Lagrange multipliers to enforce the divergence condition [3]). .…”

Full-wave analysis of dielectric waveguides at a given frequency

“…We present convergence rates for Nedelec elements [26,27] and show that numerical experiments confirm the theoretical estimates. We refer to [32] for additional numerical examples.…”