Efficient and accurate waveguide mode computation using BI-RME and Lanczos methods

Abstract

SUMMARYIn this paper, a special purpose algorithm for solving large eigenvalue problems based on the Lanczos method is successfully applied to an engineering problem: the electromagnetic analysis and design of passive waveguide devices. For dealing with such complex problems, the boundary integral-resonant mode expansion (BI-RME) technique has been recently proposed. This technique solves integral equations (IEs) through the well-known method of moments (MoM), thus leading to structured eigenvalue problems. These problems frequently become very large when solving complex arbitrary geometries with high accuracy. In such cases, the eigenvalue problem cannot be efficiently solved with standard methods by means of personal computers, essentially due to CPU time and memory allocation requirements. In this paper, we propose an alternative technique, based on the Lanczos method, for the fast and accurate solution of large BI-RME generalized eigenvalue problems. The novel theoretical aspects of this approach, as well as the impact on the original BI-RME formulation, are described. Comparative benchmarks are also successfully presented for the full-wave analysis and design of real passive microwave devices.

Parallel computation of arbitrarily shaped waveguide modes using BI‐RME and Lanczos methods

“…The algorithm proposed in Reference [6] and described above has many advantages over the standard Lapack-based software for this problem, even in sequential computing. In a parallel computing environment, the advantages are still larger: even without performing any test at all, it is fairly clear that computing the eigenvalues of each subinterval can be performed independently to the process of any other subinterval; therefore, it is an excellent algorithm to be parallelized.…”

“…In the previous paper [6], when the sequential version of the algorithm was presented, a simple adaptive strategy was chosen, since the gains to be obtained using more sophisticated strategies were not too important. However, as we will see in the next section, this matter is much more relevant considering the parallel processing of the intervals.…”

“…In the previous paper [6], the authors proposed an algorithm based on the Lanczos technique, which uses the structure of the matrices to minimize the cost, in time and especially in memory, of…”

“…The meanings of all previous block matrices, their dimensions and also the mathematical definition of their corresponding elements, are fully detailed in Reference [6]. However, it must be recalled that O and O are null matrices, the subscript t denotes transpose, I is the identity matrix, whereas U and U are diagonal matrices.…”

“…As shown in Figure 1, the generalized eigenvalue problem for the TE case presents a size of (M + N ) × (M + N ), where M is the number of standard rectangular waveguide TE modes used for expanding each arbitrary waveguide mode, and N is the number of basis functions used to expand the unknown surface current density (in most cases M is much larger than N ). For the TM problem, the same corresponding numbers are usually labelled as M and N (see Reference [6]). …”