Oblique-oblique projection in TLM-MOR for high-Q structures

The non-symmetric properties of the TLM-matrix require the application of general Krylov subspace methods for the purposes of model order reduction (MOR). Application of the Arnoldi algorithm is computational expensive. Furthermore, the classical nonsymmetric Lanczos algorithm requires the transpose TLM-matrix in order to form a biorthogonal basis for Krylov subspaces; hence, its algorithmic simplicity is also penalized and its computational complexity is increased. Here we describe a novel scattering-symmetric (S-symmetric) algorithm, which is used for the oblique projection of the TLM-system. The S-symmetric Lanczos algorithm is faster and consumes less memory in comparison to the conventional non-symmetric Lanczos algorithm, since the S-symmetric version generates a biorthogonal basis utilizing a single sequence like the symmetric Lanczos procedure. However, the reduced TLM-matrix can still be large. Instead of the conventional eigenvalue decomposition (EVD) the second oblique projection of the TLM-system can be performed in order to extract only eigenvalues corresponding to a needed frequency band. The oblique-oblique projection approach allows us to decrease the computational effort in TLM-MOR. The advantages of the proposed techniques are demonstrated trough their applications to the loss-free high-Q filters.     «

The non-symmetric properties of the TLM-matrix require the application of general Krylov subspace methods for the purposes of model order reduction (MOR). Application of the Arnoldi algorithm is computational expensive. Furthermore, the classical nonsymmetric Lanczos algorithm requires the transpose TLM-matrix in order to form a biorthogonal basis for Krylov subspaces; hence, its algorithmic simplicity is also penalized and its computational complexity is increased. Here we describe a novel sca...     »