Abstract
A typical application of numerical frequencyβdomain computations is the calculation of electromagnetic fields in cavities. Not only the field vectors of the desired modes, but also parameters such as the resonance frequency and, in the lossy case, the damping coefficient and the quality factor of the cavity can be obtained. This problem leads to an analytical eigenvalue equation, which can be transformed in an algebraic, complex, linear eigenvalue problem by the finite integration method.
The consideration of energy losses in materials is straighforward in the analytical theory, using complex material quantities, but it is still a difficult subject area to solve a complex algebraic eigenvalue problem. Generally problems with very large, complex matrices (dimension >100,000) have to be solved, and no commonly applicable algorithm is known so far.
This paper deals with a special variant of subspace iteration with polynomial acceleration, and some problems of the application of the complex Chebyshev polynomials are discussed. Two examples with weakly lossy cavities demonstrate the capability of the new algorithm, which is successfully applied to very large problems of up to 490, 000 real unknowns.