THE COMPLEX SUBSPACE ITERATION FOR THE COMPUTATION OF EIGENMODES IN LOSSY CAVITIES

A typical application of numerical frequency-domain computations is th e calculation of electromagnetic fields in cavities. Not only the fiel d vectors of the desired modes, but also parameters such as the resona nce 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 algebr aic, complex, linear eigenvalue problem by the finite integration meth od. The consideration of energy losses in materials is straightforward in the analytical theory, using complex material quantities, but it i s still a difficult subject area to solve a complex algebraic eigenval ue problem. Generally problems with very large, complex matrices (dime nsion >100,000) have to be solved, and no commonly applicable algorith m is known so far. This paper deals with a special variant of subspace iteration with polynomial acceleration, and some problems of the appl ication of the complex Chebyshev polynomials are discussed. Two exampl es with weakly lossy cavities demonstrate the capability of the new al gorithm, which is successfully applied to very large problems of up to 490,000 real unknowns.