Jacobi—Davidson algorithm and its application to modeling RF/Microwave detection circuits

Abstract

This paper presents the application of the newly developed Jacobi-Davidson (JD) algorithm to solve quadratic eigenmatrix equations. The quadratic eigenmatrix equations result from using vector finite element methods to model open domain electromagnetic cavities. The derivation for the JD algorithm presented here, uses Newton's method for solving nonlinear equation. Consequently, it is intuitive to see the quadratic convergence rate for the basic algorithm when a good initial guess is provided. The complete JD procedure is then derived by combining the basic algorithm with Davidson's subspace method. Numerical examples show superquadratic or cubic convergence even when the correction equations are solved with only 10 −1 accuracy. Moreover, in this paper, the JD algorithm is used to construct an equivalent circuit model for a slot-patch RF/Microwave detection circuit. The simulations obtained from the equivalent circuit model agree, in general, very well with the measurements for both the downlink and uplink performances.