Resonators

Resonant cavities are commonly used as elements of a microwave filter, and as beamline components in a particle accelerator or microwave tube.  These structures can be physical cavities, that is, vacuum or air surrounded by conductive walls, or they can be made of dielectric or permeable media.

Analyst eigensolvers can be used to determine the resonant frequencies and corresponding electromagnetic fields of resonant modes.  When modeling resonant cavities with highly conductive walls, the mode quality factors (Qs) and other mode parameters are determined using the fields determined from a solution obtained from perfectly conducting walls.  For situations where the wall losses are not small, or in dielectric resonators, the actual wall losses or media loss tangents can be modeled.

Both 2D and 3D problems can be modeled.  The fields are assumed to be invariant in either a Cartesian direction, or in the azimuthal direction in a cylindrical coordinate system.  In the latter case, the user may optionally consider higher-order azimuthal modes by specifying a mode number (0, 1, 2, etc.).

The Analyst OM3P and OM2P eigensolvers use the standard shift-invert Lanczos process for eigenmode extraction.  The user can specify both a shift frequency, that is, a minimum frequency for mode extraction, and also a total number of modes to be extracted.  Both degenerate (two or more modes with a common resonant frequency) and non-degenerate modes are extracted.  Many parameters typically associated with eigenmodes are reported for each mode in a mode summary table.  Entries in this table include resonant frequency, normalization energy, contributions to mode “Q” from various sources, peak fields in volume, on surface, and along a user-specified axis, and numerous other quantities.

The embedded optimization capabilities in Analyst can be used to optimize just about any characteristic of a resonator.  For example, the optimizer can iteratively adjust one or more geometric and/or material parameters in order to obtain a precise resonant frequency.
Each step of the Lanczos process requires the solution to the finite-element linear system, and this solution can be performed either using a direct LU decomposition approach or by using a pre-conditioned conjugate gradient (PCG) solver.  The PCG solver requires much smaller computer resources, but is typically slower than LU decomposition.  Several preconditioners are available for use with PCG that improve its performance, including diagonal scaling, Gauss-Seidel, and p-multigrid.  All linear solvers used by the eigensolvers can efficiently use multiprocessors, networked computers, computer clusters, and some massively parallel computers, e.g., IBM’s BG/L “Bluegene” computer.