The conceptual development of new components for use in accelerators, microwave devices, and other endeavors often starts with simplified models, typically in a reduced dimensional space. For radio frequency cavities and other beamline structures, where devices can often be reasonably approximated by rotationally symmetric analogues, a two-dimensional analysis allows for the rapid assessment of novel concepts. This project will develop an improved two-dimensional eigensolver for use in radio-frequency cavity design for accelerator applications. The code will be based upon an existing commercial eigensolver, which uses the finite element method for solving the electromagnetic eigenproblem in rotationally or translationally invariant structures. Commercial Applications and other Benefits as described by the awardee The proposed comprehensive two-dimensional modeling capability should provide designers of accelerator components with a powerful new tool for investigating novel concepts. The capability would allow for rapid, exhaustive analysis and optimization of simplified structures, providing the means to benchmark equivalent three-dimensional calculations and also to more quickly assess conceptual design modifications