MATLAB algorithm to directly calculate the derivatives of the systems

coefficients with respect to shape and material parameters. It represents a

considerable advancement over the conventional sensitivity-analysis method

which involves finding the difference between two system states, the

nominal unperturbed state and the perturbed state in which a variable has

been changed."

Traditional approaches usually require that at least one simulation be

performed for each parameter, often requiring many calculations. Typical

perturbations include changes in the dimensions of an object or changing the

material properties such as conductivity, permittivity or permeability.

The researchers have addressed this challenge by developing a new method

based on the fact that when a model is excited by a waveform by properly

manipulating its spectral components the time waveform is the same in

forward and backward time. This makes it possible to compute the

derivatives of the scattering matrix with respect to all the design parameters.

This approach eliminates the need to perform time-consuming adjoint

simulations. The sole requirement for the electromagnetic analysis software

is the ability to export the field solution at user-defined points. The S-matrix

and its derivatives with respect to all design parameters can be obtained

from a single simulation. The overhead of the sensitivity calculation is

negligible compared to the computational intensity of the full-wave

simulation.

The researchers based their new method on XFDTD finite difference time

domain (FDTD) electromagnetic simulation software from Remcom, Inc.,

State College, Pennsylvania, because of its ability to quickly and reliably

turn complicated geometries into accurate electromagnetic meshes. This

ability has been extended in XFDTD v6.2 with the addition of an advanced

meshing algorithm that makes meshing of certain difficult geometry features

possible. Adaptive meshing capabilities reduce solution times while

maintaining high levels of accuracy by automatically adjusting the mesh to

provide more cells in areas with high transients and reducing cells in areas

where there is less variation. In addition, the use of a parallel computational

code allows for multiple computers to be connected in order to perform

calculations faster as well as use larger workspaces.

Single resonator filter validation study