Error Convergence in Sonnet
Monotonic Error Convergence is Key
Convergence analysis is the process by which a problem is set up on a baseline grid and the EM analysis performed. Then, the grid is halved in size and the same problem re-analyzed. Following 
each analysis, results are compared for a convergence of the solution to an asymptotically correct value.
Convergence analysis serves two purposes.
- First, in the evaluation of multiple electromagnetic analysis software packages, it allows one to investigate which ones converge slowly, converge to a wrong answer or diverge.
- In the design phase, convergence analysis allows one to begin an analysis with a coarse grid which solves quickly. Then, by re-analyzing the problem with the grid halved and comparing solutions, one can determine whether the answer has "converged" to the desired degree of accuracy.
The convergence of Sonnet has been verified on a multitude of circuits. The graph above shows one example of a convergence test applied to Sonnet while succesively refining the background sampling grid (mesh size) in a critical dimension.
Monotonic error convergence is a particular strength of the Shielded Domain Method of Moments, and in particular, of Sonnet. Any result can be tested by either refining or relaxing the grid (sampling) size in either dimension and comparing to a baseline result. Armed with the knowledge that Sonnet exhibits reliably monotonic error convergence, you can be convinced of the quality of your simulation.
