Title:  Error Estimation and Adaptive Refinement Technique in the Method of Moments

Committee:

Dr. Andrew Peterson, ECE, Chair , Advisor

Dr. Waymond Scott, ECE

Dr. Gregory Durgin, ECE

Dr. Emmanouil Tentzeris, ECE

Dr. Federico Bonetto, Math

Abstract: The objective of this dissertation is to develop a reliable and computationally inexpensive adaptive h-refinement technique for the three-dimensional method of moments to reduce numerical errors in electromagnetics efficiently. The adaptive refinement technique consists of an error estimator and a control algorithm. Error estimation plays an important role because it determines regions where error is large. Various error estimators are investigated and implemented. With the Pearson correlation coefficient, local error plots, and scatter plots comparing the estimated errors with actual errors, we evaluate reliability and efficiency of the error estimators. Based on the study of the initial error estimators, we invent new error estimators, which satisfy accuracy and efficiency simultaneously. The controller in the adaptive h-refinement technique is required to adjust mesh sizes and to maintain mesh quality over the regions that are identified for the refinement. The control algorithm distributes new nodes on the domains to be refined and employs the advancing front Delaunay algorithm to generate refined meshes. Since the quality of refined meshes can be aggravated during this procedure, we adopt Laplacian smoothing, which adjusts node positions by taking the average of their adjacent node positions. Numerical results of the error estimator assessment and the adaptive h-refinement technique will be presented and discussed.