I wish to express my sincere gratitude and appreciation to my supervisor, Professor Steven Boggs, for his invaluable advice, supervision, encouragements, assistances, and patience during the course of this work. I am deeply grateful to my co-supervisor, Professor Reza Iravani, for his invaluable advice, supervision in my academic work, and countless helps for my survival in the University. I am indebted to my supervision committee members, Professor Douglas Lavers and Professor Adalbert Konrad, for their lectures on the numerical methods, and for their advice and suggestions on many computational difficulties. I would gratefully thank Toshiba Corporation of Japan, especially Dr. Susumu Nishiwaki and Dr. Toshiya Imai, for supporting the ZnO arrester project. The material properties and arrester design parameters supplied by Toshiba allowed realistic simulations to be carried out. Financial support from National Sciences and Engineering Research Council Canada (NSERC), China National Scholarship, University of Toronto Fellowships, Edward Rogers Fellowship, and TD Meloche Monnex aprestigious scholarship are gratefully cknowledged.