This book provides a well-balanced and comprehensive picture based on clear physics, solid mathematical formulation, and state-of-the-art useful numerical methods in deterministic, stochastic, deep neural network machine learning approaches for computer simulations of electromagnetic and transport processes in biology, microwave and optical wave devices, and nano-electronics. Computational research has become strongly influenced by interactions from many different areas including biology, physics, chemistry, engineering, etc. A multifaceted approach addressing the interconnection among mathematical algorithms and physical foundation and application is much needed to prepare graduate students and researchers in applied mathematics and sciences and engineering for innovative advanced computational research in many applications areas, such as biomolecular solvation in solvents, radar wave scattering, the interaction of lights with plasmonic materials, plasma physics, quantum dots, electronic structure, current flows in nano-electronics, and microchip designs, etc.

Prof. Wei Cai is the Clements chair professor in Applied Mathematics at the Department of Mathematics at Southern Methodist University. He obtained his B.S. and M.S. in Mathematics from the University of Science and Technology of China (USTC) in 1982 and 1985, respectively, and his Ph.D. in Applied Mathematics at Brown University in 1989. Before he joined SMU in the fall of 2017, he was an assistant and then associate professor at the University of California at Santa Barbara during 1995–1996 and a full professor at the University of North Carolina after 1999. He has also conducted collaborative research at Peking University, USTC, Shanghai Jiao Tong University, and Fudan University. He works on fast machine learning, stochastic, and deterministic numerical methods for scientific computing applications, and was awarded the Feng Kang prize in scientific computing in 2005.