This book introduces three novel numerical methods—the Stochastic Spectral Element Method, the Stochastic Finite Cell Method, and the Stochastic Spectral Cell Method—each extending its deterministic counterpart into the stochastic framework. Written for researchers and practitioners in civil, structural, earthquake, and mechanical engineering, the book provides a unified formulation and consistent notation so that readers can easily understand the correspondences between methods. Chapters progress from fundamentals to advanced topics, reviewing deterministic prerequisites (the spectral element method, the finite cell method, and the spectral cell method), presenting a self contained chapter on probability and statistics, and developing simplified yet rigorous formulations for the three stochastic methods. Throughout, worked examples and illustrative solutions demonstrate how the methods address structural mechanics and wave propagation under uncertainty. This book is suitable for engineers seeking implementable stochastic techniques, graduate students in advanced numerical methods, and researchers in uncertainty quantification for computational mechanics.

Pooya Zakian is an Associate Professor of Civil Engineering with more than a decade of experience in academia. He holds B.Sc., M.Sc., and Ph.D. degrees in Civil Engineering, with the latter two specializing in Earthquake Engineering. An active technical reviewer for international journals, his research interests include computational mechanics, structural optimization, machine learning, stochastic structural mechanics, structural dynamics, and earthquake engineering. Dr. Zakian contributed to the development of three stochastic numerical techniques applied to structural mechanics and wave propagation problems. He is the author of over 50 peer reviewed journal articles, numerous conference papers, and one book in Persian. He has received several awards in Iran, including the Postdoctoral Fellowship Award for Outstanding Graduates, the Distinguished Dissertation Award, and the Distinguished Researcher Award. He was also included on the Stanford–Elsevier list of highly cited scientists in 2025.