Stochastic Spectral Element, Finite Cell and Spectral Cell Methods

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.