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The COVID-19 pandemic that started in 2019-2020 has led to a gigantic increase in modeling and simulation of infectious diseases. There are numerous topics associated with this epoch-changing event, such as (a) disease propagation, (b) transmission, (c) decontamination, and (d) vaccines. This is an evolving field. The targeted objective of this book is to expose researchers to key topics in this area, in a very concise manner. The topics selected for discussion have evolved with the progression of the pandemic. Beyond the introductory chapter on basic mathematics, optimization, and machine learning, the book covers four themes in modeling and simulation infectious diseases, specifically: Part 1: Macroscale disease propagation, Part 2: Microscale disease transmission and ventilation system design, Part 3: Ultraviolet viral decontamination, and Part 4: Vaccine design and immune response. It is important to emphasize that the rapidspeed at which the simulations operate makes the presented computational tools easily deployable as digital twins, i.e., digital replicas of complex systems that can be inexpensively and safely optimized in a virtual setting and then used in the physical world afterward, thus reducing the costs of experiments and also accelerating development of new technologies.

The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are: • Weighted residual methods and Galerkin approximations,• A model problem for one-dimensional linear elastostatics,• Weak formulations in one dimension,• Minimum principles in one dimension,• Error estimation in one dimension,• Construction of Finite Element basis functions in one dimension,• Gaussian Quadrature,• Iterative solvers and element by element data structures,• A model problem for three-dimensional linear elastostatics,• Weak formulations in three dimensions,• Basic rules for element construction in three-dimensions,• Assembly of the system and solution schemes,• An introduction to time-dependent problems and• An introduction to rapid computation based on domain decomposition and basic parallel processing. The approach is to introduce the basic concepts first in one-dimension, then move on to three-dimensions. A relatively informal style is adopted. This primer is intended to be a “starting point”, which can be later augmented by the large array of rigorous, detailed, books in the area of Finite Element analysis. In addition to overall improvements to the first edition, this second edition also adds several carefully selected in-class exam problems from exams given over the last 15 years at UC Berkeley, as well as a large number of take-home computer projects. These problems and projects are designed to be aligned to the theory provided in the main text of this primer.

The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are:(1) Weighted residual methods and Galerkin approximations,(2) A model problem for one-dimensional linear elastostatics,(3) Weak formulations in one dimension,(4) Minimum principles in one dimension,(5) Error estimation in one dimension,(5) Construction of Finite Element basis functions in one dimension,(6) Gaussian Quadrature,(7) Iterative solvers and element by element data structures,(8) A model problem for three-dimensional linear elastostatics,(9) Weak formulations in three dimensions,(10) Basic rules for element construction in three-dimensions,(11) Assembly of the system and solution schemes,(12) Assembly of the system and solution schemes,(13) An introduction to time-dependent problems and(14) A brief introduction to rapid computation based on domain decomposition and basic parallel processing.

The recent dramatic increase in computational power available for mathematical modeling and simulation promotes the significant role of modern numerical methods in the analysis of heterogeneous microstructures. In its second corrected printing, this book presents a comprehensive introduction to computational micromechanics, including basic homogenization theory, microstructural optimization and multifield analysis of heterogeneous materials.'An Introduction to Computational Micromechanics'is valuable for researchers, engineers and for use in a first year graduate course for students in the applied sciences, mechanics and mathematics with an interest in the computational micromechanical analysis of new materials.