Automated Solution of Differential Equations by The Finite Element Method 1264258828

This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations.

The Finite Element Method and Applications with ANSYS® provides the reader with theoretical and practical knowledge of the finite element method and with the skills required to analyze engineering problems with ANSYS®, a commercially available FEA program. This self-contained, introductory text minimizes the need for additional reference material, covering the fundamental topics in finite element methods, as well as advanced topics concerning modeling and analysis with ANSYS®.

A concise introduction to numerical methodsand the mathematical framework neededto understand their performance
Numerical Solution of Ordinary Differential Equations presents a complete and easy-to-follow introduction to classical topics in the numerical solution of ordinary differential equations. The book's approach not only explains the presented mathematics, but also helps readers understand how these numerical methods are used to solve real-world problems.

This book serves as a practical guide to simulation of 3D deformable solids using the Finite Element Method (FEM). It reviews a number of topics related to the theory and implementation of FEM approaches: measures of deformation, constitutive laws of nonlinear materials, tetrahedral discretizations, and model reduction techniques for real-time simulation.