This book is intended to be a cookbook for students and researchers to understand the finite element method and optimization methods and couple them to effect shape optimization. The optimization part of the book will survey optimization methods and focus on the genetic algorithm and Powell’s method for implementation in the codes. It will contain pseudo-code for the relevant algorithms and homework problems to reinforce the theory to compile finite element programs capable of shape optimization.
The Finite Element Method. In One-dimension. In Two dimensions. In Three dimesnions. Visualization and Postprocessing. Mesh
Generation and Open Source Software. High Order Elements. The Galerkin Method. Competing Methods. The Finite Difference
Method. The Boundary Element Method. Why Finite Elements. Mesh Generation and Postprocessing for Finite Elements.
Matrix Computation with Sparse Matrices. Gauss Iterations. Gaussian Triangulation. Cholesky Decomposition. Profile Storage.
Conjugate Gradient. Sparse Storage.Finite Elements in Electric Machines. High Frequency Problems and Vector Elements.
Optimization Methods. Formulation with Constraints. Search Methods. Zeroth Order Methods. Steepest Descent. Conjugate
Gradients. Multi-object Optimization. AI Techniques in Finite Element Optimization. Case Studies from Electromagnetic Product
Design. Case Studies from Nondestructive Evaluation.