Finite Element Methods

This new edition includes three new chapters, 7 through 9, that have very broad, practical applications in engineering and science. In addition, the author's latest research results incorporated into the new textbook demonstrates better performance than the popular METIS software for partitioning graphs, partitioning finite element meshes, and producing fill-reducing orderings for sparse matrices. The new Chapter 8, and its pre-requisite, Chapter 7, present a state-of-the-art algorithm for computing the shortest paths for real-life (large-scale) transportation networks with minimum computational time. This approach has not yet appeared in any existing textbooks and it could open the doors for other transportation engineering applications. Chapter 9 vastly expands the scope of the previous edition by including sensitivity (gradient) computation and MATLAB's built-in function fmincon for obtaining the optimum (or best) solution for general engineering problems.

Greatly expands chapters 2 and 6, added appendices and adds three new chapters, 7, 8, and 9 Introduces several additional/important research topics for broad (engineering & science) applications Explains FETI-DP methods, SVD (with examples) and useful tutorial materials for improving MATLAB programming skills

Autorentext
Dr. Duc Thai Nguyen is a Structural Engineering Professor in the Department of Civil and Environmental Engineering, Old Dominion University, Norfolk, VA

Zusammenfassung

"The material is organized in 9 chapters, 8 appendices, references and subject index. This textbook should be useful for graduate students, practicing engineers, and researchers who wish to thoroughly understand the detailed step-by-step algorithms, used during the finite element (truly sparse) assembly, the 'direct' and 'iterative' sparse equation eigen-solvers and incorporating the domain decomposition formulation for efficient parallel computation. (Costica Morosanu, zbMATH 1554.65284, 2025)

Inhalt
A Review of Basic Finite Element Procedures.- Simple MPI/FORTRAN Applications.- Direct Sparse Equation Solvers.- Sparse Assembly Process.- Generalized Eigen-Solvers.- Finite Element Domain Decomposition Procedures.