Numerical methods in computational mechanics

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Numerical methods in computational mechanics

Author: M. Okrouhlık | Size: 4.3 MB | Format: PDF | Quality: Original preprint | Publisher: Institute of Thermomechanics, Prague 2008 | Year: 2012 | pages: 350 | ISBN: -

Introduction:
The presented publication might be of interest to students, teachers and researchers who are compelled to solve nonstandard tasks in solid and/or fluid mechanics requiring large scale computation.
The presented publication might be of interest to human problem solvers in continuum mechanics, who are not professional programmers by education, but by destiny and/or by personal inquisitiveness are compelled to resolve nonstandard tasks stemming from the field of solid and/or fluid mechanics requiring large sized computation.
It is dedicated to matrix algebra, in its broadest sense, which allows for the transparent formulations of principles of continuum mechanics as well as for effective notations of algebraic operations with large data objects frequently appearing in solution of continuum mechanics problems by methods discretizing continuum in time and space.
The publication has been prepared by eight authors.
The publication is composed of contributions of two kinds.
• First, there are contributions dealing with fundamentals and the background of numerical mathematics in computational mechanics, accompanied by templates and programs, which are explaining the standard matrix operations (chapter 2) 7
CHAPTER 1. INTRODUCTION 8
and procedures needed for the solution of basic tasks as the solution of linear algebraic systems, generalized eigenvalue problem, solution of nonlinear task and the solution of ordinary differential equations, etc. (Chapters 3, 4, 5). We focus on nonstandard storage schemes, chapter (11), allowing to tackle large scale tasks. By a template we understand a general broad term description of the algorithm using high level metastatements like invert the matrix, or check the convergence. The
programs accompanying the text are written in Basic, Pascal, Fortran, Matlab and C#. The presented programs are rather short and trivial and are primarily intended for reading. The e-book readers (or users?) are encouraged to fiddle with these programs.
• Second, there are advanced contributions describing modern approaches to numerical algorithmization with emphasis to novelty, programming efficiency and/or to complicated mechanical tasks as the contact treatment.
The attention is devoted to
– domain decomposition methods, (Chapter 7),
– BDDC methods, and FETI-DP methods , (Chapter 8),
– the BFGS method applied to a new contact algorithm, (Chapter 9),
– frontal solution method, (Chapter 10),
– details of sparse storage modes, (Chapter 11),
– intricacies of object programming approach, (Chapter 12),
– programming the Arbitrary Lagrangian Eulerian approach to the solid-fluid problem, (Chapter 13), etc.
Programming considerations for parallel treatment are observed. These contributions have their origin in papers that the contributing authors recently published in scientific journals and/or presented at conferences.

Personal review:
A must have, very useful book it has source code written in basic, fortran, matlab, c#, pascal, for solving system of equations. Gauss, pivot, partial pivot....
It also deals with truncation errors and other computational errors.
If you're at the beginning in writing a solvers for finite element analysis matrix method use this book, code has comments and explanation all is provided clear, clean and easy to understand.
This book although is free has helped me more than many other expensive ones.

Code:

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