Komzsik Approximation Techniques for Engineers

Second Edition
2. Auflage 2017
ISBN: 978-1-351-79272-1
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 386 Seiten

This second edition includes eleven new sections based on the approximation of matrix functions, deflating the solution space and improving the accuracy of approximate solutions, iterative solution of initial value problems of systems of ordinary differential equations, and the method of trial functions for boundary value problems. The topics of the two new chapters are integral equations and mathematical optimization. The book provides alternative solutions to software tools amenable to hand computations to validate the results obtained by "black box" solvers. It also offers an insight into the mathematics behind many CAD, CAE tools of the industry. The book aims to provide a working knowledge of the various approximation techniques for engineering practice.

Autoren/Hrsg.

Komzsik, Louis

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau
• Technische Wissenschaften Energietechnik | Elektrotechnik Elektrotechnik

Inhaltsverzeichnis

I Data approximations

1 Classical interpolation methods

1.1 Newton interpolation

1.2 Lagrange interpolation

1.3 Hermite interpolation

1.3.1 Computational example

1.4 Interpolation of functions of two variables with polynomials

References

2 Approximation with splines

2.1 Natural cubic splines

2.2 Bezier splines

2.3 Approximation with B-splines

2.4 Surface spline approximation

References

3 Least squares approximation

3.1 The least squares principle

3.2 Linear least squares approximation

3.3 Polynomial least squares approximation

3.4 Computational example

3.5 Exponential and logarithmic least squares approximations

3.6 Nonlinear least squares approximation

3.7 Trigonometric least squares approximation

3.8 Directional least squares approximation

3.9 Weighted least squares approximation

References

4 Approximation of functions

4.1 Least squares approximation of functions

4.2 Approximation with Legendre polynomials

4.3 Chebyshev approximation

4.4 Fourier approximation

4.5 Pad´e approximation

4.6 Approximating matrix functions

References

5 Numerical differentiation

5.1 Finite difference formulae

5.2 Higher order derivatives

5.3 Richardson’s extrapolation

5.4 Multipoint finite difference formulae

References

6 Numerical integration

6.1 The Newton-Cotes class

6.2 Advanced Newton-Cotes methods

6.3 Gaussian quadrature

6.4 Integration of functions of multiple variables

6.5 Chebyshev quadrature

6.6 Numerical integration of periodic functions

References

II Approximate solutions

7 Nonlinear equations in one variable

7.1 General equations

7.2 Newton’s method

7.3 Solution of algebraic equations

7.4 Aitken’s acceleration

References

8 Systems of nonlinear equations

8.1 The generalized fixed point method

8.2 The method of steepest descent

8.3 The generalization of Newton’s method

8.4 Quasi-Newton method

8.5 Nonlinear static analysis application

References

9 Iterative solution of linear systems

9.1 Iterative solution of linear systems

9.2 Splitting methods

9.3 Ritz-Galerkin method

9.4 Conjugate gradient method

9.5 Preconditioning techniques

9.6 Biconjugate gradient method

9.7 Least squares systems

9.8 The minimum residual approach

9.9 Algebraic multigrid method

9.10 Linear static analysis application

References

10 Approximate solution of eigenvalue problems

10.1 Classical iterations

10.2 The Rayleigh-Ritz procedure

10.3 The Lanczos method

10.4 The solution of the tridiagonal eigenvalue problem

10.5 The biorthogonal Lanczos method

10.6 The Arnoldi method

10.7 The block Lanczos method

10.7.1 Preconditioned block Lanczos method

10.8 Normal modes analysis application

References

11 Initial value problems

11.1 Solution of initial value problems

11.2 Single-step methods

11.3 Multistep methods

11.4 Initial value problems of systems of ordinary differential equations

11.5 Initial value problems of higher order ordinary differential equations

11.6 Linearization of second order initial value problems

11.7 Transient response analysis application

References

12 Boundary value problems

12.1 Boundary value problems of ordinary differential equations

12.2 The finite difference method for boundary value problems of

ordinary differential equations

12.3 Boundary value problems of partial differential equations

12.4 The finite difference method for boundary value problems of

partial differential equations

12.5 The finite element method

12.6 Finite element analysis of three-dimensional continuum

12.7 Fluid-structure interaction application

References

13 Integral equations

13.1 Converting initial value problems to integral equations

13.2 Converting boundary value problems to integral equations

13.3 Classification of integral equations

13.4 Fredholm solution

13.5 Neumann approximation

13.6 Nystrom method

13.7 Nonlinear integral equations

13.8 Integro-differential equations

13.8.1 Computational example

13.9 Boundary integral method application

References

14 Mathematical optimization

14.1 Existence of solution

14.2 Penalty method

14.3 Quadratic optimization

14.4 Gradient based methods

14.5 Global optimization

14.6 Topology optimization

14.7 Structural compliance application

References

List of figures

List of tables

Annotation

Index

Closing remarks

Über Autor(innen)

Dr. Komzsik is a graduate of the Technical University and the Eötvös University of Sciences, both in Budapest, Hungary. He worked for the Hungarian Shipyards in Budapest during the 1970s as an engineering analyst. After immigrating to the U.S., he worked for the McDonnell-Douglas Corporation between 1981-1982 as a senior analyst. Following that, he spent two decades as Chief Numerical Analyst at the MacNeal-Schwendler (now MSC Software) Corporation. After another decade and a half, he recently retired as Principal Key Expert from Siemens PLM Software.

He is the author of the original NASTRAN Numerical Methods Handbook, and a widely read book on The Lanczos Method that was also published in Chinese, Japanese, and Hungarian. His books titled "Computational Techniques of Finite Element Analysis" and "Applied Calculus of Variations for Engineers and Approximation Techniques for Engineers" are already in their second editions. He is also the co-author of the book, "Rotor Dynamics with Finite Elements."