M
1.

Scaling of Differential Equations
(2016)
Berlin, Heidelberg, New York, London
:
SpringerOpen
Notes:
The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models.
Scaling (or nondimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics.
The text is easily accessible and exampledriven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically.
This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations.
Pages:
XIII, 138 S., 22 schwarzweiß Abbildungen
ISBN:
9783319327259

M
2.

Programming for Computations  MATLAB/Octave : A Gentle Introduction to Numerical Simulations with MATLAB/Octave
(2016)
Heidelberg, Dordrecht, London, New York
:
SpringerOpen
Keywords:
MATLAB ; Computational Science and Engineering ; Numerical Analysis
Notes:
This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.
Pages:
XVI, 216 S., 43 schwarzweiß Abbildungen
ISBN:
9783319324517

M
3.

Programming for Computations  Python : A Gentle Introduction to Numerical Simulations with Python
(2016)
Heidelberg, Dordrecht, London, New York
:
SpringerOpen
Keywords:
Python ; Computational Science and Engineering ; Numerical Analysis
Notes:
This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students.
The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.
Pages:
XVI, 232 S., 45 schwarzweiß Abbildungen
ISBN:
9783319324272

M
4.

Python scripting for computational science
(2008)
Berlin [u.a.] : Springer
Texts in computational science and engineering
Call number:
PIK M 032080172
In:
[Texts in computational science and engineering]
Series Statement:
[Texts in computational science and engineering 3]
Description / Table of Contents:
Contents: 1 Introduction. 2 Getting Started with Python Scripting. 3 BasicPython. 4 Numerical Computing in Python. 5 Combining Python with Fortran, C, and C++. 6 Introduction to GUI Programming. 7 Web Interfaces and CGI Programming. 8 Advanced Python. 9 Fortran Programming with NumPy Arrays. 10 C and C++ Programming with NumPy Arrays. 11 More Advanced GUI Programming. 12 Tools and Examples. A Setting up the Required Software Environment. B Elements of Software Engineering.
Type of Medium:
Monograph available for loan
Pages:
xxiv, 750 S. : Ill., graph. Darst.
Edition:
3. ed.
ISBN:
9783540739159
Branch Library:
PIK Library
Item Status:

M
5.

A primer on scientific programming with Python
(2012)
Berlin [u.a.] : Springer
Texts in computational science and engineering
Call number:
18/M 13.0018
In:
[Texts in computational science and engineering]
Series Statement:
[Texts in computational science and engineering 6]
Type of Medium:
Monograph available for loan
Pages:
XXXII, 792 S. : graph. Darst.
Edition:
3rd ed.
ISBN:
9783642302923
Classification:
Informatics
Location:
Reading room
Branch Library:
GFZ Library
Item Status:

M
6.

A primer on scientific programming with Python
(2009)
Berlin [u.a.] : Springer
Texts in computational science and engineering
Call number:
PIK M 032100183
In:
[Texts in computational science and engineering]
Series Statement:
[Texts in computational science and engineering 6]
Description / Table of Contents:
Contents: Computing with Formulas ; Basic Constructions ; Input Data and Error Handling ; Array Computing and Curve Plotting ; Sequences and Difference Equations ; Files, Strings, and Dictionaries ; Introduction to Classes ; Random Numbers and Simple Games ; ObjectOriented Programming
Type of Medium:
Monograph available for loan
Pages:
XXVII, 693 S. : graph. Darst.
ISBN:
9783642024740
Branch Library:
PIK Library
Item Status:

M
7.

Paper (German National Licenses)
Instability of BuckleyLeverett flow in a heterogeneous medium
(1992)
Springer
ISSN:
15731634
Keywords
oil recovery ; instability ; heterogeneous medium ; shock waves
Source:
Springer Online Journal Archives 18602000
Topics:
Geosciences
,
Technology
Notes:
Abstract We study the simultaneous onedimensional flow of water and oil in a heterogeneous medium modelled by the BuckleyLeverett equation. It is shown both by analytical solutions and by numerical experiments that this hyperbolic model is unstable in the following sense: Perturbations in physical parameters in a tiny region of the reservoir may lead to a totally different picture of the flow. This means that simulation results obtained by solving the hyperbolic BuckleyLeverett equation may be unreliable.
Type of Medium:
Electronic Resource

M
8.

Paper (German National Licenses)
Conjugate gradient methods and ILU preconditioning of nonsymmetric matrix systems with arbitrary sparsity patterns
(1989)
Chichester
:
WileyBlackwell
ISSN:
02712091
Keywords
Preconditioning ; Conjugate gradients ; Nonsymmetric matrices ; Finite elements ; Convective transport ; Engineering ; Engineering General
Source:
Wiley InterScience Backfile Collection 18322000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
Preconditioning techniques based on incomplete Gaussian elimination for large, sparse, nonsymmetric matrix systems are described. A certain level of fillin may be specified in the incomplete factorizations. All methods considered may be applied to matrices with arbitrary sparsity patterns, for instance those associated with the general preprocessor algorithms or adaptive mesh techniques. The preconditioners have been combined with five conjugate gradientlike methods and tested on finite element discretized scalar convectiondiffusion equations in 2D and 3D. It is found from numerical experiments that an amount of fillin corresponding to about 50% of the number of original nonzero matrix entries is the optimal choice for this class of preconditioners. The preconditioners show almost no sensitivity to grid distortion. In problems with significantly variable coefficients or anisotropy the preconditioners stabilize the basic iterative schemes in addition to reducing the computational work substantially, mostly by more than 90%. The modified preconditioning technique, where fillin is added on the main diagonal, performs in general better than the standard incomplete LU factorization, but is inferior to the latter in 3D problems and for matrix systems with complicated sparsity patterns.
Additional Material:
16 Ill.
Type of Medium:
Electronic Resource

M
9.

Paper (German National Licenses)
A numerical comparison of conjugate gradientlike methods
(1988)
New York, NY [u.a.]
:
WileyBlackwell
ISSN:
07488025
Keywords
Engineering ; Engineering General
Source:
Wiley InterScience Backfile Collection 18322000
Topics:
Mathematics
,
Technology
Notes:
Three secondorder, nonselfadjoint partial differential equations in two dimensions are discretized by the finite element method, leading to nonsymmetric systems of linear equations. The systems are solved by several conjugate gradientlike methods, and compared for their computational cost. All methods are tested with and without preconditioning.
Additional Material:
1 Ill.
Type of Medium:
Electronic Resource

M
10.

Paper (German National Licenses)
Implicit finite element methods for twophase flow in oil reservoirs
(1990)
Chichester
:
WileyBlackwell
ISSN:
02712091
Keywords
Porous media ; Twophase flow ; Oil recovery ; Finite elements ; Preconditioning ; Conjugate gradients ; Engineering ; Engineering General
Source:
Wiley InterScience Backfile Collection 18322000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
The equations governing immiscible, incompressible, twophase, porous media flow are discretized by generalized streamline diffusion PetrovGalerkin methods in space and by implicit differences in time. Systems of nonlinear algebraic equations are solved by NewtonRaphson iteration employing ILUpreconditioned conjugategradientlike methods to the nonsymmetric matrix system in each iteration. The resulting solution methods are robust, enable complex grids with irregular nodal orderings and allow capillary effects.Several numerical formulations are tested and compared for one, two and threedimensional flow cases, with emphasis on problems involving saturation shocks, heterogeneous media and curved boundaries. For reservoirs consisting of multiple rock types with differing capillary pressure properties, it is shown that traditional BubnovGalerkin methods give poor results and the new PetrovGalerkin formulations are required. Investigations regarding the behaviour of several preconditioned conjugategradientlike methods in these type of problems are also reported.
Additional Material:
14 Ill.
Type of Medium:
Electronic Resource
