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Curves and surfaces for computer aided geometric design
Engineering Analysis with Boundary Elements 9 (1992) 277-280
Book reviews upwind schemes: Chapter 20 dealing with flux vector splitting and Godunov-type algorithms, and Chapter 21 which includes second-order and high-resolution schemes such as MUSCL and TVD. Finally, Part VII introduces the discretization methods for the Navier-Stokes equations in two chapters which deal with the basic mathematical formulation of Reynoldsaveraged Navier-Stokes equations with an introduction to turbulence models, and approaches for compressible and incompressible viscous conservation laws. This is an excellent book whose readership includes graduate students as well as scientists and engineers already engaged, or starting to be engaged, in computational fluid dynamics.
Numerical Computation of Internal and External Flows. Volume 2: Computational Methods for lnviscid and Viscous Flows. C. Hirsch, Wiley, Chichester, 1990. £65.00. ISBN: 0471923516 (hardcover) ISBN: 0471924520 (paperback) This is the second of two volumes which together form a treatise on the theory and practice of the numerical computation of internal and external flows. It contains a presentation of computational methods for inviscid and viscous flow models as they have evolved over the last decade. The book is divided into three parts. The first, Part V, deals with the simplest inviscid approximation which is, in certain flow regimes, equivalent to the full system of Euler equations, namely the full potential model. It contains three chapters, 13 to 15. Chapter 13 describes the various mathematical formulations of the potential model, through differential as well as integral, weak, formulations; Chapter 14 deals with the rather simple and by now classical computation of subsonic potential flows, and covers finite difference, finite volume and finite element techniques; Chapter 15 discusses the much more complex problem of transonic potential flow in which the potential equation changes from elliptic to hyperbolic type, indicating that the flow changes from a diffusive character to a propagation-dominated behaviour. It also introduces the concepts of artificial viscosity and upwinding which form the basis of several numerical schemes to be discussed in following chapters. Part VI is devoted to a detailed presentation of the Euler equations and of the basic numerical techniques developed in order to discretize the complex system of inviscid, compressible conservation laws. It covers five chapters: the initial, Chapter 16, presents the mathematical formulation of the system of Euler equations in conservative, quasi-linear, and characteristic forms; this is followed by two chapters on numerical schemes, namely the Lax-Wendroff family of space-centered schemes and central schemes with independent time integration. The treatment of boundary conditions is the subject of Chapter 19, which presents a detailed discussion of the one-dimensional boundary treatment followed by the multi-dimensional aspects, far-field conditions, and the Kutta condition. This part closes with two chapters on
L.C. Wrobel Curves and Surfaces for Computer Aided Geometric Design. G. Farin, Academic Press, Inc. 1988.
Computer representation of curves, surfaces and solids have been used for designing and manufacturing in the automotive, shipbuilding and aerospace industries and in other practical applications. Gerald Farin's book explains the beginning of computer-compatible shape description since the work of B6zier at R6nault and de Casteljan at Citroen up to the new development on computer aided geometric design (CAGD). This book presents a unified treatment of the main ideas in curve and surface design, Its emphasis is on the concepts of B6zier and B-spline methods for the representation of piecewise polynomial curves. Many interesting and useful topics are included such as rational and nonrational B~zier and B-spline curves, geometric continuity, knot insertion, parametrization, polynomial interpolation, tensor product for surface representation and Coon patches. There are two chapters on differential geometry by W. Bochm and one chapter on computer geometric representation systems by P. B~zier. At the end; there is a chapter on evaluation and comparison of different methods and a glossary for quick reference for any newcomers in the area. Overall the book is very well printed, with many carefully drawn diagrams and many bibliographic references. It is suitable as a textbook for final year course at graduate level and post-graduate courses, and it is very
Engineering Analysis with Boundary Elements (9) (1992)-© 1992 Elsevier Science Publishers Ltd. 277
278
Book reviews
useful as a practical guide for the CAD/CAM/CAE/ CAGD developers and for engineers or researchers who work with geometric modelling and computer graphics. J.J.S.P. Cabral
The Numerical Solution of Emptic Equations. Garrett Birkhoff, Regional Conference Series in Applied Mathematics 1, S.I.A.M. 1972. pp. 82. $10.00.
This regional conference series in applied mathematics contains lecture notes on solving elliptic boundary-value and eigenvalue problems with the aid of a computer. The text contains a compilation of classical techniques incorporated in the solution of such problems. The list of references given at the end of each lecture are invaluable. This series covers 9 lectures entitled, Typical Elliptic Problems, Classical Analysis, Difference Approximations, Relaxation Methods, Semi-Iterative Methods, Integral Equation Methods, Approximation of Smooth Functions, Variational Methods and Applications to Boundary Value Problems. R. Bains
Scattering Theory for Hyperi~lie Operators. V. Petkov, Elsevier Science Publishers, 1989. pp. 374, hardcover. US $92.75/Dfl 190.00. ISBN: 0 444 8056 9 Written for graduate students and researchers in mathematics and mathematical physics, this text presents an approach to the scattering theory for dissipative and time dependent systems which has been intensively studied during the last fifteen years. This approach, which can be applied simultaneously to spaces of even and of odd dimension, is based on ideas connected with the RAGE type theorem, with Enss' decomposition of the phase space and with a time-dependent proof of the existence of the operator, which exploits the decay of the local energy of the perturbed and free systems. The book also examines some inverse scattering problems for time-dependent potentials, as well as the scattering of the wave equation in the exterior of a moving obstacles with arbitrary geometry. Contents: • Contraction semigroups and power bounded operators; • The Cauchy problem for the wave equation; • Scattering theory for symmetric systems with dissipative boundary conditions; • Disappearing solutions for symmetric systems; • Wave equation with time-dependent potential; • Inverse scattering problem for time-dependent
potentials; • Leading singularity of the scattering kernel. This book is available from the Amsterdam address, or in the USA/Canada from Elsevier Science Publishing, Co Inc., P.O. Box 882, Madison Square Station, New York, USA. A. Charati
An Introduction to ~ for use in Computer Graphics & Geometric Modeling. Richard H. Bartels, John C. Beatty & Brian A. Barsky, Morgan Kaufmann Publishers, Inc., Los Altos, California, 1987.
The Killer Bs (Bartels, Beatty, Barsky) from Berkeley and Waterloo Universities have performed a good job in their Introduction to Splines, presenting some of the major concepts on splines applied to computer graphics. This book, written in an informal way, introduces terminology, notation and basic results in an intuitive fashion and is accessible to both specialists and nonspecialists who use piecewise curves and surfaces for geometric modelling. The main emphasis of the book is on B-splines and the Oslo algorithm. Many related topics are discussed, such as cubic B-splines, properties of B-splines, knot insertion, parametric spline curves and tensor product spline surfaces. The topics on Beta splines and geometric continuity are quite innovative and so are the last chapters about rendering evaluation and selected applications. The authors have used many figures, the explanations are very clear and, as a whole, one can enjoy the pleasures of reading a good book. The reviewer was particularly pleased to delve into the sections on multiple knots and non-uniform B-splines bases. This book can be considered as a standard reference in the field of computer graphics and geometric modelling and will serve theoretician and practitioner alike. It will also be useful for CAD/CAM/CAE/CAGD implementors and users. J.J.S.P. Cabral
Numerical Analysis - - A Comprehensive Introduction. H.R. Schwarz, John Wiley and Son Ltd., 1989. pp. 517. £15.95. ISBN: 0 471 92064 9
This book offers another alternative amongst the textbooks available on numerical analysis. The topics covered are well organized and explained as such. The beauty of the text is that it presents topics in a strongly algorithmic manner. These algorithms, because of their structure, can be easily translated into any programming
Book reviews upwind schemes: Chapter 20 dealing with flux vector splitting and Godunov-type algorithms, and Chapter 21 which includes second-order and high-resolution schemes such as MUSCL and TVD. Finally, Part VII introduces the discretization methods for the Navier-Stokes equations in two chapters which deal with the basic mathematical formulation of Reynoldsaveraged Navier-Stokes equations with an introduction to turbulence models, and approaches for compressible and incompressible viscous conservation laws. This is an excellent book whose readership includes graduate students as well as scientists and engineers already engaged, or starting to be engaged, in computational fluid dynamics.
Numerical Computation of Internal and External Flows. Volume 2: Computational Methods for lnviscid and Viscous Flows. C. Hirsch, Wiley, Chichester, 1990. £65.00. ISBN: 0471923516 (hardcover) ISBN: 0471924520 (paperback) This is the second of two volumes which together form a treatise on the theory and practice of the numerical computation of internal and external flows. It contains a presentation of computational methods for inviscid and viscous flow models as they have evolved over the last decade. The book is divided into three parts. The first, Part V, deals with the simplest inviscid approximation which is, in certain flow regimes, equivalent to the full system of Euler equations, namely the full potential model. It contains three chapters, 13 to 15. Chapter 13 describes the various mathematical formulations of the potential model, through differential as well as integral, weak, formulations; Chapter 14 deals with the rather simple and by now classical computation of subsonic potential flows, and covers finite difference, finite volume and finite element techniques; Chapter 15 discusses the much more complex problem of transonic potential flow in which the potential equation changes from elliptic to hyperbolic type, indicating that the flow changes from a diffusive character to a propagation-dominated behaviour. It also introduces the concepts of artificial viscosity and upwinding which form the basis of several numerical schemes to be discussed in following chapters. Part VI is devoted to a detailed presentation of the Euler equations and of the basic numerical techniques developed in order to discretize the complex system of inviscid, compressible conservation laws. It covers five chapters: the initial, Chapter 16, presents the mathematical formulation of the system of Euler equations in conservative, quasi-linear, and characteristic forms; this is followed by two chapters on numerical schemes, namely the Lax-Wendroff family of space-centered schemes and central schemes with independent time integration. The treatment of boundary conditions is the subject of Chapter 19, which presents a detailed discussion of the one-dimensional boundary treatment followed by the multi-dimensional aspects, far-field conditions, and the Kutta condition. This part closes with two chapters on
L.C. Wrobel Curves and Surfaces for Computer Aided Geometric Design. G. Farin, Academic Press, Inc. 1988.
Computer representation of curves, surfaces and solids have been used for designing and manufacturing in the automotive, shipbuilding and aerospace industries and in other practical applications. Gerald Farin's book explains the beginning of computer-compatible shape description since the work of B6zier at R6nault and de Casteljan at Citroen up to the new development on computer aided geometric design (CAGD). This book presents a unified treatment of the main ideas in curve and surface design, Its emphasis is on the concepts of B6zier and B-spline methods for the representation of piecewise polynomial curves. Many interesting and useful topics are included such as rational and nonrational B~zier and B-spline curves, geometric continuity, knot insertion, parametrization, polynomial interpolation, tensor product for surface representation and Coon patches. There are two chapters on differential geometry by W. Bochm and one chapter on computer geometric representation systems by P. B~zier. At the end; there is a chapter on evaluation and comparison of different methods and a glossary for quick reference for any newcomers in the area. Overall the book is very well printed, with many carefully drawn diagrams and many bibliographic references. It is suitable as a textbook for final year course at graduate level and post-graduate courses, and it is very
Engineering Analysis with Boundary Elements (9) (1992)-© 1992 Elsevier Science Publishers Ltd. 277
278
Book reviews
useful as a practical guide for the CAD/CAM/CAE/ CAGD developers and for engineers or researchers who work with geometric modelling and computer graphics. J.J.S.P. Cabral
The Numerical Solution of Emptic Equations. Garrett Birkhoff, Regional Conference Series in Applied Mathematics 1, S.I.A.M. 1972. pp. 82. $10.00.
This regional conference series in applied mathematics contains lecture notes on solving elliptic boundary-value and eigenvalue problems with the aid of a computer. The text contains a compilation of classical techniques incorporated in the solution of such problems. The list of references given at the end of each lecture are invaluable. This series covers 9 lectures entitled, Typical Elliptic Problems, Classical Analysis, Difference Approximations, Relaxation Methods, Semi-Iterative Methods, Integral Equation Methods, Approximation of Smooth Functions, Variational Methods and Applications to Boundary Value Problems. R. Bains
Scattering Theory for Hyperi~lie Operators. V. Petkov, Elsevier Science Publishers, 1989. pp. 374, hardcover. US $92.75/Dfl 190.00. ISBN: 0 444 8056 9 Written for graduate students and researchers in mathematics and mathematical physics, this text presents an approach to the scattering theory for dissipative and time dependent systems which has been intensively studied during the last fifteen years. This approach, which can be applied simultaneously to spaces of even and of odd dimension, is based on ideas connected with the RAGE type theorem, with Enss' decomposition of the phase space and with a time-dependent proof of the existence of the operator, which exploits the decay of the local energy of the perturbed and free systems. The book also examines some inverse scattering problems for time-dependent potentials, as well as the scattering of the wave equation in the exterior of a moving obstacles with arbitrary geometry. Contents: • Contraction semigroups and power bounded operators; • The Cauchy problem for the wave equation; • Scattering theory for symmetric systems with dissipative boundary conditions; • Disappearing solutions for symmetric systems; • Wave equation with time-dependent potential; • Inverse scattering problem for time-dependent
potentials; • Leading singularity of the scattering kernel. This book is available from the Amsterdam address, or in the USA/Canada from Elsevier Science Publishing, Co Inc., P.O. Box 882, Madison Square Station, New York, USA. A. Charati
An Introduction to ~ for use in Computer Graphics & Geometric Modeling. Richard H. Bartels, John C. Beatty & Brian A. Barsky, Morgan Kaufmann Publishers, Inc., Los Altos, California, 1987.
The Killer Bs (Bartels, Beatty, Barsky) from Berkeley and Waterloo Universities have performed a good job in their Introduction to Splines, presenting some of the major concepts on splines applied to computer graphics. This book, written in an informal way, introduces terminology, notation and basic results in an intuitive fashion and is accessible to both specialists and nonspecialists who use piecewise curves and surfaces for geometric modelling. The main emphasis of the book is on B-splines and the Oslo algorithm. Many related topics are discussed, such as cubic B-splines, properties of B-splines, knot insertion, parametric spline curves and tensor product spline surfaces. The topics on Beta splines and geometric continuity are quite innovative and so are the last chapters about rendering evaluation and selected applications. The authors have used many figures, the explanations are very clear and, as a whole, one can enjoy the pleasures of reading a good book. The reviewer was particularly pleased to delve into the sections on multiple knots and non-uniform B-splines bases. This book can be considered as a standard reference in the field of computer graphics and geometric modelling and will serve theoretician and practitioner alike. It will also be useful for CAD/CAM/CAE/CAGD implementors and users. J.J.S.P. Cabral
Numerical Analysis - - A Comprehensive Introduction. H.R. Schwarz, John Wiley and Son Ltd., 1989. pp. 517. £15.95. ISBN: 0 471 92064 9
This book offers another alternative amongst the textbooks available on numerical analysis. The topics covered are well organized and explained as such. The beauty of the text is that it presents topics in a strongly algorithmic manner. These algorithms, because of their structure, can be easily translated into any programming