Gunzburger, Max D.
Overview
Works:  30 works in 116 publications in 2 languages and 2,089 library holdings 

Roles:  Author, Editor, Other 
Classifications:  TA357, 532.052 
Publication Timeline
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Most widely held works by
Max D Gunzburger
Incompressible computational fluid dynamics : trends and advances by
Max D Gunzburger(
Book
)
19 editions published between 1992 and 2011 in English and held by 315 WorldCat member libraries worldwide
19 editions published between 1992 and 2011 in English and held by 315 WorldCat member libraries worldwide
Finite element methods for viscous incompressible flows : a guide to theory, practice, and algorithms by
Max D Gunzburger(
Book
)
13 editions published in 1989 in English and German and held by 304 WorldCat member libraries worldwide
In this book, the author examines mathematical aspects of finite element methods for the approximate solution of incompressible flow problems. The principal goal is to present some of the important mathematical results that are relevant to practical computations. In so doing, useful algorithms are also discussed. Although rigorous results are stated, no detailed proofs are supplied; rather, the intention is to present these results so that they can serve as a guide for the selection and, in certain respects, the implementation of algorithms
13 editions published in 1989 in English and German and held by 304 WorldCat member libraries worldwide
In this book, the author examines mathematical aspects of finite element methods for the approximate solution of incompressible flow problems. The principal goal is to present some of the important mathematical results that are relevant to practical computations. In so doing, useful algorithms are also discussed. Although rigorous results are stated, no detailed proofs are supplied; rather, the intention is to present these results so that they can serve as a guide for the selection and, in certain respects, the implementation of algorithms
Leastsquares finite element methods by
Pavel B Bochev(
Book
)
22 editions published between 2009 and 2011 in English and held by 232 WorldCat member libraries worldwide
Finite element methods have become one of the most versatile methodologies for the approximate numerical solution of PDEs. Suitable for both the researcher and the practitioner, this is a concise guide to the theory and practice of leastsquare finite element methods, their strengths and weaknesses, and open problems
22 editions published between 2009 and 2011 in English and held by 232 WorldCat member libraries worldwide
Finite element methods have become one of the most versatile methodologies for the approximate numerical solution of PDEs. Suitable for both the researcher and the practitioner, this is a concise guide to the theory and practice of leastsquare finite element methods, their strengths and weaknesses, and open problems
Flow control by
Max D Gunzburger(
Book
)
11 editions published in 1995 in English and German and held by 156 WorldCat member libraries worldwide
The articles in this volume cover recent work in the area of flow control from the point of view of both engineers and mathematicians. These writings are especially timely, as they coincide with the emergence of the role of mathematics and systematic engineering analysis in flow control and optimization. Recently this role has significantly expanded to the point where now sophisticated mathematical and computational tools are being increasingly applied to the control and optimization of fluid flows. These articles document some important work that has gone on to influence the practical, everyday design of flows; moreover, they represent the state of the art in the formulation, analysis, and computation of flow control problems. This volume will be of interest to both applied mathematicians and to engineers
11 editions published in 1995 in English and German and held by 156 WorldCat member libraries worldwide
The articles in this volume cover recent work in the area of flow control from the point of view of both engineers and mathematicians. These writings are especially timely, as they coincide with the emergence of the role of mathematics and systematic engineering analysis in flow control and optimization. Recently this role has significantly expanded to the point where now sophisticated mathematical and computational tools are being increasingly applied to the control and optimization of fluid flows. These articles document some important work that has gone on to influence the practical, everyday design of flows; moreover, they represent the state of the art in the formulation, analysis, and computation of flow control problems. This volume will be of interest to both applied mathematicians and to engineers
Perspectives in flow control and optimization by
Max D Gunzburger(
Book
)
13 editions published between 2002 and 2003 in English and held by 131 WorldCat member libraries worldwide
Flow control and optimization has been an important part of experimental flow science throughout the last century. As research in computational fluid dynamics (CFD) matured, CFD codes were routinely used for the simulation of fluid flows. Subsequently, mathematicians and engineers began examining the use of CFD algorithms and codes for optimization and control problems for fluid flows. Perspectives in Flow Control and Optimization presents flow control and optimization as a subdiscipline of computational mathematics and computational engineering. It introduces the development and analysis of several approaches for solving flow control and optimization problems through the use of modern CFD and optimization methods. The author discusses many of the issues that arise in the practical implementation of algorithms for flow control and optimization, and provides the reader with a clear idea of what types of flow control and optimization problems can be solved, how to develop effective algorithms for solving such problems, and potential problems in implementing the algorithms. Audience: this book is written for both those new to the field of control and optimization as well as experienced practitioners, including engineers, applied mathematicians, and scientists interested in computational methods for flow control and optimization. Readers with a solid background in calculus and only slight familiarity with partial differential equations should find the book easy to understand. Knowledge of fluid mechanics, computational fluid dynamics, calculus of variations, control theory or optimization is beneficial, but is not essential, to comprehend the bulk of the presentation. Only Chapter 6 requires a substantially higher level of mathematical knowledge, most notably in the areas of functional analysis, numerical analysis, and partial differential equations
13 editions published between 2002 and 2003 in English and held by 131 WorldCat member libraries worldwide
Flow control and optimization has been an important part of experimental flow science throughout the last century. As research in computational fluid dynamics (CFD) matured, CFD codes were routinely used for the simulation of fluid flows. Subsequently, mathematicians and engineers began examining the use of CFD algorithms and codes for optimization and control problems for fluid flows. Perspectives in Flow Control and Optimization presents flow control and optimization as a subdiscipline of computational mathematics and computational engineering. It introduces the development and analysis of several approaches for solving flow control and optimization problems through the use of modern CFD and optimization methods. The author discusses many of the issues that arise in the practical implementation of algorithms for flow control and optimization, and provides the reader with a clear idea of what types of flow control and optimization problems can be solved, how to develop effective algorithms for solving such problems, and potential problems in implementing the algorithms. Audience: this book is written for both those new to the field of control and optimization as well as experienced practitioners, including engineers, applied mathematicians, and scientists interested in computational methods for flow control and optimization. Readers with a solid background in calculus and only slight familiarity with partial differential equations should find the book easy to understand. Knowledge of fluid mechanics, computational fluid dynamics, calculus of variations, control theory or optimization is beneficial, but is not essential, to comprehend the bulk of the presentation. Only Chapter 6 requires a substantially higher level of mathematical knowledge, most notably in the areas of functional analysis, numerical analysis, and partial differential equations
Accuracy of leastsquares method for the NavierStokes equations by
Pavel B Bochev(
Book
)
3 editions published in 1993 in English and held by 91 WorldCat member libraries worldwide
3 editions published in 1993 in English and held by 91 WorldCat member libraries worldwide
Analysis, approximation, and computation of a coupled solid/fluid temperature control problem by
Max D Gunzburger(
Book
)
3 editions published in 1993 in English and held by 84 WorldCat member libraries worldwide
3 editions published in 1993 in English and held by 84 WorldCat member libraries worldwide
On substructuring algorithms and solution techniques for the numerical approximation of partial differential equations by
Max D Gunzburger(
Book
)
2 editions published in 1986 in English and held by 73 WorldCat member libraries worldwide
2 editions published in 1986 in English and held by 73 WorldCat member libraries worldwide
An adaptive wavelet viscosity method for hyperbolic conservation laws by
Daniel Castaño Díez(
Book
)
2 editions published in 2007 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 2007 in English and held by 5 WorldCat member libraries worldwide
Parallel Algorithms in the Finite Element Approximation of Flow Problems(
Book
)
2 editions published between 1988 and 1989 in English and held by 2 WorldCat member libraries worldwide
We discuss a portion of the research of the which has been carried out during the past years under AFOSR sponsorship. This includes work on finite element methods for a Ladyshenskaya model of viscous incompressible flow, hyperbolic partial differential equations, exterior problems, algebraic turbulence models, streamfunction vorticity formulations of ciscous flows and first order elliptic systems of partial differential equations, and on substructing methods for the approximate solution of partial differential equations. (MJM)
2 editions published between 1988 and 1989 in English and held by 2 WorldCat member libraries worldwide
We discuss a portion of the research of the which has been carried out during the past years under AFOSR sponsorship. This includes work on finite element methods for a Ladyshenskaya model of viscous incompressible flow, hyperbolic partial differential equations, exterior problems, algebraic turbulence models, streamfunction vorticity formulations of ciscous flows and first order elliptic systems of partial differential equations, and on substructing methods for the approximate solution of partial differential equations. (MJM)
Mixed Finite Element Methods with Applications to Flow with Other Problems(
Book
)
2 editions published between 1981 and 1983 in English and held by 2 WorldCat member libraries worldwide
Three problems were considered. These were finite element approximations due to the inhomogeneous NavierStokes equations, for potential flows, and for acoustic eigenvalue problems. In all cases both theoretical error estimates and computer codes implementing the best algorithm were developed. We also report on other activities sponsored by the grant, i.e. student research and conference talks
2 editions published between 1981 and 1983 in English and held by 2 WorldCat member libraries worldwide
Three problems were considered. These were finite element approximations due to the inhomogeneous NavierStokes equations, for potential flows, and for acoustic eigenvalue problems. In all cases both theoretical error estimates and computer codes implementing the best algorithm were developed. We also report on other activities sponsored by the grant, i.e. student research and conference talks
Selected papers presented at the Com2MaC Conference on Computational Mathematics by
Conference on Computational Mathematics(
Book
)
2 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
Finite dimensional approximation of a class of constrained nonlinear optimal control problems by
Max D Gunzburger(
Book
)
3 editions published in 1994 in English and held by 2 WorldCat member libraries worldwide
An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the GinzburgLandau equations of superconductivity, and the third, the NavierStokes equations for incompressible, viscous flows. Optimal control, Nonlinear partial differential equations, Finite dimensional approximation, Finite element methods, Von Karman equations, GinzburgLandau equations, NavierStokes equations
3 editions published in 1994 in English and held by 2 WorldCat member libraries worldwide
An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the GinzburgLandau equations of superconductivity, and the third, the NavierStokes equations for incompressible, viscous flows. Optimal control, Nonlinear partial differential equations, Finite dimensional approximation, Finite element methods, Von Karman equations, GinzburgLandau equations, NavierStokes equations
Existence of an optimal solution of a shape control problem for the stationary NavierStokes equations by
Max D Gunzburger(
Book
)
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
On mixed finite element methods for first order elliptic systems by
George J Fix(
Book
)
2 editions published in 1982 in English and held by 1 WorldCat member library worldwide
2 editions published in 1982 in English and held by 1 WorldCat member library worldwide
Analysis and approximation of optimal control problems with nonlinear constraints(
)
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
Fast Algorithms for the CMU Attached Processor System(
Book
)
1 edition published in 1986 in English and held by 1 WorldCat member library worldwide
This project concerned research on developing fast algorithms for implementation on a parallel processing system. Titles of research papers resulting from this effort include the following: Least squares methods for fourth order problems, Least squares methods for problems with corner singularities, Finite element methods for the streamfunctionvorticity equatious, and On substructuring algorithms, solution techniques for the numerical solution of partial differential equations, On central difference approximations to general second order elliptic equations, and A modified defect correction algorithm for the solution of singularly perturbed differential equations
1 edition published in 1986 in English and held by 1 WorldCat member library worldwide
This project concerned research on developing fast algorithms for implementation on a parallel processing system. Titles of research papers resulting from this effort include the following: Least squares methods for fourth order problems, Least squares methods for problems with corner singularities, Finite element methods for the streamfunctionvorticity equatious, and On substructuring algorithms, solution techniques for the numerical solution of partial differential equations, On central difference approximations to general second order elliptic equations, and A modified defect correction algorithm for the solution of singularly perturbed differential equations
On numerical methods for acoustic problems by
George J Fix(
Book
)
2 editions published between 1978 and 1982 in English and held by 1 WorldCat member library worldwide
2 editions published between 1978 and 1982 in English and held by 1 WorldCat member library worldwide
Sensitivity analysis of a shape control problem for the stationary NavierStokes equations by
Max D Gunzburger(
Book
)
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
Computational Methods for Flow Problems  Parallel Algorithms, Flow Control, and Novel Approaches(
)
1 edition published in 1992 in English and held by 0 WorldCat member libraries worldwide
A review of the research that has been carried out under the sponsorship of Air Force Office of Scientific Research grant number AFOSR900179 is given. Details are given about two research programs, namely flow control and superconductivity. In both instances we have modeled realistic physical problems, we have performed rigorous analysis on the mathematical models, we have developed approximation schemes which we have also analyzed, and we have written computer codes implementing our computational method. In both instances, were the first to carry out such a comprehensive research program, and in so doing, have developed robust and useful algorithms that also embarked on a joint research program with personnel at AEDC facility in Tullahoma, Tennessee. We also briefly discuss other accomplishments related to this grant, including other research project invited talks, journal articles, etc
1 edition published in 1992 in English and held by 0 WorldCat member libraries worldwide
A review of the research that has been carried out under the sponsorship of Air Force Office of Scientific Research grant number AFOSR900179 is given. Details are given about two research programs, namely flow control and superconductivity. In both instances we have modeled realistic physical problems, we have performed rigorous analysis on the mathematical models, we have developed approximation schemes which we have also analyzed, and we have written computer codes implementing our computational method. In both instances, were the first to carry out such a comprehensive research program, and in so doing, have developed robust and useful algorithms that also embarked on a joint research program with personnel at AEDC facility in Tullahoma, Tennessee. We also briefly discuss other accomplishments related to this grant, including other research project invited talks, journal articles, etc
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Related Identities
 Bochev, Pavel B. Author
 Nicolaides, Roy A. Other Editor
 United States National Aeronautics and Space Administration
 Lee, Hyung C.
 Cambridge University Press
 Friedman, Avner Author
 Miller, Willard
 Castaño Díez, Daniel Author
 Lewis Research Center Institute for Computational Mechanics in Propulsion
 Kunoth, Angela
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Associated Subjects
Algebra Computer scienceMathematics Differential equations, Partial Estimation theory Finite element method Fluid dynamicsMathematical models Fluid dynamicsMathematics Fluid dynamicsTechnique Global analysis (Mathematics) Hydraulic engineering Iterative methods (Mathematics) Least squares Linear systems Mathematical optimization Mathematics Matrices NavierStokes equations Nonlinear boundary value problems Numerical analysis Numerical calculations System theory Viscous flow