Oliger, Joseph 1941
Overview
Works:  46 works in 118 publications in 2 languages and 1,579 library holdings 

Roles:  Author, Editor 
Classifications:  QA374, 519.4 
Publication Timeline
.
Most widely held works by
Joseph Oliger
Timedependent problems and difference methods
by
Bertil Gustafsson(
)
16 editions published between 1995 and 2013 in English and held by 710 WorldCat member libraries worldwide
For physical scientists, engineers, or anyone who uses numerical experiments to test designs or to predict and investigate physical phenomena, this invaluable guide is destined to become a constant companion. Time Dependent Problems and Difference Methods is also extremely useful to numerical analysts, mathematical modelers, and graduate students of applied mathematics and scientific computations
16 editions published between 1995 and 2013 in English and held by 710 WorldCat member libraries worldwide
For physical scientists, engineers, or anyone who uses numerical experiments to test designs or to predict and investigate physical phenomena, this invaluable guide is destined to become a constant companion. Time Dependent Problems and Difference Methods is also extremely useful to numerical analysts, mathematical modelers, and graduate students of applied mathematics and scientific computations
Numerical analysis
by
Jacques Baranger(
Book
)
15 editions published between 1978 and 1985 in English and held by 410 WorldCat member libraries worldwide
15 editions published between 1978 and 1985 in English and held by 410 WorldCat member libraries worldwide
Methods for the approximate solution of time dependent problems
by
H Kreiss(
Book
)
10 editions published between 1973 and 1985 in English and Chinese and held by 77 WorldCat member libraries worldwide
10 editions published between 1973 and 1985 in English and Chinese and held by 77 WorldCat member libraries worldwide
Energy and maximum norm estimates for nonlinear conservation laws
by
Pelle Olsson(
Book
)
3 editions published in 1994 in English and held by 76 WorldCat member libraries worldwide
Abstract: "We have devised a technique that makes it possible to obtain energy estimates for initialboundary value problems for nonlinear conservation laws. The two major tools to achieve the energy estimates are a certain splitting of the flux vector derivative f(u)[subscript x], and a structural hypothesis, referred to as a cone condition, on the flux vector f(u). These hypotheses are fulfilled for many equations that occur in practice, such as the Euler equations of gas dynamics. It should be noted that the energy estimates are obtained without any assumptions on the gradient of the solution u. The results extend to weak solutions that are obtained as pointwise limits of vanishing viscosity solutions. As a byproduct we obtain explicit expressions for the entropy function and the entropy flux of symmetrizable systems of conservation laws. Under certain circumstances the proposed technique can be applied repeatedly so as to yield estimates in the maximum norm."
3 editions published in 1994 in English and held by 76 WorldCat member libraries worldwide
Abstract: "We have devised a technique that makes it possible to obtain energy estimates for initialboundary value problems for nonlinear conservation laws. The two major tools to achieve the energy estimates are a certain splitting of the flux vector derivative f(u)[subscript x], and a structural hypothesis, referred to as a cone condition, on the flux vector f(u). These hypotheses are fulfilled for many equations that occur in practice, such as the Euler equations of gas dynamics. It should be noted that the energy estimates are obtained without any assumptions on the gradient of the solution u. The results extend to weak solutions that are obtained as pointwise limits of vanishing viscosity solutions. As a byproduct we obtain explicit expressions for the entropy function and the entropy flux of symmetrizable systems of conservation laws. Under certain circumstances the proposed technique can be applied repeatedly so as to yield estimates in the maximum norm."
RIACS final report January 1, 1996 through September 30, 1996
by
Joseph Oliger(
Book
)
1 edition published in 1996 in English and held by 74 WorldCat member libraries worldwide
1 edition published in 1996 in English and held by 74 WorldCat member libraries worldwide
Stability and error estimation for component adaptive grid methods
by
Joseph Oliger(
Book
)
2 editions published in 1994 in English and held by 72 WorldCat member libraries worldwide
Abstract: "Component adaptive grid (CAG) methods for solving hyperbolic partial differential equations (PDE's) are discussed in this paper. Applying recent stability results for a class of numerical methods on uniform grids, the convergence of these methods for linear problems on component adaptive grids is established here. Furthermore, the computational error can be estimated on CAG's using the stability results. Using these estimates, the error can be controlled on CAG's. Thus, the solution can be computed efficiently on CAG's within a given error tolerance. Computational results for time dependent linear problems in one and two space dimensions are presented."
2 editions published in 1994 in English and held by 72 WorldCat member libraries worldwide
Abstract: "Component adaptive grid (CAG) methods for solving hyperbolic partial differential equations (PDE's) are discussed in this paper. Applying recent stability results for a class of numerical methods on uniform grids, the convergence of these methods for linear problems on component adaptive grids is established here. Furthermore, the computational error can be estimated on CAG's using the stability results. Using these estimates, the error can be controlled on CAG's. Thus, the solution can be computed efficiently on CAG's within a given error tolerance. Computational results for time dependent linear problems in one and two space dimensions are presented."
USRA/RIACS final report on cooperative agreement NCC2387, July 1, 1992  December 31, 1992
by
Joseph Oliger(
Book
)
1 edition published in 1992 in English and held by 71 WorldCat member libraries worldwide
1 edition published in 1992 in English and held by 71 WorldCat member libraries worldwide
On difference methods for hyperbolic differential equations
by
Joseph Oliger(
Book
)
4 editions published in 1973 in English and Undetermined and held by 12 WorldCat member libraries worldwide
4 editions published in 1973 in English and Undetermined and held by 12 WorldCat member libraries worldwide
RIACS final report October 1, 1996 through September 30, 1997
by
Joseph Oliger(
Book
)
3 editions published in 1997 in English and held by 12 WorldCat member libraries worldwide
3 editions published in 1997 in English and held by 12 WorldCat member libraries worldwide
Theoretical and practical aspects of some initialboundary value problems in fluid dynamics
by
Joseph Oliger(
Book
)
8 editions published in 1976 in English and Undetermined and held by 8 WorldCat member libraries worldwide
Initialboundary value problems for several systems of partial differential equations from fluid dynamics are discussed. Both rigid wall and open boundary problems are treated. Boundary conditions are formulated and shown to yield wellposed problems for the Eulerian equations for gas dynamics, the shallowwater equations, and linearized constant coefficient versions of the incompressible, anelastic equations. The primitive hydrostatic meteorological equations are shown to be illposed with any specification of local, pointwise boundary conditions. Analysis of simplified versions of this system illustrates the mechanism responsible for illposedness. (Author)
8 editions published in 1976 in English and Undetermined and held by 8 WorldCat member libraries worldwide
Initialboundary value problems for several systems of partial differential equations from fluid dynamics are discussed. Both rigid wall and open boundary problems are treated. Boundary conditions are formulated and shown to yield wellposed problems for the Eulerian equations for gas dynamics, the shallowwater equations, and linearized constant coefficient versions of the incompressible, anelastic equations. The primitive hydrostatic meteorological equations are shown to be illposed with any specification of local, pointwise boundary conditions. Analysis of simplified versions of this system illustrates the mechanism responsible for illposedness. (Author)
Stability of the Fourier method
by
H Kreiss(
Book
)
6 editions published in 1977 in English and Undetermined and held by 7 WorldCat member libraries worldwide
This paper develops a stability theory for the Fourier (or pseudospectral) method for linear hyperbolic and parabolic partial differential equations with variable coefficients
6 editions published in 1977 in English and Undetermined and held by 7 WorldCat member libraries worldwide
This paper develops a stability theory for the Fourier (or pseudospectral) method for linear hyperbolic and parabolic partial differential equations with variable coefficients
Control of the dissipativity of LaxWendroff type methods for first order systems of hyperbolic equations
by
Stanford University(
Book
)
5 editions published in 1977 in English and Undetermined and held by 6 WorldCat member libraries worldwide
5 editions published in 1977 in English and Undetermined and held by 6 WorldCat member libraries worldwide
Hybrid difference methods for the initial boundaryvalue problem for hyperbolic equations
by
Joseph Oliger(
Book
)
3 editions published in 1975 in English and Undetermined and held by 4 WorldCat member libraries worldwide
3 editions published in 1975 in English and Undetermined and held by 4 WorldCat member libraries worldwide
Adaptive Grid Refinement for Numerical Weather Prediction
by William C Skamarook(
Book
)
3 editions published in 1987 in English and held by 3 WorldCat member libraries worldwide
An adaptive atmospheric flow model is described and results of integrations with this model are presented. The adaptive technique employed is that of Berger and Oliger. The technique uses a finite difference method to integrate the dynamical equations first on a cargo grid and then on finer grids which have been placed based on a Richardson type estimate of the truncation error in the coarse grid solution. By correctly coupling the integrations on the various grids, periodically reestimating the error nad recreating the finer grids, uniformly accurate solutions are economically producted. The primitive hydrostatic equations of meteorology are solved for the advection of a barotropic cyclone and for the development of a baroclinic disturbance which results from the perturbation of an unstable jet. These integrations demonstrate the feasibility of using multiple, rotated, overlapping fine grids. Direct computations of the truncation error are used to confirm the accuracy of the Richardson type truncation error estimates
3 editions published in 1987 in English and held by 3 WorldCat member libraries worldwide
An adaptive atmospheric flow model is described and results of integrations with this model are presented. The adaptive technique employed is that of Berger and Oliger. The technique uses a finite difference method to integrate the dynamical equations first on a cargo grid and then on finer grids which have been placed based on a Richardson type estimate of the truncation error in the coarse grid solution. By correctly coupling the integrations on the various grids, periodically reestimating the error nad recreating the finer grids, uniformly accurate solutions are economically producted. The primitive hydrostatic equations of meteorology are solved for the advection of a barotropic cyclone and for the development of a baroclinic disturbance which results from the perturbation of an unstable jet. These integrations demonstrate the feasibility of using multiple, rotated, overlapping fine grids. Direct computations of the truncation error are used to confirm the accuracy of the Richardson type truncation error estimates
A System and Language Environment for Scientific Computing
by Stanford University(
Book
)
2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
We discuss the use of component adaptive methods for the solution of time dependent partial differential equations. After a brief discussion of the methods we identify several deficiencies of commonly used languages of scientific computing and introduce a graphical editor, VOUS, and a language, Vorpal, to solve these problems. We also discuss the interaction of the various components of our system and their interfaces
2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
We discuss the use of component adaptive methods for the solution of time dependent partial differential equations. After a brief discussion of the methods we identify several deficiencies of commonly used languages of scientific computing and introduce a graphical editor, VOUS, and a language, Vorpal, to solve these problems. We also discuss the interaction of the various components of our system and their interfaces
Adaptive mesh refinement for hyperbolic partial differential equations
by
Marsha J Berger(
Book
)
1 edition published in 1983 in English and held by 2 WorldCat member libraries worldwide
The authors present an adaptive method based on the idea of multiple, component grids for the solution of hyperbolic partial differential equations using finite difference techniques. Based upon Richardsontype estimates of the truncation error, refined grids are created or existing ones removed to attain a given accuracy for a minimum amount of work. Their approach is recursive in that fine grids can themselves contain even finer grids. The grids with finer mesh width in space also have a smaller mesh width in time, making this a mesh refinement algorithm in time and space. This document includes algorithm, data structures and grid generation procedure, and concludes with numerical examples in one and two space dimensions. (Author)
1 edition published in 1983 in English and held by 2 WorldCat member libraries worldwide
The authors present an adaptive method based on the idea of multiple, component grids for the solution of hyperbolic partial differential equations using finite difference techniques. Based upon Richardsontype estimates of the truncation error, refined grids are created or existing ones removed to attain a given accuracy for a minimum amount of work. Their approach is recursive in that fine grids can themselves contain even finer grids. The grids with finer mesh width in space also have a smaller mesh width in time, making this a mesh refinement algorithm in time and space. This document includes algorithm, data structures and grid generation procedure, and concludes with numerical examples in one and two space dimensions. (Author)
Symbolic expressions of composite grid structures
by Stanford University(
Book
)
2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
In summary, graphs and sexpressions are really different manifestations of the same entities. While graphs are visual, they nonetheless possess dual representations in the textual sexpression alphabet. As a result, LISP, which is based entirely on sexpressions, is an ideal language for dealing with applications that perform extensive manipulations on graphbased objects. Scientific applications which make extensive use of both graph based objects as well as traditional numerical arrays can benefit by implementating their higher level data and control structures in LISP. Segments of code that are computationally intensive can be written in a static language such as C or FORTRAN and linked in with the higher level code. Such a design strategy could preserve the benefits of static compilation (i, e, . faster execution speed) while retaining the power and flexibility needed to manipulate complex data structures
2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
In summary, graphs and sexpressions are really different manifestations of the same entities. While graphs are visual, they nonetheless possess dual representations in the textual sexpression alphabet. As a result, LISP, which is based entirely on sexpressions, is an ideal language for dealing with applications that perform extensive manipulations on graphbased objects. Scientific applications which make extensive use of both graph based objects as well as traditional numerical arrays can benefit by implementating their higher level data and control structures in LISP. Segments of code that are computationally intensive can be written in a static language such as C or FORTRAN and linked in with the higher level code. Such a design strategy could preserve the benefits of static compilation (i, e, . faster execution speed) while retaining the power and flexibility needed to manipulate complex data structures
3D Composite Grids for Flow Computations: the Grid Generation
by Stanford University(
Book
)
2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
Flow situations involving localized phenomena and 3D, complex geometries are very important and are often encountered in engineering applications in the aerospace, chemical and petroleum industries. Such geometries defy attempts to lay a single grid over the entire domain, for numerical solution of the problem using finitedifference methods. In a Composite Grid method, the domain is decomposed into overlapping regions which communicate at their boundaries. Each of these is individually transformed to a discrete, orthogonal parallelepiped grid. The transformed flow equations are then solved on these grids, in conjunction with the other grids which communicate with them, by using any of the wide variety of solvers including adaptive, multigrid versions. In this paper, we will describe the grid generation procedure, the data structure used to create the composite grid and some communication and other design issues
2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
Flow situations involving localized phenomena and 3D, complex geometries are very important and are often encountered in engineering applications in the aerospace, chemical and petroleum industries. Such geometries defy attempts to lay a single grid over the entire domain, for numerical solution of the problem using finitedifference methods. In a Composite Grid method, the domain is decomposed into overlapping regions which communicate at their boundaries. Each of these is individually transformed to a discrete, orthogonal parallelepiped grid. The transformed flow equations are then solved on these grids, in conjunction with the other grids which communicate with them, by using any of the wide variety of solvers including adaptive, multigrid versions. In this paper, we will describe the grid generation procedure, the data structure used to create the composite grid and some communication and other design issues
3D Composite Grids Using Bezier Curves and Surfaces in Component Adaptive Methods
by Stanford University(
Book
)
2 editions published in 1993 in English and held by 2 WorldCat member libraries worldwide
We discuss the use of component adaptive methods for the solution of timedependent partial differential equations on complex geometries. After a brief exposition of the system and language requirements for an efficient use of these methods, we describe a grid generation procedure M*E*S*H, built upon Bezier constructs, coupled with a graphical editor VOUS to serve as a visualization platform, and a programming language Vorpal designed to facilitate their implementation. We also discuss the interaction of the various components of our system and their interfaces
2 editions published in 1993 in English and held by 2 WorldCat member libraries worldwide
We discuss the use of component adaptive methods for the solution of timedependent partial differential equations on complex geometries. After a brief exposition of the system and language requirements for an efficient use of these methods, we describe a grid generation procedure M*E*S*H, built upon Bezier constructs, coupled with a graphical editor VOUS to serve as a visualization platform, and a programming language Vorpal designed to facilitate their implementation. We also discuss the interaction of the various components of our system and their interfaces
Numerical Methods Based on Additive Splittings for Hyperbolic Partial Differential Equations
(
Book
)
1 edition published in 1981 in English and held by 2 WorldCat member libraries worldwide
We derive and analyze several methods for systems of hyperbolic equations with wide ranges of signal speeds. These techniques are also useful for problems whose coefficients have large mean values about which they oscillate with small amplitude. Our methods are based on additive splittings of the operators into components that can be approximated independently on the different time scales, some of which are sometimes treated exactly. The efficiency of the splitting methods is seen to depend on the error incurred in splitting the exact solution operator. This is analyzed and a technique is discussed for reducing this error through a simple change of variables. A procedure for generating the appropriate boundary data for the intermediate solutions is also presented. (Author)
1 edition published in 1981 in English and held by 2 WorldCat member libraries worldwide
We derive and analyze several methods for systems of hyperbolic equations with wide ranges of signal speeds. These techniques are also useful for problems whose coefficients have large mean values about which they oscillate with small amplitude. Our methods are based on additive splittings of the operators into components that can be approximated independently on the different time scales, some of which are sometimes treated exactly. The efficiency of the splitting methods is seen to depend on the error incurred in splitting the exact solution operator. This is analyzed and a technique is discussed for reducing this error through a simple change of variables. A procedure for generating the appropriate boundary data for the intermediate solutions is also presented. (Author)
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Related Identities
 Kreiss, H. (HeinzOtto) Author
 Gustafsson, Bertil 1930 Author
 Golub, Gene H. (Gene Howard) 19322007 Editor
 Research Institute for Advanced Computer Science (U.S.)
 Olsson, Pelle Author
 Zhu, Xiaolei Author
 Gustafsson, Bertil Author
 Global Atmospheric Research Programme Joint Organizing Committee
 International Council of Scientific Unions
 World Meteorological Organization
Associated Subjects
AeronauticsComputer programs Boundary value problems Boundary value problemsNumerical solutions Computational grids (Computer systems) Computer science Conservation laws (Mathematics) Difference equations Differential equations, Hyperbolic Differential equations, HyperbolicNumerical solutions Differential equations, ParabolicNumerical solutions Differential equations, Partial Differential equations, PartialNumerical solutions Differential equationsNumerical solutions Equations Error analysis (Mathematics) Faulttolerant computing Fluid dynamics Fluid dynamicsMathematical models Fourier analysis Initial value problemsNumerical solutions Interpolation Mathematics MeteorologyResearch Nets (Mathematics) Numerical analysis Numerical weather forecasting Numerical weather forecastingMathematical models