McCormick, S. F. (Stephen Fahrney) 1944
Overview
Works:  43 works in 151 publications in 1 language and 2,314 library holdings 

Genres:  Conference papers and proceedings Academic theses 
Roles:  Author, Editor, Other 
Classifications:  QA377, 515.353 
Publication Timeline
.
Most widely held works by
S. F McCormick
Multilevel adaptive methods for partial differential equations by
S. F McCormick(
Book
)
18 editions published in 1989 in English and held by 389 WorldCat member libraries worldwide
"A practical handbook for understanding and using fast adaptive composite grid (FAC) methods for discretization and solution of partial differential equations (PDEs). Contains fundamental concepts. These socalled FAC are characterized by their use of a composite grid, which is nominally the union of various uniform grids. FAC is capable of producing a composite grid with tailored resolution, and a corresponding solution with commensurate accuracy, at a cost proportional to the number of composite grid points. Moreover, special asynchronous versions of the fast adaptive composite grid methods (AFAC) studied here have seemingly optimal complexity in a parallel computing environment. Most of the methods treated in this book were discovered only within the last decade, and in many cases their development is still in its infancy. While this is not meant to be comprehensive, it does provide a theoretical and practical guide to multilevel adaptive methods and relevant discretization techniques"Publisher description
18 editions published in 1989 in English and held by 389 WorldCat member libraries worldwide
"A practical handbook for understanding and using fast adaptive composite grid (FAC) methods for discretization and solution of partial differential equations (PDEs). Contains fundamental concepts. These socalled FAC are characterized by their use of a composite grid, which is nominally the union of various uniform grids. FAC is capable of producing a composite grid with tailored resolution, and a corresponding solution with commensurate accuracy, at a cost proportional to the number of composite grid points. Moreover, special asynchronous versions of the fast adaptive composite grid methods (AFAC) studied here have seemingly optimal complexity in a parallel computing environment. Most of the methods treated in this book were discovered only within the last decade, and in many cases their development is still in its infancy. While this is not meant to be comprehensive, it does provide a theoretical and practical guide to multilevel adaptive methods and relevant discretization techniques"Publisher description
Multigrid methods by
S. F McCormick(
Book
)
20 editions published between 1987 and 1994 in English and Undetermined and held by 386 WorldCat member libraries worldwide
A thoughtful consideration of the current level of development of multigrid methods, this volume is a carefully edited collection of papers that addresses its topic on several levels. The first three chapters orient the reader who is familiar with standard numerical techniques to multigrid methods, first by discussing multigrid in the context of standard techniques, second by detailing the mechanics of use of the method, and third by applying the basic method to some current problems in fluid dynamics. The fourth chapter provides a unified development, complete with theory, of algebraic multigrid (AMG), which is a linear equation solver based on multigrid principles. The last chapter is an ambitious development of a very general theory of multigrid methods for variationally posed problems. Included as an appendix is the latest edition of the Multigrid Bibliography, an attempted compilation of all existing research publications on multigrid
20 editions published between 1987 and 1994 in English and Undetermined and held by 386 WorldCat member libraries worldwide
A thoughtful consideration of the current level of development of multigrid methods, this volume is a carefully edited collection of papers that addresses its topic on several levels. The first three chapters orient the reader who is familiar with standard numerical techniques to multigrid methods, first by discussing multigrid in the context of standard techniques, second by detailing the mechanics of use of the method, and third by applying the basic method to some current problems in fluid dynamics. The fourth chapter provides a unified development, complete with theory, of algebraic multigrid (AMG), which is a linear equation solver based on multigrid principles. The last chapter is an ambitious development of a very general theory of multigrid methods for variationally posed problems. Included as an appendix is the latest edition of the Multigrid Bibliography, an attempted compilation of all existing research publications on multigrid
A multigrid tutorial by
William L Briggs(
Book
)
25 editions published between 2000 and 2011 in English and Undetermined and held by 381 WorldCat member libraries worldwide
Mathematics of Computing  Numerical Analysis
25 editions published between 2000 and 2011 in English and Undetermined and held by 381 WorldCat member libraries worldwide
Mathematics of Computing  Numerical Analysis
Multilevel projection methods for partial differential equations by
S. F McCormick(
Book
)
12 editions published in 1992 in English and held by 358 WorldCat member libraries worldwide
The multilevel projection method is a new formalism that provides a framework for the development of multilevel algorithms in a very general setting. This methodology guides the choices of all the major multilevel processes, including relaxation and coarsening, and it applies directly to global or locallyrefined discretizations. This book was developed from lectures at the CBMSNSF Regional Conference on Multigrid and Multilevel Adaptive Methods for Partial Differential Equations in June 1991, and is a supplement to Multilevel Adaptive Methods for Partial Differential Equations, also written by Stephen F. McCormick
12 editions published in 1992 in English and held by 358 WorldCat member libraries worldwide
The multilevel projection method is a new formalism that provides a framework for the development of multilevel algorithms in a very general setting. This methodology guides the choices of all the major multilevel processes, including relaxation and coarsening, and it applies directly to global or locallyrefined discretizations. This book was developed from lectures at the CBMSNSF Regional Conference on Multigrid and Multilevel Adaptive Methods for Partial Differential Equations in June 1991, and is a supplement to Multilevel Adaptive Methods for Partial Differential Equations, also written by Stephen F. McCormick
Multigrid methods : theory, applications, and supercomputing by
S. F McCormick(
Book
)
15 editions published between 1988 and 2020 in English and held by 297 WorldCat member libraries worldwide
This book is a collection of research papers on a wide variety of multigrid topics, including applications, computation and theory. It represents proceedings of the Third Copper Mountain Conference on Multigrid Methods, which was held at Copper Mountain, Colorado
15 editions published between 1988 and 2020 in English and held by 297 WorldCat member libraries worldwide
This book is a collection of research papers on a wide variety of multigrid topics, including applications, computation and theory. It represents proceedings of the Third Copper Mountain Conference on Multigrid Methods, which was held at Copper Mountain, Colorado
Optimization in solving elliptic problems by
E. G Dʹi︠a︡konov(
Book
)
6 editions published between 1996 and 2018 in English and held by 207 WorldCat member libraries worldwide
Optimization in Solving Elliptic Problems focuses on one of the most interesting and challenging problems of computational mathematics  the optimization of numerical algorithms for solving elliptic problems. It presents detailed discussions of how asymptotically optimal algorithms may be applied to elliptic problems to obtain numerical solutions meeting certain specified requirements. Beginning with an outline of the fundamental principles of numerical methods, this book describes how to construct special modifications of classical finite element methods such that for the arising grid systems, asymptotically optimal iterative methods can be applied. Optimization in Solving Elliptic Problems describes the construction of computational algorithms resulting in the required accuracy of a solution and having a predetermined computational complexity. Construction of asymptotically optimal algorithms is demonstrated for multidimensional elliptic boundary value problems under general conditions. In addition, algorithms are developed for eigenvalue problems and NavierStokes problems. The development of these algorithms is based on detailed discussions of topics that include accuracy estimates of projective and difference methods, topologically equivalent grids and triangulations, general theorems on convergence of iterative methods, mixed finite element methods for Stokestype problems, methods of solving fourthorder problems, and methods for solving classical elasticity problems. Furthermore, the text provides methods for managing basic iterative methods such as domain decomposition and multigrid methods. These methods, clearly developed and explained in the text, may be used to develop algorithms for solving applied elliptic problems
6 editions published between 1996 and 2018 in English and held by 207 WorldCat member libraries worldwide
Optimization in Solving Elliptic Problems focuses on one of the most interesting and challenging problems of computational mathematics  the optimization of numerical algorithms for solving elliptic problems. It presents detailed discussions of how asymptotically optimal algorithms may be applied to elliptic problems to obtain numerical solutions meeting certain specified requirements. Beginning with an outline of the fundamental principles of numerical methods, this book describes how to construct special modifications of classical finite element methods such that for the arising grid systems, asymptotically optimal iterative methods can be applied. Optimization in Solving Elliptic Problems describes the construction of computational algorithms resulting in the required accuracy of a solution and having a predetermined computational complexity. Construction of asymptotically optimal algorithms is demonstrated for multidimensional elliptic boundary value problems under general conditions. In addition, algorithms are developed for eigenvalue problems and NavierStokes problems. The development of these algorithms is based on detailed discussions of topics that include accuracy estimates of projective and difference methods, topologically equivalent grids and triangulations, general theorems on convergence of iterative methods, mixed finite element methods for Stokestype problems, methods of solving fourthorder problems, and methods for solving classical elasticity problems. Furthermore, the text provides methods for managing basic iterative methods such as domain decomposition and multigrid methods. These methods, clearly developed and explained in the text, may be used to develop algorithms for solving applied elliptic problems
Sixth Copper Mountain Conference on Multigrid Methods : proceedings of a workshop cosponsored by the National Aeronautics
and Space Administration [and others] and held at Copper Mountain, Colorado, April 49, 1993 by Copper Mountain Conference on Multigrid Methods(
Book
)
1 edition published in 1993 in English and held by 114 WorldCat member libraries worldwide
1 edition published in 1993 in English and held by 114 WorldCat member libraries worldwide
Multigrid methods : an alternate viewpoint by
S. F McCormick(
Book
)
1 edition published in 1979 in English and held by 70 WorldCat member libraries worldwide
1 edition published in 1979 in English and held by 70 WorldCat member libraries worldwide
Multilevel projection methods for partial differential equations by
S. F McCormick(
Book
)
1 edition published in 1992 in English and held by 22 WorldCat member libraries worldwide
Wavelets are a mathematical development that may revolutionize the world of information storage and retrieval according to many experts. They are a fairly simple mathematical tool now being applied to the compression of datasuch as fingerprints, weather satellite photographs, and medical xraysthat were previously thought to be impossible to condense without losing crucial details. This monograph contains 10 lectures presented by Dr. Daubechies as the principal speaker at the 1990 CBMSNSF Conference on Wavelets and Applications. The author has worked on several aspects of the wavelet transform and has developed a collection of wavelets that are remarkably efficient
1 edition published in 1992 in English and held by 22 WorldCat member libraries worldwide
Wavelets are a mathematical development that may revolutionize the world of information storage and retrieval according to many experts. They are a fairly simple mathematical tool now being applied to the compression of datasuch as fingerprints, weather satellite photographs, and medical xraysthat were previously thought to be impossible to condense without losing crucial details. This monograph contains 10 lectures presented by Dr. Daubechies as the principal speaker at the 1990 CBMSNSF Conference on Wavelets and Applications. The author has worked on several aspects of the wavelet transform and has developed a collection of wavelets that are remarkably efficient
Sixth Copper Mountain Conference on Multigrid Methods : proceedings of a workshop cosponsored by the National Aeronautics
and Space Administration [and others] and held at Copper Mountain, Colorado, April 49, 1993 by
N. Duane Melson(
Book
)
6 editions published in 1993 in English and held by 19 WorldCat member libraries worldwide
6 editions published in 1993 in English and held by 19 WorldCat member libraries worldwide
Second Copper Mountain Conference on Multigrid Methods : Copper Mountain, Colorado, March 31April 3, 1985 by Copper Mountain Conference on Multigrid Methods(
Book
)
3 editions published in 1986 in English and Undetermined and held by 9 WorldCat member libraries worldwide
3 editions published in 1986 in English and Undetermined and held by 9 WorldCat member libraries worldwide
Multigrid methods(
Book
)
1 edition published in 1988 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 8 WorldCat member libraries worldwide
Strategy in action : a stepbystep guide and workbook, for small and mediumsized businesses by
S. F McCormick(
Book
)
2 editions published in 2001 in English and held by 8 WorldCat member libraries worldwide
2 editions published in 2001 in English and held by 8 WorldCat member libraries worldwide
Multigrid methods selected papers from the Internat. Conference on Multigrid Methods, April 6  8, 1983, Dillon, Colo by Conference on Multigrid Methods(
Book
)
4 editions published in 1983 in English and Undetermined and held by 4 WorldCat member libraries worldwide
4 editions published in 1983 in English and Undetermined and held by 4 WorldCat member libraries worldwide
Seventh Copper Mountain Conference on Multigrid Methods : proceedings of a workshop cosponsored by the National Aeronautics
and Space Administration, Washington, D.C., and the Department of Energy, Washington, D.C., and held at Copper Mountain, Colorado,
April 27, 1995 by Copper Mountain Conference on Multigrid Methods(
Book
)
4 editions published between 1995 and 1996 in English and held by 4 WorldCat member libraries worldwide
4 editions published between 1995 and 1996 in English and held by 4 WorldCat member libraries worldwide
Relaxationcorrected Bootstrap Algebraic Multigrid (rBAMG) by Minho Park(
)
1 edition published in 2010 in English and held by 3 WorldCat member libraries worldwide
Bootstrap Algebraic Multigrid (BAMG) is a multigridbased solver for matrix equations of the form Ax = b. Its aim is to automatically determine the interpolation weights used in algebraic multigrid (AMG) by locally fitting a set of test vectors that have been relaxed as solutions to the corresponding homogeneous equation, Ax = 0. This thesis introduces an indirect operatorbased interpolation scheme for BAMG that determines the interpolation weights indirectly by "collapsing" the unwanted connections in "operator interpolation". Compared to BAMG, this indirect BAMG approach (iBAMG) is more in the spirit of classical AMG, which collapses unwanted connections in operator interpolation based on the (restrictive) assumption that smooth error is locally constant
1 edition published in 2010 in English and held by 3 WorldCat member libraries worldwide
Bootstrap Algebraic Multigrid (BAMG) is a multigridbased solver for matrix equations of the form Ax = b. Its aim is to automatically determine the interpolation weights used in algebraic multigrid (AMG) by locally fitting a set of test vectors that have been relaxed as solutions to the corresponding homogeneous equation, Ax = 0. This thesis introduces an indirect operatorbased interpolation scheme for BAMG that determines the interpolation weights indirectly by "collapsing" the unwanted connections in "operator interpolation". Compared to BAMG, this indirect BAMG approach (iBAMG) is more in the spirit of classical AMG, which collapses unwanted connections in operator interpolation based on the (restrictive) assumption that smooth error is locally constant
Parallel efficiencybased adaptive local refinement by Lei Tang(
)
1 edition published in 2010 in English and held by 3 WorldCat member libraries worldwide
Accommodations of the ALR strategies to parallel computer architectures involve a geometric binning strategy to reduce communication cost. Load balancing begins at very coarse levels. Elements and nodes are redistributed using parallel quadtree structures and a space filling curve. This automatically ameliorates load balancing issues at finer levels. Numerical results produced on Frost, the NCAR/CU Blue Gene/L supercomputer, are presented for a 2D Poisson problem with steep gradients, a 2D backward facing step incompressible Stokes equations and NavierStokes equations. The NIFOSLAMGACE approach is able to provide highly resolved approximations to rapidly varying solutions using a small number of work units. Excellent weak and strong scalability of parallel ALR are demonstrated on up to 4,096 processors for problems with up to 15 million biquadratic elements
1 edition published in 2010 in English and held by 3 WorldCat member libraries worldwide
Accommodations of the ALR strategies to parallel computer architectures involve a geometric binning strategy to reduce communication cost. Load balancing begins at very coarse levels. Elements and nodes are redistributed using parallel quadtree structures and a space filling curve. This automatically ameliorates load balancing issues at finer levels. Numerical results produced on Frost, the NCAR/CU Blue Gene/L supercomputer, are presented for a 2D Poisson problem with steep gradients, a 2D backward facing step incompressible Stokes equations and NavierStokes equations. The NIFOSLAMGACE approach is able to provide highly resolved approximations to rapidly varying solutions using a small number of work units. Excellent weak and strong scalability of parallel ALR are demonstrated on up to 4,096 processors for problems with up to 15 million biquadratic elements
Algebraic Multigrid Methods for Parallel Computing, Systems, and Graphs by Tobias M Jones(
)
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
Historically, AMG was used to solve linear systems that arise from the discretization of differential equations. However, due to the ON scalability of the method, it seems natural to investigate it in other contexts that generate large sparse linear systems. Data mining in graph theory applications generate very large, but extremely sparse, linear systems called Graph Laplacians. As a step in the process of targeting AMG for these problems, eigenvectors of matrices formed from graphs are investigated
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
Historically, AMG was used to solve linear systems that arise from the discretization of differential equations. However, due to the ON scalability of the method, it seems natural to investigate it in other contexts that generate large sparse linear systems. Data mining in graph theory applications generate very large, but extremely sparse, linear systems called Graph Laplacians. As a step in the process of targeting AMG for these problems, eigenvectors of matrices formed from graphs are investigated
Multilevel Techniques in Large Scale Computation(
)
2 editions published between 1992 and 1996 in English and held by 2 WorldCat member libraries worldwide
Techniques have been demonstrated for time dependent problems that allow rare activation of finest grids; new multiscale approaches in statistical mechanics and many particle problems; fast integral transforms and solvers for integrodifferential equations; fast Dirac solvers, and multigrid algorithms on decomposed domains
2 editions published between 1992 and 1996 in English and held by 2 WorldCat member libraries worldwide
Techniques have been demonstrated for time dependent problems that allow rare activation of finest grids; new multiscale approaches in statistical mechanics and many particle problems; fast integral transforms and solvers for integrodifferential equations; fast Dirac solvers, and multigrid algorithms on decomposed domains
Multigrid methods for nearly singular linear equations and Eigenvalue problems by Zhiqiang Cai(
Book
)
1 edition published in 1993 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1993 in English and held by 2 WorldCat member libraries worldwide
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Related Identities
 Society for Industrial and Applied Mathematics Editor
 Briggs, William L. Author Editor
 Henson, Van Emden Editor
 Dʹi︠a︡konov, E. G. (Evgeniĭ Georgievich) Author
 Manteuffel, Thomas Albert 1948 Editor
 Melson, N. Duane Author Editor
 United States National Aeronautics and Space Administration Scientific and Technical Information Program
 United States Department of Energy
 Lawrence Livermore Laboratory
 Copper Mountain Conference on Multigrid Methods (3, 1987)
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Associated Subjects
Algorithms Boundary value problemsNumerical solutions Differential equations, Elliptic Differential equations, EllipticAsymptotic theory Differential equations, Partial Differential equations, PartialNumerical solutions Eigenvalues Multigrid methods (Numerical analysis) Numerical grid generation (Numerical analysis) Small businessManagement Strategic planning
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Alternative Names
Fahrney McCormick Stephen
Fahrney McCormick, Stephen 1944
Mac Cormick Stephen Fahrney
Mac Cormick Steve F.
MacCormick, Stephen F. 1944
MacCormick Stephen Fahrney
MacCormick, Stephen Fahrney 1944
MacCormick Steve F.
MacCormick, Steve F. 1944
Mc Cormick, Stephen F. 1944
Mc Cormick Stephen Fahrney
Mc Cormick Steve F.
McCormick, S. F.
McCormick, S.F. 1944
McCormick, Stephen F.
McCormick, Stephen Fahrney 1944
McCormick, Steve.
McCormick, Steve 1944
McCormick Steve F.
McCormick, Steve F. 1944
Steve McCormick
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