Brandt, Achi
Overview
Works:  30 works in 105 publications in 2 languages and 1,231 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Contributor, Editor, Other 
Publication Timeline
.
Most widely held works by
Achi Brandt
Multigrid techniques : 1984 guide with applications to fluid dynamics by
Achi Brandt(
)
24 editions published between 1984 and 2011 in English and German and held by 402 WorldCat member libraries worldwide
This classic text presents the best practices of developing multigrid solvers for largescale computational problems in science and engineering. By representing a problem at multiple scales and employing suitable interscale interactions, multigrid avoids slowdown due to stiffness and reduces the computational cost of classical algorithms by orders of magnitude. Starting from simple examples, this book guides the reader through practical stages for developing reliable multigrid solvers, methodically supported by accurate performance predictors. The revised edition presents discretization and fast solution of linear and nonlinear partial differential systems; treatment of boundary conditions, global constraints and singularities; grid adaptation, highorder approximations, and system design optimization; applications to fluid dynamics, from simple models to advanced systems; new quantitative performance predictors, a MATLAB sample code, and more. Readers will also gain access to the Multigrid Guide 2.0 Web site, where updates and new developments will be continually posted, including a chapter on Algebraic Multigrid
24 editions published between 1984 and 2011 in English and German and held by 402 WorldCat member libraries worldwide
This classic text presents the best practices of developing multigrid solvers for largescale computational problems in science and engineering. By representing a problem at multiple scales and employing suitable interscale interactions, multigrid avoids slowdown due to stiffness and reduces the computational cost of classical algorithms by orders of magnitude. Starting from simple examples, this book guides the reader through practical stages for developing reliable multigrid solvers, methodically supported by accurate performance predictors. The revised edition presents discretization and fast solution of linear and nonlinear partial differential systems; treatment of boundary conditions, global constraints and singularities; grid adaptation, highorder approximations, and system design optimization; applications to fluid dynamics, from simple models to advanced systems; new quantitative performance predictors, a MATLAB sample code, and more. Readers will also gain access to the Multigrid Guide 2.0 Web site, where updates and new developments will be continually posted, including a chapter on Algebraic Multigrid
Multigrid solutions to quasielliptic schemes by
Achi Brandt(
)
4 editions published in 1985 in English and held by 292 WorldCat member libraries worldwide
4 editions published in 1985 in English and held by 292 WorldCat member libraries worldwide
Multigrid method for nearly singular and slightly indefinite problems by
Achi Brandt(
)
5 editions published in 1985 in English and held by 247 WorldCat member libraries worldwide
5 editions published in 1985 in English and held by 247 WorldCat member libraries worldwide
Textbook multigrid efficiency for the incompressible NavierStokes equations : high Reynolds number wakes and boundary layers by
James L Thomas(
Book
)
4 editions published in 1999 in English and held by 95 WorldCat member libraries worldwide
Textbook multigrid efficiencies for high Reynolds number simulations based on the incompressible Navier Stokes equations are attained for a model problem of flow past a finite flat plate. Elements of the Full Approximation Scheme multigrid algorithm, including distributed relaxation, defect correction, and boundary treatment, are presented for the three main physical aspects encountered: entering flow, wake flow, and boundary layer flow. Textbook efficiencies, i.e., reduction of algebraic errors below discretization errors in one full multigrid cycle, are attained for second order accurate simulations at a laminar Reynolds number of 10,000
4 editions published in 1999 in English and held by 95 WorldCat member libraries worldwide
Textbook multigrid efficiencies for high Reynolds number simulations based on the incompressible Navier Stokes equations are attained for a model problem of flow past a finite flat plate. Elements of the Full Approximation Scheme multigrid algorithm, including distributed relaxation, defect correction, and boundary treatment, are presented for the three main physical aspects encountered: entering flow, wake flow, and boundary layer flow. Textbook efficiencies, i.e., reduction of algebraic errors below discretization errors in one full multigrid cycle, are attained for second order accurate simulations at a laminar Reynolds number of 10,000
Multiscale computational methods in chemistry and physics(
Book
)
9 editions published between 2000 and 2001 in English and held by 86 WorldCat member libraries worldwide
9 editions published between 2000 and 2001 in English and held by 86 WorldCat member libraries worldwide
Multigrid by
U Trottenberg(
Book
)
8 editions published between 2001 and 2015 in English and held by 34 WorldCat member libraries worldwide
Mathematics of Computing  Numerical Analysis
8 editions published between 2001 and 2015 in English and held by 34 WorldCat member libraries worldwide
Mathematics of Computing  Numerical Analysis
Barriers to achieving textbook multigrid efficiency (TME) in CFD by
Achi Brandt(
Book
)
4 editions published in 1998 in English and held by 20 WorldCat member libraries worldwide
4 editions published in 1998 in English and held by 20 WorldCat member libraries worldwide
Multigrid algorithms for the solution of linear complementarity problems arising from free boundary problems by
Achi Brandt(
Book
)
6 editions published between 1980 and 1983 in English and held by 7 WorldCat member libraries worldwide
We show that the multigrid algorithms of Brandt can be adapted to solve linear complementarity problems arising from free boundary problems. The multigrid algorithms are significantly faster than previous algorithms. Using the multigrid algorithms, which are simple modifications of multigrid algorithms for equalities, it is possible to solve the difference equations to within truncation error using less work than the equivalent of six GaussSeidel sweeps on the finest grid. (Author)
6 editions published between 1980 and 1983 in English and held by 7 WorldCat member libraries worldwide
We show that the multigrid algorithms of Brandt can be adapted to solve linear complementarity problems arising from free boundary problems. The multigrid algorithms are significantly faster than previous algorithms. Using the multigrid algorithms, which are simple modifications of multigrid algorithms for equalities, it is possible to solve the difference equations to within truncation error using less work than the equivalent of six GaussSeidel sweeps on the finest grid. (Author)
Recent advances in achieving textbook multigrid efficiency for computational fluid dynamics simulations by
Achi Brandt(
Book
)
4 editions published in 2002 in English and held by 6 WorldCat member libraries worldwide
Recent advances in achieving textbook multigrid efficiency for fluid simulations are presented. Textbook multigrid efficiency is defined as attaining the solution to the governing system of equations in a computational work which is a small multiple of the operation counts associated with discretizing the system. Strategies are reviewed to attain this efficiency by exploiting the factorizability properties inherent to a range of fluid simulations, including the compressible NavierStokes equations. factorizability is used to separate the elliptic and hyperbolic factors contributing to the target system; each of the factors can then be treated individually and optimally. Boundary regions and discontinuities are addressed with separate (local) treatments. New formulations and recent calculations demonstrating the attainment of textbook efficiency for aerodynamic simulations are shown
4 editions published in 2002 in English and held by 6 WorldCat member libraries worldwide
Recent advances in achieving textbook multigrid efficiency for fluid simulations are presented. Textbook multigrid efficiency is defined as attaining the solution to the governing system of equations in a computational work which is a small multiple of the operation counts associated with discretizing the system. Strategies are reviewed to attain this efficiency by exploiting the factorizability properties inherent to a range of fluid simulations, including the compressible NavierStokes equations. factorizability is used to separate the elliptic and hyperbolic factors contributing to the target system; each of the factors can then be treated individually and optimally. Boundary regions and discontinuities are addressed with separate (local) treatments. New formulations and recent calculations demonstrating the attainment of textbook efficiency for aerodynamic simulations are shown
Multigrid course(
Book
)
1 edition published in 1992 in German and held by 6 WorldCat member libraries worldwide
1 edition published in 1992 in German and held by 6 WorldCat member libraries worldwide
GRIDPACK : toward unification of general grid programming by
Achi Brandt(
Book
)
6 editions published in 1983 in English and German and held by 6 WorldCat member libraries worldwide
GRIDPACK is a fully portable Fortran extension, including economic data structures, routines and macrostatements, for simplifying and unifying the programming of grid operations in general twodimensional domains. These operations include the introduction and modification of grids, boundaries, inner and outer subgrids, grid functions, boundary functions and finitedifference operators, including operators near and on boundaries; interpolation between grids; sweeping conveniently and with full efficiency over grids; displaying grids, grid functions, boundary functions and boundary shapes; etc. The software will facilitate and modularize multigrid programming, permitting writing many processes once for all, including combinations of fast solvers with flexible local grid adaptations. (Author)
6 editions published in 1983 in English and German and held by 6 WorldCat member libraries worldwide
GRIDPACK is a fully portable Fortran extension, including economic data structures, routines and macrostatements, for simplifying and unifying the programming of grid operations in general twodimensional domains. These operations include the introduction and modification of grids, boundaries, inner and outer subgrids, grid functions, boundary functions and finitedifference operators, including operators near and on boundaries; interpolation between grids; sweeping conveniently and with full efficiency over grids; displaying grids, grid functions, boundary functions and boundary shapes; etc. The software will facilitate and modularize multigrid programming, permitting writing many processes once for all, including combinations of fast solvers with flexible local grid adaptations. (Author)
Nonlinear Dynamics Of Ocean Waves  Proceedings Of The Symposium by
Michael F Shlesinger(
)
2 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
Multigrid solutions to steadystate compressible NavierStokes equations by
Achi Brandt(
Book
)
4 editions published between 1981 and 1982 in English and German and held by 5 WorldCat member libraries worldwide
4 editions published between 1981 and 1982 in English and German and held by 5 WorldCat member libraries worldwide
Multiscale algorithm for atmospheric data assimilation by
Achi Brandt(
Book
)
2 editions published in 1995 in English and held by 3 WorldCat member libraries worldwide
Abstract: "A multiscale algorithm for the problem of optimal statistical interpolation of the observed data has been developed. This problem includes the calculation of the vector of the 'analyzed' (best estimated) atmosphere flow field w[to the power alpha] by the formula [formula] where the quantity y is defined by the equation [formula] using the given model forecast first guess w[to the power f] and the vector of observations w[to the power o]. H is an interpolation operator from the regular grid to the observation network, P[to the power f] is the forecast error covariance matrix, and R is the observation error covariance matrix. At this initial stage the case of univariate analysis of single level radiosonde height data is considered. The matrix R is assumed to be diagonal, and the matrix P[to the power f] to be given by the formula [formula] where [mu subscript ij] is a smooth decreasing function of the distance between the ith and jth points. Two different multiscale constructions can be used for efficient solving the problem of optimal statistical interpolation: a technique for fast evaluation of the discrete integral transform [formula] and a fast iterative process which effectively works with a sequence of spatial scales. In this paper we describe a multiscale iterative process based on a multiresolution simultaneous displacement technique and a localized variational calculation of iteration parameters."
2 editions published in 1995 in English and held by 3 WorldCat member libraries worldwide
Abstract: "A multiscale algorithm for the problem of optimal statistical interpolation of the observed data has been developed. This problem includes the calculation of the vector of the 'analyzed' (best estimated) atmosphere flow field w[to the power alpha] by the formula [formula] where the quantity y is defined by the equation [formula] using the given model forecast first guess w[to the power f] and the vector of observations w[to the power o]. H is an interpolation operator from the regular grid to the observation network, P[to the power f] is the forecast error covariance matrix, and R is the observation error covariance matrix. At this initial stage the case of univariate analysis of single level radiosonde height data is considered. The matrix R is assumed to be diagonal, and the matrix P[to the power f] to be given by the formula [formula] where [mu subscript ij] is a smooth decreasing function of the distance between the ith and jth points. Two different multiscale constructions can be used for efficient solving the problem of optimal statistical interpolation: a technique for fast evaluation of the discrete integral transform [formula] and a fast iterative process which effectively works with a sequence of spatial scales. In this paper we describe a multiscale iterative process based on a multiresolution simultaneous displacement technique and a localized variational calculation of iteration parameters."
Multiscale Methods in Molecular Mechanics(
Book
)
2 editions published in 1995 in English and held by 2 WorldCat member libraries worldwide
This report results from a contract tasking Department of Applied Mathematics and Computer Science, The Weizmann Institute of Science as follows: Develop multiscale methods using parallel processing capabilities for linking atomistic level simulations and continuum level material or structural modeling
2 editions published in 1995 in English and held by 2 WorldCat member libraries worldwide
This report results from a contract tasking Department of Applied Mathematics and Computer Science, The Weizmann Institute of Science as follows: Develop multiscale methods using parallel processing capabilities for linking atomistic level simulations and continuum level material or structural modeling
Multilevel adaptive techniques (mlat), 1; the multigrid method by
Achi Brandt(
Book
)
3 editions published in 1976 in English and held by 2 WorldCat member libraries worldwide
3 editions published in 1976 in English and held by 2 WorldCat member libraries worldwide
Multigrid solutions to elliptic flow problems by
Achi Brandt(
Book
)
2 editions published in 1979 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1979 in English and held by 2 WorldCat member libraries worldwide
Multiscale Computational Methods in Molecular Simulations(
Book
)
2 editions published in 2001 in English and held by 2 WorldCat member libraries worldwide
This report results from a contract tasking The Weizmann Institute of Science as follows: the contractor will investigate: (1) adjusting and packaging the software for fast electrostatic summations, so that it can be used by other Air Force projects; (2) the improvement of the simple models used for outlining the coarsening methods to more complex bonded molecular systems; and (3) the algorithm for improving the efficiency of Density Functional Theory (DFT) has been demonstrated so far only in one dimension and requires further work for three dimensions, and implementation
2 editions published in 2001 in English and held by 2 WorldCat member libraries worldwide
This report results from a contract tasking The Weizmann Institute of Science as follows: the contractor will investigate: (1) adjusting and packaging the software for fast electrostatic summations, so that it can be used by other Air Force projects; (2) the improvement of the simple models used for outlining the coarsening methods to more complex bonded molecular systems; and (3) the algorithm for improving the efficiency of Density Functional Theory (DFT) has been demonstrated so far only in one dimension and requires further work for three dimensions, and implementation
Bootstrap Algebraic Multigrid: Status Report, Open Problems, and Outlook(
)
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
Abstract: This paper provides an overview of the main ideas driving the bootstrap algebraic multigrid methodology, including compatible relaxation and algebraic distances for defining effective coarsening strategies, the least squares method for computing accurate prolongation operators and the bootstrap cycles for computing the test vectors that are used in the least squares process. We review some recent research in the development, analysis and application of bootstrap algebraic multigrid and point to open problems in these areas. Results from our previous research as well as some new results for some model diffusion problems with highly oscillatory diffusion coefficient are presented to illustrate the basic components of the BAMG algorithm
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
Abstract: This paper provides an overview of the main ideas driving the bootstrap algebraic multigrid methodology, including compatible relaxation and algebraic distances for defining effective coarsening strategies, the least squares method for computing accurate prolongation operators and the bootstrap cycles for computing the test vectors that are used in the least squares process. We review some recent research in the development, analysis and application of bootstrap algebraic multigrid and point to open problems in these areas. Results from our previous research as well as some new results for some model diffusion problems with highly oscillatory diffusion coefficient are presented to illustrate the basic components of the BAMG algorithm
Multigrid solvers on parallel computers by
Achi Brandt(
Book
)
2 editions published in 1980 in English and held by 1 WorldCat member library worldwide
2 editions published in 1980 in English and held by 1 WorldCat member library worldwide
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Algorithms Boundary layer Boundary value problems Chemistry ChemistryData processing Computational fluid dynamics Convergence Differential equations Differential equations, Elliptic Differential equations, EllipticNumerical solutions Differential equations, Partial Differential equations, PartialNumerical solutions Eigenvectors Fluid dynamicsMathematical models Fluid dynamicsMathematics Laminar flow Linear complementarity problem Multigrid methods (Numerical analysis) NavierStokes equations NavierStokes equationsNumerical solutions Numerical analysis Numerical grid generation (Numerical analysis) Physics PhysicsData processing Reynolds number
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Alternative Names
Achi Brandt Israeli mathematician
Achi Brandt israelischer Mathematiker
Achi Brandt matemático israelí
Achi Brandt mathématicien israélien
Brandt, Aḥî 1938
Brandṭ, ʾAḥiy
Brandṭ ʾAḥiy 1938....
Branṭ, ʾAḥiy
Branṭ ʾAḥiy 1938....
אחי ברנדט
ברנדט, אחי
ברנדט אחי 1938....
ברנט, אחי
ברנט אחי 1938....
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