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On the “Preconditioning ” Function Used in Planewave DFT Calculations and its Generalization
"... Received xxx; Accepted (in revised version) xxx Abstract. The Teter, Payne, and Allan “preconditioning ” function plays a significant role in planewave DFT calculations. This function is often called the TPA precondi-tioner. We present a detailed study of this “preconditioning ” function. We develop ..."
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Received xxx; Accepted (in revised version) xxx Abstract. The Teter, Payne, and Allan “preconditioning ” function plays a significant role in planewave DFT calculations. This function is often called the TPA precondi-tioner. We present a detailed study of this “preconditioning ” function. We
The stages of economic growth.
- Economic History Review , 2nd series 12,
, 1959
"... JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about J ..."
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Cited by 297 (0 self)
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JSTOR, please contact support@jstor.org. economic history. The form of this generalization is a set of stages of growth, which can be designated as follows: the traditional society; the preconditions for take-off; the take-off; the drive to maturity; the age of high mass consumption. Beyond the age
Preconditioning stochastic Galerkin saddle point systems
- SIAM J. MATRIX ANAL. APPL
, 2009
"... Mixed finite element discretizations of deterministic second-order elliptic partial differential equations (PDEs) lead to saddle point systems for which the study of iterative solvers and preconditioners is mature. Galerkin approximation of solutions of stochastic second-order elliptic PDEs, which ..."
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Cited by 110 (4 self)
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, approximated via a nonlinear function of a finite number of unbounded random parameters. We study the resulting saddle point systems and investigate the efficiency of block-diagonal preconditioners of Schur complement and augmented type, for use with minres. By introducing so-called Kronecker product
Simulating Water and Smoke with an Octree Data Structure
, 2004
"... We present a method for simulating water and smoke on an unrestricted octree data structure exploiting mesh refinement techniques to capture the small scale visual detail. We propose a new technique for discretizing the Poisson equation on this octree grid. The resulting linear system is symmetric ..."
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Cited by 210 (18 self)
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positive definite enabling the use of fast solution methods such as preconditioned conjugate gradients, whereas the standard approximation to the Poisson equation on an octree grid results in a non-symmetric linear system which is more computationally challenging to invert. The semi
Bounds for the entries of matrix functions with applications to preconditioning
- BIT
, 1999
"... Let A be a symmetric matrix and let f be a smooth function defined on an interval containing the spectrum of A. Generalizing a well-known result of Demko, Moss and Smith on the decay of the inverse we show that when A is banded, the entries of f(A)are bounded in an exponentially decaying manner away ..."
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Cited by 45 (15 self)
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Let A be a symmetric matrix and let f be a smooth function defined on an interval containing the spectrum of A. Generalizing a well-known result of Demko, Moss and Smith on the decay of the inverse we show that when A is banded, the entries of f(A)are bounded in an exponentially decaying manner
Multilevel functional preconditioning for shape optimisation
- Int. J. for CFD
, 2006
"... We study the application of a multi-level preconditioner to a prac-tical optimal shape design problem. The preconditioner is based on the Bramble-Pasciak-Xu series. We extend it to the unstructured parametrization of 3D shapes by using the volume-agglomeration heuris-tics. The choice of the smoothin ..."
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Cited by 12 (3 self)
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of the smoothing parameter is analysed from func-tional arguments. Application to the shape design for optimising aero-dynamic and sonic boom performances of a wing is demonstrated. Key words: multilevel, optimal shape design, partial dierential equations, Computational Fluid Dynamics, nite element, unstructured
Locally adapted hierarchical basis preconditioning
- ACM Transactions on Graphics
, 2006
"... This paper develops locally adapted hierarchical basis functions for effectively pre-conditioning large optimization problems that arise in computer vision, computer graphics, and computational photography applications such as surface interpolation, optic flow, tone mapping, gradient-domain blending ..."
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Cited by 44 (6 self)
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This paper develops locally adapted hierarchical basis functions for effectively pre-conditioning large optimization problems that arise in computer vision, computer graphics, and computational photography applications such as surface interpolation, optic flow, tone mapping, gradient
Green's Functions For Preconditioning
, 1999
"... . In this paper we look at the connection between Green's functions and preconditioners for systems of equations arising through the discretization of linear partial differential equations. We find that Green's functions, as generalized inverses of differential operators, can sometimes off ..."
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Cited by 4 (2 self)
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. In this paper we look at the connection between Green's functions and preconditioners for systems of equations arising through the discretization of linear partial differential equations. We find that Green's functions, as generalized inverses of differential operators, can sometimes
Preischaemic bradykinin and ischaemic preconditioning in functional
, 1995
"... Objectives: Substantial release of bradykinin has been demonstrated to occur during short periods of myocardial ischaemia in various species. The aim of the present study was to investigate the protective effect of bradykinin in ischaemia and whether bradykinin could be involved in ischaemic precond ..."
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Cited by 1 (0 self)
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preconditioning in the rat heart. Methods: Isolated, buffer-perfused hearts were subjected to 30 min of global ischaemia, followed by 30 min of reperfusion. Postischaemic functional recovery was recorded in the following groups: (1) control; (2) treatment with 0.1 WM bradykinin for 10 min before ischaemia (BK
Multigrid Preconditioning and Toeplitz Matrices
, 1999
"... In this paper we discuss Multigrid methods for Toeplitz matrices. Then the restriction and prolongation operator can be seen as projected Toeplitz matrices. Because of the intimate connection between such matrices and trigonometric series we can express the Multigrid algorithm in terms of the underl ..."
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Cited by 16 (1 self)
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of the underlying functions with special zeroes. This shows how to choose the prolongation/restriction operator in order to get fast convergence. This approach allows Multigrid methods for general Toeplitz systems as long as we have some information on the underlying function. Furthermore, we can define projections
Results 1 - 10
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1,230
