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625
An accurate Cartesian grid method for viscous incompressible flows with complex boundaries
 J. Comput. Phys
, 1999
"... A Cartesian grid method has been developed for simulating twodimensional unsteady, viscous, incompressible flows with complex immersed boundaries. A finitevolume method based on a secondorder accurate centraldifference scheme is used in conjunction with a twostep fractionalstep procedure. The k ..."
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Cited by 91 (12 self)
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A Cartesian grid method has been developed for simulating twodimensional unsteady, viscous, incompressible flows with complex immersed boundaries. A finitevolume method based on a secondorder accurate centraldifference scheme is used in conjunction with a twostep fractionalstep procedure. The key aspects that need to be considered in developing such a solver are imposition of boundary conditions on the immersed boundaries and accurate discretization of the governing equation in cells that are cut by these boundaries. A new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the secondorder spatial accuracy of the underlying solver. The presence of immersed boundaries alters the conditioning of the linear operators and this can slow down the iterative solution of these equations. The convergence is accelerated by using a preconditioned conjugate gradient method where the preconditioner takes advantage of the structured nature of the underlying mesh. The accuracy and fidelity of the solver is validated by simulating a number of canonical flows and the ability of the solver to simulate flows with very complicated immersed boundaries is
Matrix Market: A Web Resource for Test Matrix Collections
 The Quality of Numerical Software: Assessment and Enhancement
, 1997
"... We describe a repository of data for the testing of numerical algorithms and mathematical software for matrix computations. The repository is designed to accommodate both dense and sparse matrices, as well as software to generate matrices. It has been seeded with the wellknown HarwellBoeing sparse ..."
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Cited by 88 (8 self)
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We describe a repository of data for the testing of numerical algorithms and mathematical software for matrix computations. The repository is designed to accommodate both dense and sparse matrices, as well as software to generate matrices. It has been seeded with the wellknown HarwellBoeing sparse matrix collection. The raw data files have been augmented with an integrated World Wide Web interface which describes the matrices in the collection quantitatively and visually. For example, each matrix has a Web page which details its attributes, graphically depicts its sparsity pattern, and provides access to the matrix itself in several formats. In addition, a search mechanism is included which allows retrieval of matrices based on a variety of attributes, such as type and size, as well as through freetext search in abstracts. The URL is http://math.nist.gov/MatrixMarket/ .
Recent computational developments in Krylov subspace methods for linear systems
 NUMER. LINEAR ALGEBRA APPL
, 2007
"... Many advances in the development of Krylov subspace methods for the iterative solution of linear systems during the last decade and a half are reviewed. These new developments include different versions of restarted, augmented, deflated, flexible, nested, and inexact methods. Also reviewed are metho ..."
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Cited by 86 (12 self)
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Many advances in the development of Krylov subspace methods for the iterative solution of linear systems during the last decade and a half are reviewed. These new developments include different versions of restarted, augmented, deflated, flexible, nested, and inexact methods. Also reviewed are methods specifically tailored to systems with special properties such as special forms of symmetry and those depending on one or more parameters.
A TwoDimensional Data Distribution Method For Parallel Sparse MatrixVector Multiplication
 SIAM REVIEW
"... A new method is presented for distributing data in sparse matrixvector multiplication. The method is twodimensional, tries to minimise the true communication volume, and also tries to spread the computation and communication work evenly over the processors. The method starts with a recursive bipar ..."
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Cited by 83 (9 self)
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A new method is presented for distributing data in sparse matrixvector multiplication. The method is twodimensional, tries to minimise the true communication volume, and also tries to spread the computation and communication work evenly over the processors. The method starts with a recursive bipartitioning of the sparse matrix, each time splitting a rectangular matrix into two parts with a nearly equal number of nonzeros. The communication volume caused by the split is minimised. After the matrix partitioning, the input and output vectors are partitioned with the objective of minimising the maximum communication volume per processor. Experimental results of our implementation, Mondriaan, for a set of sparse test matrices show a reduction in communication compared to onedimensional methods, and in general a good balance in the communication work.
Scientific Computing on Bulk Synchronous Parallel Architectures
"... We theoretically and experimentally analyse the efficiency with which a wide range of important scientific computations can be performed on bulk synchronous parallel architectures. ..."
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Cited by 75 (16 self)
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We theoretically and experimentally analyse the efficiency with which a wide range of important scientific computations can be performed on bulk synchronous parallel architectures.
LargeScale Information Retrieval with Latent Semantic Indexing
, 1997
"... . As the amount of electronic information increases, traditional lexical (or Boolean) information retrieval techniques will become less useful. Large, heterogeneous collections will be difficult to search since the sheer volume of unranked documents returned in response to a query will overwhelm the ..."
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Cited by 71 (6 self)
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. As the amount of electronic information increases, traditional lexical (or Boolean) information retrieval techniques will become less useful. Large, heterogeneous collections will be difficult to search since the sheer volume of unranked documents returned in response to a query will overwhelm the user. Vectorspace approaches to information retrieval, on the other hand, allow the user to search for concepts rather than specific words and rank the results of the search according to their relative similarity to the query. One vectorspace approach, Latent Semantic Indexing (LSI), has achieved up to 30% better retrieval performance than lexical searching techniques by employing a reducedrank model of the termdocument space. However, the original implementation of LSI lacked the execution efficiency required to make LSI useful for large data sets. A new implementation of LSI, LSI++, seeks to make LSI efficient, extensible, portable, and maintainable. The LSI++ Application Programming ...
Comparing ConstraintBased Motion Editing Methods
 Graphical Models
, 2001
"... This paper explores the range of constraintbased techniques used to alter motions while preserving specific spatial features. We examine a variety of methods, defining a taxonomy of these methods that is categorized by the mechanism employed to enforce temporal constraints. We pay particular at ..."
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Cited by 66 (1 self)
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This paper explores the range of constraintbased techniques used to alter motions while preserving specific spatial features. We examine a variety of methods, defining a taxonomy of these methods that is categorized by the mechanism employed to enforce temporal constraints. We pay particular attention to a less explored category of techniques that we term perframe inverse kinematics plus filtering, and we show how these methods may provide an easier to implement while retaining the benefits of other approaches
Flexible conjugate gradients
 SIAM J. Sci. Comput
, 2000
"... Abstract. We analyze the conjugate gradient (CG) method with preconditioning slightly variable from one iteration to the next. To maintain the optimal convergence properties, we consider a variant proposed by Axelsson that performs an explicit orthogonalization of the search directions vectors. For ..."
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Cited by 64 (8 self)
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Abstract. We analyze the conjugate gradient (CG) method with preconditioning slightly variable from one iteration to the next. To maintain the optimal convergence properties, we consider a variant proposed by Axelsson that performs an explicit orthogonalization of the search directions vectors. For this method, which we refer to as flexible CG, we develop a theoretical analysis that shows that the convergence rate is essentially independent of the variations in the preconditioner as long as the latter are kept sufficiently small. We further discuss the real convergence rate on the basis of some heuristic arguments supported by numerical experiments. Depending on the eigenvalue distribution corresponding to the fixed reference preconditioner, several situations have to be distinguished. In some cases, the convergence is as fast with truncated versions of the algorithm or even with the standard CG method, whereas quite large variations are allowed without too much penalty. In other cases, the flexible variant effectively outperforms the standard method, while the need for truncation limits the size of the variations that can be reasonably allowed.
Orderings for incomplete factorization preconditioning of nonsymmetric problems
 SIAM J. SCI. COMPUT
, 1999
"... Numerical experiments are presented whereby the effect of reorderings on the convergence of preconditioned Krylov subspace methods for the solution of nonsymmetric linear systems is shown. The preconditioners used in this study are different variants of incomplete factorizations. It is shown that c ..."
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Cited by 60 (11 self)
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Numerical experiments are presented whereby the effect of reorderings on the convergence of preconditioned Krylov subspace methods for the solution of nonsymmetric linear systems is shown. The preconditioners used in this study are different variants of incomplete factorizations. It is shown that certain reorderings for direct methods, such as reverse Cuthill–McKee, can be very beneficial. The benefit can be seen in the reduction of the number of iterations and also in measuring the deviation of the preconditioned operator from the identity.