A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

Non-constructive interval simulation of dynamic systems

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A New Walk on Equations Monte Carlo Method for Linear Algebraic Problems

International audienceA new Walk on Equations (WE) Monte Carlo algorithm for Linear Algebra (LA) problem is proposed and studied. This algorithm relies on a non-discounted sum of an absorbed random walk. It can be applied for either real or complex matrices. Several techniques like simultaneous scoring or the sequential Monte Carlo method are applied to improve the basic algorithm. Numerical tests are performed on examples with matrices of different size and on systems coming from various applications. Comparisons with standard deterministic or Monte Carlo algorithms are also done

Algebraic Multigrid for Disordered Systems and Lattice Gauge Theories

The construction of multigrid operators for disordered linear lattice operators, in particular the fermion matrix in lattice gauge theories, by means of algebraic multigrid and block LU decomposition is discussed. In this formalism, the effective coarse-grid operator is obtained as the Schur complement of the original matrix. An optimal approximation to it is found by a numerical optimization procedure akin to Monte Carlo renormalization, resulting in a generalized (gauge-path dependent) stencil that is easily evaluated for a given disorder field. Applications to preconditioning and relaxation methods are investigated.Comment: 43 pages, 14 figures, revtex4 styl

The hybrid grid implemented DSMC method used in 2D triangular micro cavity flows

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.In this study a new hybrid grid is implemented in a 2D DSMC solver to be used in 2D triangular micro cavity flows. Currently DSMC is the prominent method to analyze micro scale gas flows which are rarefied. Because of the computational cost, DSMC solvers are generally used in rarefied gas conditions in which continuum based solvers are useless. If the efficiency of DSMC solvers is improved, the application range of these solvers can be increased further where the continuum based solvers dominate. Indexing the particles according to their cells is one of the main steps in the DSMC method. Either the particles are traced cell-by-cell along their trajectories or coordinate transformation techniques are used in this step. The first option requires complex trigonometric operations and search algorithms which are computationally expensive. But it can be used in both structured and unstructured grids. Although the second option is computationally more efficient, it demands specially tailored structured grids which are more geometry dependent compared to the unstructured grids. Here it is shown that a novel hybrid grid structure can be used successfully in 2D DSMC solver to analyze triangular shaped lid-driven micro cavity flows. Hybrid grids used in this study are much less dependent of the geometry like unstructured grids. Additionally, hybrid grids like structured grids facilitate coordinate transformation techniques in order to increase the efficiency of the particle indexing step in the DSMC method