In this article, we propose an adaptive mesh-refining based on the multi-level algorithm and derive a unified a posteriori error estimate for a class of nonlinear problems. We have shown that the multi-level algorithm...
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In this article, we propose an adaptive mesh-refining based on the multi-level algorithm and derive a unified a posteriori error estimate for a class of nonlinear problems. We have shown that the multi-level algorithm on adaptive meshes retains quadratic convergence of Newton's method across different mesh levels, which is numerically validated. Our framework facilitates to use the general theory established for a linear problem associated with given nonlinear equations. In particular, existing a posteriori error estimates for the linear problem can be utilized to find reliable error estimators for the given nonlinear problem. As applications of our theory, we consider the pseudostress-velocity formulation of Navier-Stokes equations and the standard Galerkin formulation of semilinear elliptic equations. Reliable and efficient a posteriori error estimators for both approximations are derived. Finally, several numerical examples are presented to test the performance of the algorithm and validity of the theory developed.
Partitioning is a fundamental problem with applications to many areas including data mining, parellel processing and Very-large-scale integration （VLSI） design. An effective multi-level algorithm for bisecting graph...
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Partitioning is a fundamental problem with applications to many areas including data mining, parellel processing and Very-large-scale integration （VLSI） design. An effective multi-level algorithm for bisecting graph is proposed. During its coarsening phase, an improved matching approach based on the global information of the graph core is developed with its guidance function. During the refinement phase, the vertex gain is exploited as ant＇s heuristic information and a positive feedback method based on pheromone trails is used to find the global approximate bipartitioning. It is implemented with American National Standards Institute （ANSI） C and compared to MeTiS. The experimental evaluation shows that it performs well and produces encouraging solutions on 18 different graphs benchmarks.
We consider the solution of the convection-diffusion equation in two dimensions by various multi-level algorithms (MLAs). We study the convergence rate of the MLAs and the stability of the coarse-grid operators, depen...
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We consider the solution of the convection-diffusion equation in two dimensions by various multi-level algorithms (MLAs). We study the convergence rate of the MLAs and the stability of the coarse-grid operators, depending on the choice of artificial viscosity at the different levels. Four strategies are formulated and examined. A method to determine the convergence rate is described and applied to the MLAs, both in a problem with constant and in one with variable coefficients. As relaxation procedures the 7-point ILU and symmetric point Gauss–Seidel (SGS) methods are used.
This paper presents parallel algorithms for matrix-matrix multiplication which are built up from several algorithms in a multi-level structure. The upper level consists of Strassen's algorithm which is performed f...
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This paper presents parallel algorithms for matrix-matrix multiplication which are built up from several algorithms in a multi-level structure. The upper level consists of Strassen's algorithm which is performed for a predefined number of recursions. The number of recursions can be adapted to the specific execution platform. The intermediate level is performed by a parallel non-hierarchical algorithm and the lower level uses efficient one-processor implementations of matrix-matrix multiplication like BLAS or ATLAS. Both the number of recursions of Strassen's algorithm and the specific algorithms of the intermediate and lower level can be chosen so that a variety of different multi-level algorithms results. Each level of the multi-level algorithms is associated with a hierarchical partition of the set of available processors into disjoint subsets so that deeper levels of the algorithm employ smaller groups of processors in parallel. The algorithms are expressed in the multiprocessor task programming model and are coded with the runtime library Tlib. Performance experiments on several parallel platforms show that the multi-level algorithms can lead to significant performance gains. (C) 2008 Elsevier B.V. All rights reserved.
Computational fluid dynamic (CFD) models are ubiquitous in aerodynamic design. Variable-fidelity optimization algorithms have proven to be computationally efficient and therefore suitable to reduce high CPU-cost relat...
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Computational fluid dynamic (CFD) models are ubiquitous in aerodynamic design. Variable-fidelity optimization algorithms have proven to be computationally efficient and therefore suitable to reduce high CPU-cost related to the design process solely based on accurate CFD models. A convenient way of constructing the variable-fidelity models is by using the high-fidelity solver, but with a varying degree of discretization and reduced number of flow solver iterations. So far, selection of the appropriate parameters has only been guided by the designer experience. In this paper, an automated low- fidelity model selection technique is presented. By defining the problem as a constrained nonlinear optimization problem, suitable grid and flow solver parameters are obtained. Our approach is compared to conventional methods of generating a family of variable-fidelity models. Comparison of the standard and the proposed approaches in the context of aerodynamic design of a transonic airfoil indicates that the automated model generation can yield significant computational savings.
A parameter identification problem for the hydraulic properties of porous media is considered. Numerically, this inverse problem is solved by minimizing an output least-squares functional. The unknown hydraulic proper...
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A parameter identification problem for the hydraulic properties of porous media is considered. Numerically, this inverse problem is solved by minimizing an output least-squares functional. The unknown hydraulic properties which are nonlinear coefficients of a partial differential equation are approximated by spline functions. The identification is embedded into a multi-level algorithm and coupled with a linear sensitivity analysis to describe the ill-posedness of the inverse problem. (C) 2002 Elsevier Science B.V. All rights reserved.
String sorting is an important part of tasks such as building index data structures. Unfortunately, current string sorting algorithms do not scale to massively parallel distributed-memory machines since they either ha...
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ISBN:
(纸本)9798400704161
String sorting is an important part of tasks such as building index data structures. Unfortunately, current string sorting algorithms do not scale to massively parallel distributed-memory machines since they either have latency (at least) proportional to the number of processors.. or communicate the data a large number of times (at least logarithmic). We present practical and efficient algorithms for distributed-memory string sorting that scale to large p. Similar to state-of-the-art sorters for atomic objects, the algorithms have latency of about p(1/k) when allowing the data to be communicated k times. Experiments show good scaling behavior on a wide range of inputs on up to 49 152 cores. We achieve speedups of up to 5 over the current state-of-the-art distributed string sorting algorithms.
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