A cell vertex finite volume method for the solution of steady compressible turbulent flow problems on unstructured hybrid
meshes of tetrahedra, prisms, pyramids and hexahedra is described. These hybrid meshes are constructed by firstly discretising
the computational domain using tetrahedral elements and then by merging certain tetrahedra. A one equation turbulence model
is employed and the solution of the steady flow equations is obtained by explicit relaxation. The solution process is accelerated
by the addition of a multigrid method, in which the coarse meshes are generated by agglomeration, and by parallelisation.
The approach is shown to be effective for the simulation of a number of 3D flows of current practical interest.
Sponsored by The Research Council of Norway, project number 125676/410
Dedicated to the memory of Prof. Mike Crisfield, a respected colleague 相似文献
Based on the fact that 3-D model discretization by artificial could not always be successfully implemented especially for large-scaled problems when high accuracy and efficiency were required, a new adaptive multigrid finite element method was proposed. In this algorithm, a-posteriori error estimator was employed to generate adaptively refined mesh on a given initial mesh. On these iterative meshes, V-cycle based multigrid method was adopted to fast solve each linear equation with each initial iterative term interpolated from last mesh. With this error estimator, the unknowns were nearly optimally distributed on the final mesh which guaranteed the accuracy. The numerical results show that the multigrid solver is faster and more stable compared with ICCG solver. Meanwhile, the numerical results obtained from the final model discretization approximate the analytical solutions with maximal relative errors less than 1%, which remarkably validates this algorithm. 相似文献
We present a novel approach for extreme simplification of point set models, in the context of real-time rendering. Point sets
are often rendered using simple point primitives, such as oriented discs. However, this requires using many primitives to
render even moderately simple shapes. Often, one wishes to render a simplified model using only a few primitives, thus trading
accuracy for simplicity. For this goal, we propose a more complex primitive, called a splat, that is able to approximate larger and more complex surface areas than oriented discs. We construct our primitive by decomposing
the model into quasi-flat regions, using an efficient algebraic multigrid algorithm. Next, we encode these regions into splats
implemented as planar support polygons textured with color and transparency information and render the splats using a special
blending algorithm. Our approach combines the advantages of mesh-less point-based techniques with traditional polygon-based
techniques. We demonstrate our method on various models. 相似文献
The convergence analysis of multigrid methods for boundary element equations arising from negative-order pseudo-differential operators is quite different from the usual finite element multigrid analysis for elliptic partial differential equations. In this paper, we study the convergence of geometrical multigrid methods for solving large-scale, data-sparse boundary element equations. In particular, we investigate multigrid methods for \(\mathcal{H}\)-matrices arising from the adaptive cross approximation to the single layer potential operator. 相似文献
Parallel computers are having a profound impact on computational science. Recently highly parallel machines have taken the lead as the fastest supercomputers, a trend that is likely to accelerate in the future. We describe some of these new computers, and issues involved in using them. We present elliptic PDE solutions currently running at 3.8 gigaflops, and an atmospheric dynamics model running at 1.7 gigaflops, on a 65 536-processor computer.
One intrinsic disadvantage of a parallel machine is the need to perform inter-processor communication. It is important to ensure that such communication time is maintained at a small fraction of computation time. We analyze standard multigrid algorithms in two and three dimensions from this point of view, indicating that performance efficiencies in excess of 95% are attainable under suitable conditions on moderately parallel machines. We also demonstrate that such performance is not attainable for multigrid on massively parallel computers, as indicated by an example of poor multigrid efficiency on 65 536 processors. The fundamental difficulty is the inability to keep 65 536 processors busy when operating on very coarse grids.
Most algorithms used for implementing applications on parallel machines have been derived directly from algorithms designed for serial machines. The previously mentioned multigrid example indicates that such ‘parallelized’ algorithms may not always be optimal. Parallel machines open the possibility of finding totally new approaches to solving standard tasks—intrinsically parallel algorithms. In particular, we present a class of superconvergent multiple scale methods that were motivated directly by massevely parallel machines. These methods differ from standard multigrid methods in an intrinsic way, and allow all processors to be used at all times, even when processing on the coarsest grid levels. Their serial versions are not sensible algorithms. The idea that parallel hardware—the Connection Machine in this case—can lead to discovery of new mathematical algorithms was surprising for us. 相似文献
This paper informs about number-theoretical and geometrical estimates of worst-case bounds for quantization errors in calculating features such as moments, moment based features, or perimeters in image analysis, and about probability-theoretical estimates of error bounds (e.g. standard deviations) for such digital approximations. New estimates (with proofs) and a review of previously known results are provided. 相似文献