A Black-Box Multigrid Preconditioner for the Biharmonic by Silvester D. J., Mihajlovic M. D. PDF

By Silvester D. J., Mihajlovic M. D.

We study the convergence features of a preconditioned Krylov subspace solver utilized to the linear structures bobbing up from low-order combined finite aspect approximation of the biharmonic challenge. the main function of our technique is that the preconditioning could be discovered utilizing any "black-box" multigrid solver designed for the discrete Dirichlet Laplacian operator. This results in preconditioned structures having an eigenvalue distribution including a tightly clustered set including a small variety of outliers. Numerical effects convey that the functionality of the technique is aggressive with that of specialised quickly new release equipment which were built within the context of biharmonic difficulties.

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Aided Geom. Design 20, pp. 319-341, 2003. Polyhedral Gauss Maps and Curvature Characterisation of Triangle Meshes 33 6. , Smooth approximation of polyhedral surfaces with respect to curvature measures. In: Global differential geometry, pp. 64-68, 1979. 7. Calladine, C. , Gaussian Curvature and Shell Structures, In: J. A. ), The Mathematics of Surfaces, pp. 179-196, University of Manchester, 1984. 8. Dyn N. , Optimising 3D triangulations using discrete curvature analysis. , and Schumaker, L. L. ), Mathematical Methods in CAGD, pp.

Alboul and G. Echeverria Fig. 5. Gauss images of the basic types of vertices: convex, saddle and mixed Fig. 6. A complex mixed vertex and its spherical indicatrix (left) and Gauss image (right) 4 Results—Examples of Curvature Visualisation Examples of Gauss map visualisations are given below. The display of the Gauss Map is done in two different views, or scenes, and is implemented using OpenGl. The left scene shows the model of the original object and, in the right scene, the areas for the Gauss Map are drawn on top of a sphere.

Stated succinctly, the problem is that of locating a mapping between the nodes of the graph and points in space. Once graph nodes have been mapped to points, then geometric methods can be used to characterise the original graph. Drawing the graph becomes the problem of joining the points, graph matching the problem of aligning them, and graphclustering the problem of characterising the point distribution using moments or variance measurements. In other words, by using the mapping the discrete problems of graph manipulation can be re-posed as computationally simpler geometric operations.

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A Black-Box Multigrid Preconditioner for the Biharmonic Equation by Silvester D. J., Mihajlovic M. D.


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