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We propose an appropriate and efficient multiresolution visualization method for piecewise higher order polynomial data on locally refined computational grids. Given some suitable error indicators, we efficiently extract a continuous hpadaptive projection with respect to any prescribed threshold value for the visual error. This projection can then be processed by various local rendering methods, e...
In contrast to the existing plethora of adaptive numerical methods for differential and integro-differential equations, there seems to be a shortage of adaptive methods for purely integral equations with weakly singular kernels, such as the first kind Abel equation. In order to make up this deficiency, an adaptive procedure based on the product-integration method of Huber is developed in this work...
In the previous work of this author (Bieniasz in Computing 83:25–39, 2008) an adaptive numerical method for solving the first kind Abel integral equation was described. It was assumed that the starting value of the solution was known and equal zero. This is a frequent situation in some applications of the Abel equation (for example in electrochemistry), but in general the starting solution value is...
Numerical methods for weakly singular Volterra integral equations with non-linear dependencies between unknowns and their integrals, are almost non-existent in the literature. In the present work an adaptive Huber method for such equations is proposed, by extending the method previously formulated for the first kind Abel equations. The method is tested on example integral equations involving integrals...
Starting from an abstract mathematical notion of discrete function spaces and operators, we derive a general abstraction for a large class of grid-based discretization schemes for stationary and instationary partial differential equations. Special emphasis is put on concepts for local adaptivity and parallelization with dynamic load balancing. The concepts are based on a corresponding abstract definition...
Multi-policy resource management have been considered as an efficient methodology for delivering ready-to-use media-optimized applications in Software-Defined Networks (SDNs). Prioritized flow scheduling ensures high-speed communication in SDNs under large-scale distribution, heterogeneity of network resources, and exponential distribution of the flows granularity. The effectiveness of priority-based...
In the previous work of this author (Bieniasz in Computing 83:25–39, 2008) an adaptive numerical method for solving the first kind Abel integral equation was described. It was assumed that the starting value of the solution was known and equal zero. This is a frequent situation in some applications of the Abel equation (for example in electrochemistry), but in general the starting solution value is...
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