Matthias Grajewski

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The first part of this paper surveys co-processor approaches for commodity based clusters in general, not only with respect to raw performance, but also in view of their system integration and power consumption. We then extend previous work on a small GPU cluster by exploring the heterogeneous hardware approach for a large-scale system with up to 160 nodes.(More)
Among a variety of grid deformation methods, the method proposed by Liao [4, 7, 17] seems to be one of the most favourables. In this article, we introduce a generalisation of Liao's method which allows for generating a desired mesh size distribution for quite arbitrary grids without giving rise to mesh tangling. Furthermore, we tackle the efficient(More)
Among a variety of grid deformation methods, the method proposed by Liao [4, 6, 18] is one of the most favourables, because it prevents mesh tangling and offers precise control over the element volumes. Its numerical realisation only requires solving a Poisson problem and a system of fully decoupled initial value problems. Many other deformation methods in(More)
Recently, we introduced and mathematically analysed a new method for grid deformation [15] we call basic deformation method (BDM) here. It generalises the method proposed by Liao [4,6,19]. In this article, we employ the BDM as core of a new mul-tilevel deformation method (MDM) which leads to vast improvements regarding robustness, accuracy and speed. We(More)
After a short introduction of a new nonconforming linear finite element on quadri-laterals recently developed by Park, we derive a dual weighted residual-based a posteriori error estimator (in the sense of Becker and Rannacher) for this finite element. By computing a corresponding dual solution we estimate the error with respect to a given target error(More)
Processor technology is still dramatically advancing and promises further enormous improvements in processing data for the next decade. On the other hand, much lower advances in moving data are expected such that the efficiency of many numerical software tools for Partial Differential Equations (PDEs) is restricted by the cost for memory access. In this(More)
Starting with a short introduction of the new nonconforming linear quadrilateral˜P 1-finite element which has been recently proposed by Park ([13, 14]), we examine in detail the numerical behaviour of this element with special emphasis on the treatment of Dirichlet boundary conditions, efficient matrix assembly, solver aspects and the use as Stokes element(More)
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