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|Title:||Optimizing the performance of the spectral/hp element method with collective linear algebra operations|
|Keywords:||Applied Mathematics; Mathematical Sciences;Engineering|
|Publisher:||Elsevier;Royal Academy Of Engineering|
|place:||Engineering & Physical Science Research Council (EPSRC);Engineering & Physical Science Research Council (E;Engineering & Physical Science Research Council (EPSRC);Engineering & Physical Science Research Council (E;Engineering & Physical Science Research Council (E|
|Description:||As computing hardware evolves, increasing core counts mean that memory bandwidth is becoming the deciding factor in attaining peak performance of numerical methods. High-order finite element methods, such as those implemented in the spectral/hp framework Nektar++, are particularly well-suited to this environment. Unlike low-order methods that typically utilize sparse storage, matrices representing high-order operators have greater density and richer structure. In this paper, we show how these qualities can be exploited to increase runtime performance on nodes that comprise a typical high-performance computing system, by amalgamating the action of key operators on multiple elements into a single, memorye!cient block. We investigate di↵erent strategies for achieving optimal performance across a range of polynomial orders and element types. As these strategies all depend on external factors such as BLAS implementation and the geometry of interest, we present a technique for automatically selecting the most e!cient strategy at runtime.|
|Type Of Material:||Other|
|Appears in Collections:||Faculty of Engineering|
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