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Published in:
2021 | OriginalPaper | Chapter
Strategies for the Vectorized Block Conjugate Gradients Method
Authors : Nils-Arne Dreier, Christian Engwer
Published in: Numerical Mathematics and Advanced Applications ENUMATH 2019
Publisher: Springer International Publishing
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Abstract
Block Krylov methods have recently gained a lot of attraction. Due to their increased arithmetic intensity they offer a promising way to improve performance on modern hardware. Recently Frommer et al. (Electron Trans Numer Anal 47:100–126, 2017). presented a block Krylov framework that combines the advantages of block Krylov methods and data parallel methods. We review this framework and apply it on the Block Conjugate Gradients method, to solve linear systems with multiple right hand sides. In this course we consider challenges that occur on modern hardware, like a limited memory bandwidth, the use of SIMD instructions and the communication overhead. We present a performance model to predict the efficiency of different Block CG variants and compare these with experimental numerical results.