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Impact of mixed precision and storage layout on additive Schwarz smoothers

Please always quote using this URN: urn:nbn:de:0297-zib-71305
  • The growing discrepancy between CPU computing power and memory bandwidth drives more and more numerical algorithms into a bandwidth- bound regime. One example is the overlapping Schwarz smoother, a highly effective building block for iterative multigrid solution of elliptic equations with higher order finite elements. Two options of reducing the required memory bandwidth are sparsity exploiting storage layouts and representing matrix entries with reduced precision in floating point or fixed point format. We investigate the impact of several options on storage demand and contraction rate, both analytically in the context of subspace correction methods and numerically at an example of solid mechanics. Both perspectives agree on the favourite scheme: fixed point representation of Cholesky factors in nested dissection storage.

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Author:Jakob Schneck, Martin WeiserORCiD, Florian WendeORCiD
Document Type:ZIB-Report
Tag:higher order finite elements; mixed precision; overlapping Schwarz smoother
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M55 Multigrid methods; domain decomposition
65-XX NUMERICAL ANALYSIS / 65Yxx Computer aspects of numerical algorithms / 65Y10 Algorithms for specific classes of architectures
65-XX NUMERICAL ANALYSIS / 65Yxx Computer aspects of numerical algorithms / 65Y20 Complexity and performance of numerical algorithms [See also 68Q25]
Date of first Publication:2019/01/09
Series (Serial Number):ZIB-Report (18-62)
Published in:accepted for Numerical Linear Algebra with Applications
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