Journal
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
Volume 96, Issue -, Pages 194-208Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.enganabound.2018.08.015
Keywords
Boundary element method; Quadrature; SIMD; Vectorization; Intel Xeon Phi; Many-core
Funding
- Ministry of Education, Youth and Sports [7AMB17AT028]
- OeAD [CZ 16/2017]
- Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPU II) project 'IT4Innovations excellence in science' [LQ1602]
- Large Infrastructures for Research, Experimental Development and Innovations project 'IT4Innovations National Super computing Center' [LM2015070]
- VSB - Technical University of Ostrava [SP2017/165]
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In this paper, we describe an efficient analytic evaluation of boundary integral operators. Firstly, we concentrate on a novel approach based on the simultaneous evaluation of all three linear shape functions defined on a boundary triangle. This results in a speedup of 2.35-3.15 times compared to the old approach of separate evaluations. In the second part we comment on the OpenMP parallelized and vectorized implementation of the suggested formulae. The employed code optimizations include techniques such as data alignment and padding, array-of-structures to structure-of-arrays data transformation, or unit-strided memory accesses. The presented scalability results, with respect both to the number of threads employed and the width of the SIMD register obtained on an Intel (R) Xeon (TM) processor and two generations of the Intel (R) Xeon Phi (TM) family (co)processors, validate the performed optimizations and show that vectorization needs to be an inherent part of modern scientific codes.
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