Article

Article title DYNAMICAL STRESS-STRAIN SIMULATION SPEEDUP USING SIMD INSTRUCTIONS
Authors V.V. Getmanskiy, E.O. Movchan, A.E. Andreev
Section SECTION II. MATHEMATICAL AND SOFTWARE OF SUPERCOMPUTERS
Month, Year 11, 2016 @en
Index UDC 004.272.32, 519.683.4, 519.683.8
DOI 10.18522/2311-3103-2016-11-2739
Abstract One way to speedup a multibody system dynamics simulation by code optimization for CPU architecture with vector registers is considered. The problem is up to date because of necessity to perform a lot of computations in a short amount of time. Mathematical formulation of problem and computational algorithm are described. The efficient code development for dynamic stress-strain solver for bodies in complex mechanism is proposed. The code runs on processors supporting SIMD operations of SSE, AVX, FMA and KNC (Xeon Phi Knights Corner) instruction set exten-sions. The discrete elements method is used as one of the implementations of multibody system dynamics simulation. The most computational expensive parts of the code are right-hand side calculation using 3-dimensional matrix-vector transformations, Euler angles and rotation matrices calculation, numerical integration using Runge-Kutta 4-th order method. Computational algorithm has a limited scalability in case of using parallel computing because of strong data dependency between parallel code branches. Therefore the optimization of code is an important study for achieving speedup of computations. Special data format for storing matrices and vectors in memory and efficient vectorization of matrix-vector operations is considered. Block multiplication of matrices and vectors with greater dimension than the vector register length is developed. In case of dimension of matrices and vectors lower than vector register length (single precision floating point data for AVX and double precision for KNC) special microalgorithms for packing several matrix rows and vectors with elements permutation are developed. The microalgorithms are implemented using intrinsic functions for each vector instructions set. Speedup of up to 3 times is achieved using vectorization. The computation time of intrinsic-implemented algorithm is compared with compiler auto-vectorization feature. The microalgorithms are implemented using intrinsic functions for each vector instructions set. Speedup of up to 3 times is achieved using vectorization. The computation time of intrinsic-implemented algorithm is compared with compiler auto-vectorization feature.

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Keywords Auto-vectorization; code optimization; intrinsic; vector registers; multibody dynamics; SIMD.
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