Super linear speedup in a local parallel meshless solution of thermo-fluid problems

The performance of the parallel implementation of the local meshless numerical method in solving system of coupled partial differential equations is explored. Presented numerical approach makes the computation convenient for parallel implementation using OpenMP based parallelisation. The numerical experiments are performed on the de Vahl Davis natural convection case, with superlinear computational speedup regime identified. The phenomenon is further investigated through measurements of the central processing unit cache hit rates. It is demonstrated that the accumulation of L3 caches governs the superlinear speedup. Considering the presented analyses, basic rules for effective computation strategy regarding the multicore computations are suggested.

[1]  Luiz C. Wrobel,et al.  Applications in thermo-fluids and acoustics , 2002 .

[2]  Sophie Papst,et al.  Computational Methods For Fluid Dynamics , 2016 .

[3]  G. D. Davis.  Natural convection of air in a square cavity: A bench mark numerical solution , 1983 .

[4]  R. Trobec,et al.  Comparison of local weak and strong form meshless methods for 2-D diffusion equation , 2012 .

[5]  M. N. Özişik,et al.  Finite Difference Methods in Heat Transfer , 2017 .

[6]  Ching-Shyang Chen,et al.  Radial basis function collocation method solution of natural convection in porous media , 2004 .

[7]  Lucy T. Zhang,et al.  A Parallelized Meshfree Method with Boundary Enrichment for Large-Scale CFD , 2002 .

[8]  Roman Trobec,et al.  Computational complexity and parallelization of the meshless local Petrov-Galerkin method , 2009 .

[9]  Alain J. Kassab,et al.  Localized Meshless Modeling of Natural-Convective Viscous Flows , 2008 .

[10]  B. Šarler,et al.  Solution of a phase-field model for dissolution of primary particles in binary aluminum alloys by an r-adaptive mesh-free method , 2005 .

[11]  Satya N. Atluri,et al.  MESHLESS LOCAL PETROV-GALERKIN (MLPG) METHOD FOR CONVECTION DIFFUSION PROBLEMS , 2000 .

[12]  Roman Trobec,et al.  Meshless solution of a diffusion equation with parameter optimization and error analysis , 2008 .

[13]  B. Šarler,et al.  Meshless local radial basis function collocation method for convective‐diffusive solid‐liquid phase change problems , 2006 .

[14]  C. Hong,et al.  Computer Modelling of Heat and Fluid Flow in Materials Processing , 2019 .

[15]  Tn Venkatesh,et al.  Super-linear speed-up of a parallel multigrid Navier-Stokes solver on Flosolver , 2005 .

[16]  B. Šarler,et al.  H-Adaptive Local Radial Basis Function Collocation Meshless Method , 2011 .

[17]  P. Salagnac,et al.  Diffuse approximation method for solving natural convection in porous media , 1996 .

[18]  Guangming Yao,et al.  Assessment of global and local meshless methods based on collocation with radial basis functions for parabolic partial differential equations in three dimensions , 2012 .

[19]  Decheng Wan,et al.  A NEW BENCHMARK QUALITY SOLUTION FOR THE BUOYANCY-DRIVEN CAVITY BY DISCRETE SINGULAR CONVOLUTION , 2001 .

[20]  Marc Duflot,et al.  Meshless methods: A review and computer implementation aspects , 2008, Math. Comput. Simul..

[21]  Gregor Kosec,et al.  A Meshless Approach Towards Solution of Macrosegregation Phenomena , 2011 .

[22]  R. Franke.  Scattered data interpolation: tests of some methods , 1982 .

[23]  Gui-Rong Liu,et al.  An Introduction to Meshfree Methods and Their Programming , 2005 .

[24]  Arnaud G. Malan,et al.  An artificial compressibility CBS method for modelling heat transfer and fluid flow in heterogeneous porous materials , 2011 .

[25]  Enrico Nobile,et al.  Simulation of time-dependent flow in cavities with the additive-correction multigrid method, part I: Mathematical formulation , 1996 .

[26]  Hamou Sadat,et al.  A new meshless approach for three dimensional fluid flow and related heat transfer problems , 2012, 1809.02502.

[27]  Indra Vir Singh,et al.  Parallel implementation of the EFG Method for heat transfer and fluid flow problems , 2004 .

[28]  David Kaeli,et al.  Introduction to Parallel Programming , 2013 .

[29]  Hamou Sadat,et al.  Evaluation of high order versions of the diffuse approximate meshless method , 2007, Appl. Math. Comput..

[30]  Michel Bellet,et al.  Numerical modelling in materials science and engineering , 2002 .

[31]  B. Šarler,et al.  Weight Function Shape Parameter Optimization in Meshless Methods for Non-uniform Grids , 2007 .

[32]  Moncho Gómez-Gesteira,et al.  New multi-GPU implementation for smoothed particle hydrodynamics on heterogeneous clusters , 2013, Comput. Phys. Commun..

[33]  Adrian Bejan,et al.  The Ra-Pr domain of laminar natural convection in an enclosure heated from the side , 1991 .

[34]  Yu Zhang,et al.  PR OO Anatomy-based face reconstruction for animation using multi-layer deformation , 2004 .

[35]  Robert Vertnik,et al.  Meshfree explicit local radial basis function collocation method for diffusion problems , 2006, Comput. Math. Appl..

[36]  E. Kansa.  Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates , 1990 .

[37]  Gregor Kosec,et al.  Solution of thermo‐fluid problems by collocation with local pressure correction , 2008 .

[38]  Rohit Chandra,et al.  Parallel programming in openMP , 2000 .

[39]  S. C. Fan,et al.  Local multiquadric approximation for solving boundary value problems , 2003 .

[40]  Przemyslaw Stpiczynski,et al.  Book Review: Parallel Programming in OpenMP Helps Novices (A review of Parallel Programming in OpenMP by Rohit Chandra, Leonardo Dagum, Dave Kohr, Dror Maydan, Jeff McDonald, and Ramesh Menon) , 2002, IEEE Distributed Syst. Online.

[41]  R. Schaback,et al.  Direct Meshless Local Petrov-Galerkin (DMLPG) method: A generalized MLS approximation , 2013, 1303.3095.

[42]  Guirong Liu,et al.  A point interpolation meshless method based on radial basis functions , 2002 .

[43]  Enrico Nobile,et al.  SIMULATION OF TIME-DEPENDENT FLOW IN CAVITIES WITH THE ADDITIVE-CORRECTION MULTIGRID METHOD, PART II: APPLICATIONS , 1996 .