OpenMP versus MPI for PDE solvers based on regular sparse numerical operators

Nordén, Markus; Holmgren, Sverker; Thuné, Michael

doi:10.1016/j.future.2003.09.004

Cited by 8 publications

(2 citation statements)

References 9 publications

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“…Finally, good scalability is achieved on two cores but this quickly degrades as the core count increases. This is likely to be related to the non-optimal data placement in Non-Uniform Memory Access architectures [16]. This issue will be addressed in the future.…”

Section: Parallel Performancementioning

confidence: 98%

A parallel compact-TVD method for compressible fluid dynamics employing shared and distributed-memory paradigms

2011

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A novel multi-block compact-TVD finite difference method for the simulation of compressible flows is presented. The method combines distributed and shared-memory paradigms to take advantage of the configuration of modern supercomputers that host many cores per shared-memory node. In our approach a domain decomposition technique is applied to a compact scheme using explicit flux formulas at block interfaces. This method offers great improvement in performance over earlier parallel compact methods that rely on the parallel solution of a linear system. A test case is presented to assess the accuracy and parallel performance of the new method

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Section: Parallel Performancementioning

confidence: 98%

A parallel compact-TVD method for compressible fluid dynamics employing shared and distributed-memory paradigms

2011

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“…In Wu and Zou (2003), the convergence speed for multipoint one-sided upwind schemes using time-lagging interface conditions for parallel computation were analyzed for the Euler equations in gas dynamics. In Nordén et al . (2002), two parallel programming models based on OpenMP and MPI paradigms were compared for solving the Euler equations in the context of fluid flow using finite differences schemes.…”

Section: Introductionmentioning

confidence: 99%

A parallel wavelet adaptive WENO scheme for 2D conservation laws

Schmidt

Kozakevicius

Jakobsson

2017

HFF

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Purpose - The current work aims to present a parallel code using the open multi-processing (OpenMP) programming model for an adaptive multi-resolution high-order finite difference scheme for solving 2D conservation laws, comparing efficiencies obtained with a previousmessage passing interface formulation for the same serial scheme and considering the same type of 2D formulations laws. Design/methodology/approach - The serial version of the code is naturally suitable for parallelization because the spatial operator formulation is based on a splitting scheme per direction for which the flux components are numerically computed by a Lax-Friedrichs factorization independently for each row or column. High-order approximations for numerical fluxes are computed by the third-order essentially non-oscillatory (ENO) and fifth-order weighted essentially non-oscillatory (WENO) interpolation schemes, assuming sparse grids in each direction. The grid adaptivity is obtained by a cubic interpolating wavelet transform applied in each space dimension, associated to a threshold operator. Time is evolved by a third order TVD Runge-Kutta method. Findings - The parallel formulation is implemented automatically at compiling time by the OpenMP library routines, being virtually transparent to the programmer. This over simplifies any concerns about managing and/ or updating the adaptive grid when compared to what is necessary to be done when other parallel approaches are considered. Numerical simulations results and the large speedups obtained for the Euler equations in gas dynamics highlight the efficiency of the OpenMP approach. Research limitations/implications - The resulting speedups reflect the effectiveness of the OpenMP approach but are, to a large extension, limited by the hardware used (2 E5-2620 Intel Xeon processors, 6 cores, 2 threads/core, hyper-threading enabled). As the demand for OpenMP threads increases, the code starts to make explicit use of the second logical thread available in each E5-2620 processor core and efficiency drops. The speedup peak is reached near the possible maximum (24) at about 22, 23 threads. This peak reflects the hardware configuration and the true software limit should be located way beyond this value. Practical implications - So far no attempts have been made to parallelize other possible code segments (for instance, the ENO|-WENO-TVD code lines that process the different data components which could potentially push the speed up limit to higher values even further. The fact that the speedup peak is located close to the present hardware limit reflects the scalability properties of the OpenMP programming and of the splitting scheme as well. Consequently, it is likely that the speedup peak with the OpenMP approach for this kind of problem formulation will be close to the physical (and/or logical) limit of the hardware used. Social implications - This work is the result of a successful collaboration among researchers from two different institutions, one internationally well-known and with a long-term ...

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