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Computer Research and Modeling, 2018, Volume 10, Issue 5, Pages 667–678 (Mi crm678)  


Parallel implementation of the grid-characteristic method in the case of explicit contact boundaries

A. M. Ivanov, N. I. Khokhlov

Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, Moscow Region, 141701, Russia

Abstract: We consider an application of the Message Passing Interface (MPI) technology for parallelization of the program code which solves equation of the linear elasticity theory. The solution of this equation describes the propagation of elastic waves in demormable rigid bodies. The solution of such direct problem of seismic wave propagation is of interest in seismics and geophysics. Our implementation of solver uses grid-characteristic method to make simulations. We consider technique to reduce time of communication between MPI processes during the simulation. This is important when it is necessary to conduct modeling in complex problem formulations, and still maintain the high level of parallelism effectiveness, even when thousands of processes are used. A solution of the problem of effective communication is extremely important when several computational grids with arbirtrary geometry of contacts between them are used in the calculation. The complexity of this task increases if an independent distribution of the grid nodes between processes is allowed. In this paper, a generalized approach is developed for processing contact conditions in terms of nodes reinterpolation from a given section of one grid to a certain area of the second grid. An efficient way of parallelization and establishing effective interprocess communications is proposed. For provided example problems we provide wave fileds and seismograms for both 2D and 3D formulations. It is shown that the algorithm can be realized both on Cartesian and on structured (curvilinear) computational grids. The considered statements demonstrate the possibility of carrying out calculations taking into account the surface topographies and curvilinear geometry of curvilinear contacts between the geological layers. Application of curvilinear grids allows to obtain more accurate results than when calculating only using Cartesian grids. The resulting parallelization efficiency is almost 100% up to 4096 processes (we used 128 processes as a basis to find efficiency). With number of processes larger than 4096, an expected gradual decrease in efficiency is observed. The rate of decline is not great, so at 16384 processes the parallelization efficiency remains at 80%.

Keywords: MPI, parallel programming, grid-characteristic method, MPI, structured grids.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-07-00914
The reported study was funded by RFBR according to the research project No. 18-07-00914 A. This work has been carried out using computing resources of the federal collective usage center Complex for Simulation and Data Processing for Megascience Facilities at NRC “Kurchatov Institute”,


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UDC: 519.633
Received: 07.09.2018
Revised: 20.09.2018

Citation: A. M. Ivanov, N. I. Khokhlov, “Parallel implementation of the grid-characteristic method in the case of explicit contact boundaries”, Computer Research and Modeling, 10:5 (2018), 667–678

Citation in format AMSBIB
\by A.~M.~Ivanov, N.~I.~Khokhlov
\paper Parallel implementation of the grid-characteristic method in the case of explicit contact boundaries
\jour Computer Research and Modeling
\yr 2018
\vol 10
\issue 5
\pages 667--678

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