Abstract
A common problem arising in expanding front simulations is to restore the signed distance field property of a discretized domain (i.e., a mesh), by calculating the minimum distance of mesh points to an interface. This problem is referred to as re-distancing and a widely used method for its solution is the fast marching method (FMM). In many cases, a particular high accuracy in specific regions around the interface is required. There, meshes with a finer resolution are defined in the regions of interest, enabling the problem to be solved locally with a higher accuracy. Additionally, this gives rise to coarse-grained parallelization, as such meshes can be re-distanced in parallel. An efficient parallelization approach, however, has to deal with interface-sharing meshes, load-balancing issues, and must offer reasonable parallel efficiency for narrow band and full band re-distancing. We present a parallel multi-mesh FMM to tackle these challenges: Interface-sharing meshes are resolved using a synchronized data exchanges strategy. Parallelization is introduced by applying a pool of tasks concept, implemented using OpenMP tasks. Meshes are processed by OpenMP tasks as soon as threads become available, efficiently balancing out the computational load of unequally sized meshes over the entire computation. Our investigations cover parallel performance of full and narrow band re-distancing. The resulting algorithm shows a good parallel efficiency, if the problem consists of significantly more meshes than the available processor cores.
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References
Breuß, M., Cristiani, E., Gwosdek, P., Vogel, O.: An adaptive domain-decomposition technique for parallelization of the fast marching method. Appl. Math. Comput. 218(1), 32–44 (2011). https://doi.org/10.1016/j.amc.2011.05.041
Chacon, A., Vladimirsky, A.: Fast two-scale methods for Eikonal equations. SIAM J. Sci. Comput. 34(2), A547–A578 (2012). https://doi.org/10.1137/10080909X
Chacon, A., Vladimirsky, A.: A parallel two-scale method for Eikonal equations. SIAM J. Sci. Comput. 37(1), A156–A180 (2015). https://doi.org/10.1137/12088197X
Diamantopoulos, G., Weinbub, J., Hössinger, A., Selberherr, S.: Evaluation of the shared-memory parallel fast marching method for re-distancing problems. In: Proceedings of the 17th International Conference on Computational Science and Its Applications (ICCSA), pp. 1–8. https://doi.org/10.1109/ICCSA.2017.7999648 (2017)
Dijkstra, E.W.: A note on two problems in connexion with graphs. Numer. Math. 1(1), 269–271 (1959). https://doi.org/10.1007/BF01386390
Herrmann, M.: A domain decomposition parallelization of the fast marching method. In: Anual Research Briefs, pp. 213–225. Center for Turbulence Research, Stanford University (2003)
Jeong, W.K., Whitaker, R.T.: A fast iterative method for Eikonal equations. SIAM J. Sci. Comput. 30(5), 2512–2534 (2008). https://doi.org/10.1137/060670298
Manstetten, P.: Efficient Flux Calculations for Topography Simulation. Ph.D. thesis, TU Wien (2018). http://www.iue.tuwien.ac.at/phd/manstetten/
Rouy, E., Tourin, A.: A viscosity solutions approach to shape-from-shading. SIAM J. Numer. Anal. 29(3), 867–884 (1992). https://doi.org/10.1137/0729053
Sethian, J.A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science, 2nd edn. Cambridge University Press (1999)
Weinbub, J., Hössinger, A.: Comparison of the parallel fast marching method, the fast iterative method, and the parallel semi-ordered fast iterative method. Procedia Comput. Sci. 80, 2271–2275 (2016). https://doi.org/10.1016/j.procs.2016.05.408
Weinbub, J., Hössinger, A.: Shared-memory parallelization of the fast marching method using an overlapping domain-decomposition approach. In: Proceedings of the 24th High Performance Computing Symposium, pp. 18:1–18:8. https://doi.org/10.22360/SpringSim.2016.HPC.052 (2016)
Yang, J., Stern, F.: A highly scalable massively parallel fast marching method for the Eikonal equation. J. Comput. Phys. 332, 333–362 (2017). https://doi.org/10.1016/j.jcp.2016.12.012
Zhao, H.: A fast sweeping method for Eikonal equations. Math. Comput. 74 (250), 603–627 (2005). https://doi.org/10.1090/S0025-5718-04-01678-3
Zhao, H.: Parallel implementations of the fast sweeping method. J. Comput. Math. 25(4), 421–429 (2007). https://www.jstor.org/stable/43693378
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The financial support by the Austrian Federal Ministry for Digital and Economic Affairs and the National Foundation for Research, Technology and Development is gratefully acknowledged. The computational results presented have been achieved using the Vienna Scientific Cluster (VSC).
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Communicated by: Pavel Solin
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Diamantopoulos, G., Hössinger, A., Selberherr, S. et al. A shared memory parallel multi-mesh fast marching method for re-distancing. Adv Comput Math 45, 2029–2045 (2019). https://doi.org/10.1007/s10444-019-09683-z
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DOI: https://doi.org/10.1007/s10444-019-09683-z