Advances in Computational Mathematics

, Volume 45, Issue 4, pp 2029–2045 | Cite as

A shared memory parallel multi-mesh fast marching method for re-distancing

  • Georgios DiamantopoulosEmail author
  • Andreas Hössinger
  • Siegfried Selberherr
  • Josef Weinbub


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.


Fast marching method Shared memory parallelism Eikonal equation Re-distancing 

Mathematics Subject Classification (2010)

68W10 65Y05 65Y10 65Y20 


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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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Georgios Diamantopoulos
    • 1
    Email author
  • Andreas Hössinger
    • 2
  • Siegfried Selberherr
    • 3
  • Josef Weinbub
    • 1
  1. 1.Christian Doppler Laboratory for High Performance TCAD, Institute for MicroelectronicsTU WienViennaAustria
  2. 2.Silvaco Europe Ltd.St IvesUK
  3. 3.Institute for MicroelectronicsTU WienViennaAustria

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