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Efficient Algorithms for the Line-SIAC Filter

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Abstract

Visualizing high-order finite element simulation data using current visualization tools has many challenges: discontinuities at element boundaries, interpolating artifacts, and evaluating derived quantities. These challenges have been addressed by postprocessing the simulation data using the L-SIAC filter. However, the time required to postprocess using this filter needs to be addressed to enable using it on large datasets. In this work, we introduce an efficient technique to speed-up the L-SIAC filter and alternate ways to gain further speed-up at the cost of accuracy. This method is also ideal to postprocess at regularly spaced locations, which would be suitable for standard visualization software. Our results show that our method can achieve up to two orders of magnitude speed-up as compared to our interpretation of the technique presented in Docampo-Sánchez (SIAM J Sci Comput 39(5):A2179–A2200, 2017).

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References

  1. Docampo-Sánchez, J., Ryan, J.K., Mirzargar, M., Kirby, R.M.: Multi-dimensional filtering: reducing the dimension through rotation. SIAM J. Sci. Comput. 39(5), A2179–A2200 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bramble, J.H., Schatz, A.H.: Higher order local accuracy by averaging in the finite element method. Math. Comput. 31(137), 94–111 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cockburn, B., Luskin, M., Shu, C.-W., Süli, E.: Post-processing of Galerkin methods for hyperbolic problems. In: Discontinuous Galerkin Methods, pp. 291–300. Springer, Berlin, Heidelberg (2000)

  4. Cockburn, B., Luskin, M., Shu, C.-W., Süli, E.: Enhanced accuracy by post-processing for finite element methods for hyperbolic equations. Math. Comput. 72(242), 577–606 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. Mirzaee, H., Ryan, J.K., Kirby, R.M.: Efficient implementation of smoothness-increasing accuracy-conserving (SIAC) filters for discontinuous Galerkin solutions. J. Sci. Comput. 52(1), 85–112 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. Mirzaee, H., King, J., Ryan, J.K., Kirby, R.M.: Smoothness-increasing accuracy-conserving filters for discontinuous Galerkin solutions over unstructured triangular meshes. SIAM J. Sci. Comput. 35(1), A212–A230 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  7. Mirzaee, H., Ji, L., Ryan, J.K., Kirby, R.M.: Smoothness-increasing accuracy-conserving (SIAC) postprocessing for discontinuous Galerkin solutions over structured triangular meshes. SIAM J. Numer. Anal. 49(5), 1899–1920 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Mirzaee, H., Ryan, J.K., Kirby, R.M.: Smoothness-increasing accuracy-conserving (SIAC) filters for discontinuous Galerkin solutions: application to structured tetrahedral meshes. J. Sci. Comput. 58(3), 690–704 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  9. King, J., Mirzaee, H., Ryan, J.K., Kirby, R.M.: Smoothness-increasing accuracy-conserving (SIAC) filtering for discontinuous Galerkin solutions: improved errors versus higher-order accuracy. J. Sci. Comput. 53(1), 129–149 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Mirzaee, H., Ryan, J.K., Kirby, R.M.: Quantification of errors introduced in the numerical approximation and implementation of smoothness-increasing accuracy conserving (SIAC) filtering of discontinuous Galerkin (dG) fields. J. Sci. Comput. 45(1–3), 447–470 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Mirzargar, M., Jallepalli, A., Ryan, J.K., Kirby, R.M.: Hexagonal smoothness-increasing accuracy-conserving filtering. J. Sci. Comput. 73(2–3), 1072–1093 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  12. Steffen, M., Curtis, S., Kirby, R.M., Ryan, J.K.: Investigation of smoothness-increasing accuracy-conserving filters for improving streamline integration through discontinuous fields. IEEE Trans. Vis. Comput. Graph. 14(3), 680–692 (2008)

    Article  Google Scholar 

  13. Jallepalli, A., Docampo-Sánchez, J., Ryan, J.K., Haimes, R., Kirby, R.M.: On the treatment of field quantities and elemental continuity in FEM solutions. IEEE Trans. Vis. Comput. Graph. 24(1), 903–912 (2017)

    Article  Google Scholar 

  14. Jallepalli, A., Haimes, R., Kirby, R.M.: Adaptive characteristic length for L-SIAC filtering of FEM data. J. Sci. Comput. (2018). https://doi.org/10.1007/s10915-018-0868-6

  15. Nelson, B., Liu, E., Haimes, R., Kirby, R.M.: ElVis: a system for the accurate and interactive visualization of high-order finite element solutions. IEEE Trans. Vis. Comput. Graph. 18(12), 2325–2334 (2012)

    Article  Google Scholar 

  16. Nelson, B., Kirby, R.M.: Ray-tracing polymorphic multidomain spectral/hp elements for isosurface rendering. IEEE Trans. Vis. Comput. Graph. 12(1), 114–125 (2006)

    Article  Google Scholar 

  17. Nelson, B., Kirby, R.M., Haimes, R.: Gpu-based interactive cut-surface extraction from high-order finite element fields. IEEE Trans. Vis. Comput. Graph. 17, 1803–1811 (2011)

    Article  Google Scholar 

  18. Loseille, A., Feuillet, R.: Vizir: high-order mesh and solution visualization using opengl 4.0 graphic pipeline. In: 2018 AIAA Aerospace Sciences Meeting, p. 1174 (2018)

  19. Squillacote, A.: The Paraview Guide. Kitware, Inc., ParaView, vol. 3 (2008)

  20. Bellevue, W.: Tecplot User’s Manual. Amtec Engineering Inc, New Plymouth (2003)

    Google Scholar 

  21. Light, I.: Fieldview reference manual, software version, vol. 11 (2006)

  22. Scheinerman, E.: Mathematics: A Discrete Introduction. Nelson Education, Toronto (2012)

    MATH  Google Scholar 

  23. Moxey, D., Sastry, S.P., Kirby, R.M.: Interpolation error bounds for curvilinear finite elements and their implications on adaptive mesh refinement. J. Sci. Comput. 78(2), 1045–1062 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  24. Nelson, B., Kirby, R.M., Haimes, R.: Gpu-based volume visualization from high-order finite element fields. IEEE Trans. Vis. Comput. Graph. 20, 70–83 (2014)

    Article  Google Scholar 

  25. Cantwell, C.D., Moxey, D., Comerford, A., Bolis, A., Rocco, G., Mengaldo, G., De Grazia, D., Yakovlev, S., Lombard, J.-E., Ekelschot, D., Jordi, B., Xu, H., Mohamied, Y., Eskilsson, C., Nelson, B., Vos, P., Biotto, C., Kirby, R.M., Sherwin, S.J.: Nektar++ : an open-source spectral/hp element framework. Comput. Phys. Commun. 192, 205–219 (2015)

    Article  MATH  Google Scholar 

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Acknowledgements

The authors wish to thank Professor Spencer Sherwin (Imperial College London, UK), and the Nektar++ [25] Group for helpful discussions. We also acknowledge Mr. Bob Haimes (MIT), which whom our collaborations on visualization motived this work. The authors acknowledge support from ARO W911NF-15-1-0222 (Program Manager Dr. Mike Coyle).

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Correspondence to Ashok Jallepalli.

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Jallepalli, A., Kirby, R.M. Efficient Algorithms for the Line-SIAC Filter. J Sci Comput 80, 743–761 (2019). https://doi.org/10.1007/s10915-019-00954-x

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