×

Efficient algorithms for the line-SIAC filter. (English) Zbl 1422.65260

Summary: 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 [J. Docampo-Sánchez et al., SIAM J. Sci. Comput. 39, No. 5, A2179–A2200 (2017; Zbl 1448.65155)].

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65D32 Numerical quadrature and cubature formulas
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)

Citations:

Zbl 1448.65155
PDFBibTeX XMLCite
Full Text: DOI

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) · Zbl 1448.65155 · doi:10.1137/16M1097845
[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) · Zbl 0353.65064 · doi:10.1090/S0025-5718-1977-0431744-9
[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) · Zbl 0946.65085
[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) · Zbl 1015.65049 · doi:10.1090/S0025-5718-02-01464-3
[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) · Zbl 1255.65176 · doi:10.1007/s10915-011-9535-x
[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) · Zbl 1264.65162 · doi:10.1137/120874059
[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) · Zbl 1269.65100 · doi:10.1137/110830678
[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) · Zbl 1301.65107 · doi:10.1007/s10915-013-9748-2
[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) · Zbl 1254.65106 · doi:10.1007/s10915-012-9593-8
[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) · Zbl 1203.65186 · doi:10.1007/s10915-009-9342-9
[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) · Zbl 1381.65083 · doi:10.1007/s10915-017-0517-5
[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) · doi:10.1109/TVCG.2008.9
[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) · doi:10.1109/TVCG.2017.2744058
[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 · Zbl 1444.65067
[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) · doi:10.1109/TVCG.2012.218
[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) · doi:10.1109/TVCG.2006.12
[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) · doi:10.1109/TVCG.2011.206
[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)
[21] Light, I.: Fieldview reference manual, software version, vol. 11 (2006)
[22] Scheinerman, E.: Mathematics: A Discrete Introduction. Nelson Education, Toronto (2012) · Zbl 1329.00005
[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) · Zbl 1417.65207 · doi:10.1007/s10915-018-0795-6
[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) · doi:10.1109/TVCG.2013.96
[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) · Zbl 1380.65465 · doi:10.1016/j.cpc.2015.02.008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.