1. 1D. Giljohann / Nov, 2001 Mesh Decimation Algorithms for the Finite Element Method in Structural Dynamics Dietmar Giljohann FENET/NAFEMS Seminar “FEM in der Strukturdynamik” Wiesbaden 2001

2. 2 D. Giljohann / Nov, 2001 Overview What is Mesh Decimation using FEM/BEM? Algorithms Examples in Structural Dynamics Other Applications Summary

3. 3 D. Giljohann / Nov, 2001 Capabilities of Mesh Decimation Original linear mesh for multi-physics simulations Coarser mesh and quadr. element type Locally varying element lengths Multiple stages Coarser mesh

4. 4 D. Giljohann / Nov, 2001 Basic Principle of common Algorithms Remove triangles, beams and tetrahedra at vanishing edge Convert quads Move node B to node A Detect shortest edge

5. 5 D. Giljohann / Nov, 2001 Features of Mesh Decimation Algorithm This Mesh Decimation Algorithm removes current shortest edge of mesh promotes uniform edge lengths throughout the mesh retains material boundaries supports tetrahedra, beams, triangles, and quads supports linear & quadratic element types takes care of transitions to other mesh regions containing hexaeder, etc. contains mechanisms to preserve sharp corners & edges writes intermediate stages of mesh may produce a few distorted elements

6. 6 D. Giljohann / Nov, 2001 Rectangular Box: Structural Eigenfreq. 1.5 mm2.0 mm 3.0 mm4.0 mm 108mm x 100 mm x 81 mm, thickness 2 mm, material steel Calculation of the first 10 eigenfrequencies max. difference Eigenfreq. < 4 % total CPU time reduced by 74 % 47000 elements

7. 7 D. Giljohann / Nov, 2001 Happy Buddha: Structural eigenfrequencies 144 k nodes 22.4 k nodes 2000 mm Shell thickness 2 mm, material steel Eigenmodes and Eigenfrequencies are significantly different! Algorithm does not preserve the local curvature Do not trust in the visual appearance!

8. 8 D. Giljohann / Nov, 2001 Mirage: Coupled acoustic analysis Original mesh 3600 nodes Mesh decimation Min. edge length: 7 cm 550 nodes

9. 9 D. Giljohann / Nov, 2001 Mirage: Results of analysis CPU time Mesh Decimation: 7s, P3, 750 MHz, Win ME min. edge length increased from 0.3 cm to 7 cm max. difference of first 15 eigenfrequencies < 3% Total reduction of interior acoustic calculation times > 50% Mode 1: 78 HzMode 15: 310 Hz

10. 10 D. Giljohann / Nov, 2001 Moving acoustic source, M = 0.8 acoustic pressure wavelength in front of the source wavelength behind the source

11. 11 D. Giljohann / Nov, 2001 Summary & future research Mesh Decimation Algorithms for Structural Dynamics was presented Examples show features and current limits of the algorithm Future algorithm will closer look at local variation of curvature Applications in other areas of dynamics/acoustics were shown

12. 12 D. Giljohann / Nov, 2001 Mirage: Distribution of edge length

13. 13 D. Giljohann / Nov, 2001 calculate node to remove A ji B h 1A h 2A h 3A h 4A h 1B h 2B h 3B

14. 14 D. Giljohann / Nov, 2001 Move node B to A A ji B E 1 E 3 E 4 E 2

15. 15 D. Giljohann / Nov, 2001 after nodal transaction A ji E 1 E 3 E 4