Conservative interpolation between volume meshes by local Galerkin projection

Computer Methods in Applied Mechanics and Engineering

Volumn 200, Issue 1-4, 2011, Pages 89-100

  Farrell, P E ^a   Maddison, J R ^b  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Conservation; Discontinuous Galerkin; Galerkin projection; Interpolation; Supermesh

Indexed keywords

COMPUTATIONAL PHYSICS; CONSERVATIVE INTERPOLATION; DISCONTINUOUS GALERKIN; GALERKIN PROJECTIONS; SUBOPTIMALITY; SUPERMESH; THREE DIMENSIONS;

INTERPOLATION;

GALERKIN METHODS;

EID: 78649635809     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2010.07.015     Document Type: Article

References (44)

1. F. Alauzet, M. Mehrenberger, P1-conservative solution interpolation on unstructured triangular meshes, Tech. Rep. RR-6804, INRIA Rocquencourt, Rocquencourt, Le Chesnay, France, 2009, http://hal.inria.fr/inria-00354509/en/.
2. Below A., De Loera J.A., Richter-Gebert J. The complexity of finding small triangulations of convex 3-polytopes. J. Algorithms 2004, 50(2):134-167.
3. Berger E.D., McKinley K.S., Blumofe R.D., Wilson P.R. Hoard: a scalable memory allocator for multithreaded applications. ACM SIGPLAN Notices 2000, 35(11):117-128.
4. Carstensen C. Clément Interpolation and Its Role in Adaptive Finite Element Error Control. Operator Theory: Advances and Applications 2006, vol. 168. Birkhäuser Basel, pp. 27-43 (Chapter 2).
5. Chazelle B. An optimal algorithm for intersecting three-dimensional convex polyhedra. SIAM J. Comput. 1992, 21(4):671-696.
6. Clément P. Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 1975, 9:77-84.
7. Cools R., Haegemans A. Algorithm 824: CUBPACK: a package for automatic cubature; framework description. ACM Trans. Math. Software 2003, 29(3):287-296.
8. Cotter C.J., Ham D.A., Pain C.C. A mixed discontinuous/continuous finite element pair for shallow-water ocean modelling. Ocean Model. 2009, 26(1-2):86-90.
9. Cotter C.J., Ham D.A., Pain C.C., Reich S. LBB stability of a mixed Galerkin finite element pair for fluid flow simulations. J. Comput. Phys. 2009, 228(2):336-348.
10. Davies D.R., Davies J.H., Hassan O., Morgan K., Nithiarasu P. Investigations into the applicability of adaptive finite element methods to two-dimensional infinite Prandtl number thermal and thermochemical convection. Geochem. Geophys. Geosyst. 2007, 8(5).
11. Eberly D.H. 3D Game Engine Design: A Practical Approach to Real-time Computer Graphics 2001, Morgan Kaufmann.
12. Edelsbrunner H., Preparata F.P., West D.B. Tetrahedrizing point sets in three dimensions. J. Symb. Comput. 1990, 10(3/4):335-348.
13. El Hraiech A., Borouchaki H., Villon P., Moreau L. Mechanical field interpolation. Proceedings of the Sixth International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Process 2005, 201-208. AIP, Detroit, Michigan. L.M. Smith, F. Pourboghrat, J. Cao, T.B. Stoughton, J.-W. Yoon, M.F. Shi, C.-T. Wang, L. Zhang (Eds.).
14. Farhat C., Lesoinne M., Tallec P.L. Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: momentum and energy conservation, optimal discretization and application to aeroelasticity. Comput. Methods Appl. Mech. Engrg. 1998, 157(1-2):95-114.
15. P.E. Farrell, Galerkin projection of discrete fields via supermesh construction, Ph.D. Thesis, Imperial College London, 2009.
16. Farrell P.E., Piggott M.D., Pain C.C., Gorman G.J., Wilson C.R.G. Conservative interpolation between unstructured meshes via supermesh construction. Comput. Methods Appl. Mech. Engrg. 2009, 198(33-36):2632-2642.
17. Formaggia L., Perotto S. Anisotropic error estimates for elliptic problems. Numer. Math. 2003, 94(1):67-92.
18. George P.L., Borouchaki H. Delaunay Triangulation and Meshing: Application to Finite Elements 1998, Hermes.
19. Geuzaine C., Meys B., Henrotte F., Dular P., Legros W. A Galerkin projection method for mixed finite elements. IEEE Trans. Magn. 1999, 35(3):1438-1441.
20. Geuzaine C., Remacle J.-F. Gmsh: a 3-D finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Numer. Methods Engrg. 2009, 79(11):1309-1331.
21. Guttman A. R-trees: a dynamic index structure for spatial searching. ACM SIGMOD Record 1984, 14(2):47-57.
22. Härtel C., Meiburg E., Necker F. Analysis and direct numerical simulation of the flow at a gravity-current head. Part I. Flow topology and front speed for slip and no-slip boundaries. J. Fluid Mech. 2000, 418(1):189-212.
23. Heinstein M.W., Laursen T.A. A three dimensional surface-to-surface projection algorithm for non-coincident domains. Commun. Numer. Methods Engrg. 2003, 19(6):421-432.
24. Jiao X., Heath M.T. Common-refinement-based data transfer between non-matching meshes in multiphysics simulations. Int. J. Numer. Methods Engrg. 2004, 61:2402-2427.
25. Jiao X., Heath M.T. Overlaying surface meshes, Part I: algorithms. Int. J. Comput. Geom. Appl. 2004, 14(6):379-402.
26. Leonard B.P. The ultimate conservative difference scheme applied to unsteady one-dimensional advection. Comput. Methods Appl. Mech. Engrg. 1991, 88(1):17-74.
27. J. Levon, P. Elie, Oprofile: a system profiler for Linux, 2009, http://oprofile.sourceforge.net.
28. Löhner R. Robust, vectorized search algorithms for interpolation on unstructured grids. J. Comput. Phys. 1995, 118(2):380-387.
29. Manolopoulos Y., Nanopoulos A., Papadopoulos A., Theodoridis Y. R-trees: Theory and Applications 2005, Springer.
30. Micheletti S., Perotto S. Reliability and efficiency of an anisotropic Zienkiewicz-Zhu error estimator. Comput. Methods Appl. Mech. Engrg. 2006, 195(9-12):799-835.
31. Mount D.M. Geometric intersection. Handbook of Discrete and Computational Geometry 1997, 615-630. CRC Press, Inc., Boca Raton, FL, USA. J.E. Goodman, J. O'Rourke (Eds.).
32. Özgökmen T.M., Iliescu T., Fischer P.F., Srinivasan A., Duan J. Large eddy simulation of stratified mixing in two-dimensional dam-break problem in a rectangular enclosed domain. Ocean Model. 2007, 16(1-2):106-140.
33. Pain C.C., Umpleby A.P., de Oliveira C.R.E., Goddard A.J.H. Tetrahedral mesh optimisation and adaptivity for steady-state and transient finite element calculations. Comput. Methods Appl. Mech. Engrg. 2001, 190(29-30):3771-3796.
34. Parent G., Dular P., Ducreux J.P., Piriou F. Using a Galerkin projection method for coupled problems. IEEE Trans. Magn. 2008, 44(6):830-833.
35. Peraire J., Vahdati M., Morgan K., Zienkiewicz O. Adaptive remeshing for compressible flow computations. J. Comput. Phys. 1987, 72(2):449-466.
36. Piggott M.D., Pain C.C., Gorman G.J., Power P.W., Goddard A.J.H. h, r, and hr adaptivity with applications in numerical ocean modelling. Ocean Model. 2005, 10(1-2):95-113.
37. Preparata F.P., Shamos M.I. Computational Geometry: An Introduction 1985, Springer. second ed.
38. Seidel R. Convex hull computations. Handbook of Discrete and Computational Geometry 2004, 495-512. Chapman & Hall/CRC. J.E. Goodman, J. O'Rourke (Eds.).
39. M.I. Shamos, D. Hoey, Geometric intersection problems, in: Proceedings of the 17th Annual Symposium on Foundations of Computer Science, 1976, pp. 208-215.
40. Si H., Gärtner K. Meshing piecewise linear complexes by constrained Delaunay tetrahedralizations. Proceedings of the 14th International Meshing Roundtable 2005, 147-163. Springer, San Diego, California. B.W. Hanks (Ed.).
41. Sutherland I.E., Hodgman G.W. Reentrant polygon clipping. Commun. ACM 1974, 17(1):32-42.
42. Sweby P.K. High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Numer. Anal. 1984, 21(5):995-1011.
43. Vasilevskii Y., Lipnikov K. An adaptive algorithm for quasioptimal mesh generation. Comput. Math. Math. Phys. 1999, 39(9):1468-1486.
44. C.R. Wilson, Modelling multiple-material flows on adaptive unstructured meshes, Ph.D. Thesis, Imperial College London, London, UK, 2009.