Reduced order mesh optimisation using proper orthogonal decomposition and a modified cuckoo search

International Journal for Numerical Methods in Engineering

Volumn 93, Issue 5, 2013, Pages 527-550

  Walton, S ^a   Hassan, O ^a   Morgan, K ^a  

^a SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

Co volume method; Dual orthogonal mesh; Gradient free optimisation; Modified cuckoo search; Proper orthogonal decomposition; Unstructured mesh optimisation

Indexed keywords

CO-VOLUME METHOD; CUCKOO SEARCHES; DUAL ORTHOGONAL MESH; OPTIMISATIONS; PROPER ORTHOGONAL DECOMPOSITIONS; UNSTRUCTURED MESHES;

ALGORITHMS; PRINCIPAL COMPONENT ANALYSIS; PROBLEM SOLVING;

OPTIMIZATION;

EID: 84872262139     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.4400     Document Type: Article

References (36)

1. Harlow FH, Welch JE. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. The Physics of Fluids 1965; 8:2182-2189. DOI: 10.1063/1.1761178.
2. Yee K. Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Transactions on Antennas and Propagation 1966; 14:302-307. DOI: 10.1.1.172.6957.
3. Xie ZQ, Hassan O, Morgan K. Tailoring unstructured meshes for use with a 3D time domain co-volume algorithm for computational electromagnetics. International Journal for Numerical Methods in Engineering 2011; 87:48-65. DOI: 10.1002/nme.2970.
4. Sazonov I, Hassan O, Morgan K, Weatherill NP. Smooth Delaunay-Voronoi dual meshes for co-volume integration schemes. In Proceedings of the 15th International Meshing Roundtable, Pebay PP (ed.). Springer: Berlin, 2006; 529-541, DOI: 10.1.1.81.2299.
5. Sazonov I, Wang D, Hassan O, Morgan K, Weatherill N. A stitching method for the generation of unstructured meshes for use with co-volume solution techniques. Computer Methods in Applied Mechanics and Engineering 2006; 195:1826-1845. DOI: 10.1016/j.cma.2005.05.037.
6. Peraire J, Vahdati M, Morgan K, Zienkiewicz OC. Adaptive remeshing for compressible flow computations. Journal of Computational Physics 1987; 72:449-466. DOI: 10.1016/0021-9991(87)90093-3.
7. Weatherill NP, Hassan O. Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints. International Journal for Numerical Methods in Engineering 1994; 37:2005-2040. DOI: 10.1002/nme.1620371203.
8. Morgan K, Peraire J, Peiro J. Unstructured grid methods for compressible flows. Report 787: special course on unstructured grid methods for advection dominated flows, AGARD, Paris, 1992, 5.1-5.39.
9. Diez M, Peri D. Robust optimization for ship conceptual design. Ocean Engineering 2010; 37:966-977. DOI: 10.1016/j.oceaneng.2010.03.010.
10. Michalewicz Z. Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag: Berlin, Heidelberg, New York, 1992.
11. Bratton D, Kennedy J. Defining a standard for particle swarm optimization. In Proceedings of the 2007 IEEE Swarm Intelligence Symposium. IEEE Publications: Honolulu, Hawaii, 2007; 120-127, DOI: 10.1109/SIS.2007.368035.
12. Praveen C, Duvigneau R. Low cost PSO using metamodels and inexact pre-evaluation: application to aerodynamic shape design. Computer Methods in Applied Mechanics and Engineering 2009; 198:1087-1096. DOI: 10.1016/j.cma.2008.11.019.
13. Park J, Shontz SM. Two derivative-free optimization algorithms for mesh quality improvement. Procedia Computer Science 2010; 1:387-396. DOI: 10.1016/j.procs.2010.04.042.
14. Walton S, Hassan O, Morgan K, Brown MR. Modified cuckoo search: a new gradient free optimisation algorithm. Chaos, Solitons & Fractals 2011; 44(9):710-718. DOI: 10.1016/j.chaos.2011.06.004.
15. Cui Z, Cai X, Zeng J, Sun G. Particle swarm optimization with FUSS and RWS for high dimensional functions. Applied Mathematics and Computation 2008; 205:98-108.
16. Yilmaz A, Kuzuoglu M. A particle swarm optimization approach for hexahedral mesh smoothing. International Journal for Numerical Methods in Fluids 2009; 60:55-78. DOI: 10.1002/fld.1878.
17. Kerschen G, Golinval J, Vakakis AF, Bergman LA. The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: an overview. Nonlinear Dynamics 2005; 41:147-169. DOI: 10.1007/s11071-005-2803-2.
18. Ly HV, Tran HT. Modeling and control of physical processes using proper orthogonal decomposition. Mathematical and Computer Modelling 2001; 33:223-236.
19. Bergmann M, Cordier L. Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models. Journal of Computational Physics 2008; 227:7813-7840. DOI: 10.1016/j.jcp.2008.04.034.
20. Barone MF, Kalashnikova I, Segalman DJ, Thornquist HK. Stable Galerkin reduced order models for linearized compressible flow. Journal of Computational Physics 2009; 228:1932-1946. DOI: 10.1016/j.jcp.2008.11.015.
21. Gilliam X, Dunyak JP, Smith DA, Wu F. Using projection pursuit and proper orthogonal decomposition to identify independent flow mechanisms. Journal of Wind Engineering and Industrial Aerodynamics 2004; 92:53-69. DOI: 10.1016/j.jweia.2003.09.041.
22. Fang F, Pain CC, Navon IM, Gorman GJ, Piggott MD, Allison PA, Ferrell PE, Goddard AJH. A POD reduced order unstructured mesh ocean modelling method for moderate Reynolds number flows. Ocean Modelling 2009; 28:127-136. DOI: 10.1016/j.ocemod.2008.12.006.
23. Sastry SP, Shontz SM, Vavasis SA. A log-barrier method for mesh quality improvement. Proceedings of the 20th International Meshing Roundtable, 2011, Accepted.
24. Du Q, Wang D. Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations. International Journal for Numerical Methods in Engineering 2003; 56:1355-1373.
25. Ohtake Y, Belyaev A, Bogaevski I. Mesh regularization and adaptive smoothing. Computer-Aided Design 2001; 33:789-800. DOI: 10.1016/S0010-4485(01)00095-1.
26. Lloyd S. Least square quantization in the PCM. IEEE Transactions on Information Theory 1982; 28:129-137. DOI: 10.1.1.131.1338.
27. VanderZee E, Hirani A, Guoy D, Ramos E. Well-centered planar triangulation: an iterative approach. In Proceedings of the 16th International Meshing Roundtable, Brewer ML, Marcum D (eds). SpringerLink, Session 1B: Berlin, Heidelberg, New York, 2008; 121-138, DOI: 10.1.1.131.700.
28. Yang X-S, Deb S. Cuckoo search via Lévy flights. In Proceedings of World Congress on Nature & Biologically Inspired Computing, Abraham A, Carvalho A, Herrera F, Pai V (eds). IEEE Publications: Coimbatore, India, 2009; 210-214, DOI: 10.1109/NABIC.2009.5393690.
29. Yang X-S, Deb S. Engineering optimisation by cuckoo search. International Journal of Mathematical Modeling and Numerical Optimisation 2010; 1:55-78.
30. Viswanathan GM. Lévy flights and superdiffusion in the context of biological encounters and random searches. Physics of Life Reviews 2008; 5:133-150. DOI: 10.1016/j.plrev.2008.03.002.
31. Klingner BM, Shewchuk JR. Aggressive tetrahedral mesh improvement. Proceedings of the 16th International Meshing Roundtable, (Seattle, Washington), October 2007; 3-23.
32. MATLAB version 7.8.0. Natick. The MathWorks Inc.: Massachusetts, 2009.
33. Freitag LA, Plassmann P. Local optimization-based simplicial mesh untangling and improvement. International Journal for Numerical Methods in Engineering 2000; 49:109-125.
34. Pritchard R, Hassan O, Morgan K. An efficient marker and cell solver for unstructured hybrid meshes. In Proceedings of the 16th International Conference on Finite Elements in Flow Problems, Wall WA, Gravemeier V (eds): Munich, 2011; 27.
35. Schöberl J. NETGEN: an advancing front 2D/3D-mesh generator based on abstract rules. Computing and Visualization in Science 2007; 1:41-52.
36. Alliez P, Cohen-Steiner D, Yvinec M, Desbrun M. Variational tetrahedral meshing. ACM Transactions on Graphics, special issue on Proceedings of SIGGRAPH 2005; 24:617-625.