Meshfree simulation of deforming domains

CAD Computer Aided Design

Volumn 31, Issue 7, 1999, Pages 459-471

  Shapiro, V ^a   Tsukanov, I ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; FUNCTIONS;

DEFORMING DOMAINS; MESHFREE SIMULATION;

COMPUTER AIDED DESIGN;

EID: 0032631418     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0010-4485(99)00043-3     Document Type: Article

References (37)

1. Liu Y, Reitz RD. Multidimensional modeling of engine combustion chamber surface temperatures. In: Advances in SI and Diesel Engine Modeling (SP-1276), SAE-971594, May 1997, pp. 57-71.
2. Rvachev V.L. Theory of R-functions and some applications (in Russian). 1982;Naukova Dumka, Kiev.
3. Rvachev V.L., Manko G.P., Shevchenko A.N. The R-function approach and software for the analysis of physical and mechanical fields. Crestin J.P., McWaters J.F. Software for discrete manufacturing. 1986;North-Holland, Paris.
4. Rvachev V.L., Sheiko T.I. R-functions in boundary value problems in mechanics. Appl Mech Rev. 48:(4):1996;151-188.
5. Cox J.J., Anderson D.C. Single model formulation that link engineering analysis with geometric modeling. Turner J., Pegna J., Wozny M. Product modeling for computer-aided design and manufacturing. 1991;Elsevier Science, Amsterdam.
6. Wilson TC, Talbert JA, Cox JJ. Modeling primitives: an object oriented formulation of boundary value problems in a solid geometric modeling context. In: Rossignac R, Turner J, Allen G, editors. Second Symposium on Solid Modeling and Applications, Montreal, Canada, 19-21 May 1993, pp. 441-448.
7. Zagajac J. fast method for estimating discrete field values in early engineering design. IEEE Trans Visualization Comput Graph. 2:(1):1996;35-43.
8. Sethian J.A. Level set methods: evolving interfaces in geometry, fluid mechanics, computer vision and material sciences. 1996;Cambridge University Press, Cambridge, MA.
9. Belytschko T., Krongauz Y., Organ D., Fleming M., Krysl P. Meshless methods: an overview and recent developments. Comput Meth Appl Mech Engng. 139:(1-2):1996;3-47.
10. Proceedings of the 6th International Meshing Roundtable, Sandia National Laboratories. Park City, Utah, 13-15 October 1997.
11. Rvachev V.L. Methods of logic algebra in mathematical physics (in Russian). 1974;Naukova Dumka, Kiev.
12. Kantorovich L.V., Krylov V.I. Approximate methods of higher analysis. 1958;Interscience, New York.
13. Shapiro V. Theory of R-functions and applications: a primer. Tech. Report TR91-1219, Computer Science Department, Cornell University, Ithaca, NY, 1991.
14. Shapiro V. Real functions for representation of rigid solids. Comput-Aided Geom Design. 11:(2):1994;153-175.
15. Shapiro V, Tsukanov I. Implicit functions with guaranteed differential properties. In: Solid Modeling '99, Proc. Fifth Symposium on Solid Modeling and Applications, June 1999.
16. Kharrik I.Yu. On approximation of functions that have zero values and derivatives on domain boundary by special functions. Siberian Math J. 4:(2):1963;408-425.
17. Shigley J.E. Jr., Uicker J.J. Theory of machines and mechanisms. 1995;McGraw-Hill, New York.
18. Carl de Boor. A practical guide to splines. 1978;Springer, Berlin.
19. Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P. Numerical recipes in C. 2 :1992;Cambridge University Press.
20. Liu Y., Reitz R.D. Modeling of heat conduction within chamber walls for multidimensional internal combustion engine simulation. Int J Heat Mass Transfer. 41:(6-7):1998;859-869.
21. Requicha A.A.G. Representations for rigid solids: theory, methods, and systems. ACM Computing Surveys. 12:(4):1980;437-464.
22. Shapiro V. Well-formed set representations of solids. Int J Comput Geom Appl. 9:(2):1999;125-150.
23. Pasko A., Adzhiev V., Sourin A., Savchenko V. Function representation in geometric modeling: concepts, implementation and applications. The Visual Computer. 11:(8):1995;429-446.
24. Sourin A, Pasko A. Function representation for sweeping by a moving solid. In: Proc. Third Symposium on Solid Modeling Foundations and CAD/CAM applications, 17-19 May 1995.
25. Bloomenthal J. Introduction to implicit surfaces. 1997;Morgan Kaufmann, Los Altos, CA.
26. Rvachev V.L., Shevchenko A.N. Problem-oriented languages and systems for engineering computations (in Russian). 1988;Tekhnika, Kiev.
27. Barr A.H. Global and local deformation of solid primitives. Comput Graph. 18:(3):1984;21-30.
28. Bechmann D. Space deformation models survey. Comput Graph. 18:(4):1994;571-586.
29. Savchenko V., Pasko A. Transformation of functionally defined shapes by extended space mappings. The Visual Computer. 14:(5-6):1998;257-270.
30. Rvachev V., Sheiko T., Shapiro V., Uicker J. Implicit function modeling of solidification in metal casting. Trans ASME, J Mech Design. 119:1997;466-473.
31. Rall LB, Corliss GF. An introduction to automatic differentiation. In: Berz M, Bischof C, Corliss G, Griewank A, editors. Computational differentiation, Proc. Second International Workshop on Computational Differentiation, SIAM, 1996.
32. Rvachev V.L., Manko G.P. Automation of programming for boundary value problems (in Russian). 1983;Naukova Dumka, Kiev.
33. Shevchenko A.N., Rokityanskaya V.N. Automatic differentiation of functions of many variables. Cybernet System Anal. 32:(5):1996;709-723.
34. Lutz ED. Numerical methods for hypersingular and near-singular boundary integrals in fracture mechanics, PhD thesis, Cornell University, Computer Science Department, May 1991.
35. Lee Y.T., Requicha A.A.G. Algorithms for computing the volume and other integral properties of solids: parts I and II. Commun ACM. 25:(9):1982;635-650.
36. Cheng S-W, Edelsbrunner H. Design and analysis of planar shape deformation. In: 14th Annual ACM Symposium on Computational Geometry, Minneapolis, MN, 1998.
37. Raghothama S, Shapiro V. Necessary conditions for boundary representation variance. In: Proceedings of the Thirteenth ACM Symposium on Computational Geometry, 4-6 June 1997.