Application of a generic domain-decomposition strategy to solve shell-like problems through 3D BE models

Communications in Numerical Methods in Engineering

Volumn 23, Issue 8, 2007, Pages 771-785

  Araujo F C ^a   Silva, K I ^a   Telles, J C F ^b  

^a FEDERAL UNIVERSITY OF OURO PRETO   (Brazil)

^b FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Discontinuous boundary elements; Generic BE BE coupling algorithm; Krylov solvers; Shell like elements; Singular and quasi singular integration algorithms

Indexed keywords

BOUNDARY ELEMENT METHOD; CONJUGATE GRADIENT METHOD; INTEGRAL EQUATIONS; INTEGRATION; JACOBIAN MATRICES; MATHEMATICAL TRANSFORMATIONS; SHELLS (STRUCTURES); THREE DIMENSIONAL;

KRYLOV SOLVER; MATRIX ASSEMBLY ROUTINE; TELLES CO-ORDINATE TRANSFORMATION; TRIANGULAR POLAR CO-ORDINATE TRANSFORMATION;

DOMAIN DECOMPOSITION METHODS;

BOUNDARY ELEMENT METHOD; CONJUGATE GRADIENT METHOD; DOMAIN DECOMPOSITION METHODS; INTEGRAL EQUATIONS; INTEGRATION; JACOBIAN MATRICES; MATHEMATICAL TRANSFORMATIONS; SHELLS (STRUCTURES); THREE DIMENSIONAL;

EID: 34547814103     PISSN: 10698299     EISSN: 10990887     Source Type: Journal    
DOI: 10.1002/cnm.926     Document Type: Article

References (40)

1. Bernadou M. Finite Element Method for Thin Shell Problems. Wiley: Chichester, 1996.
2. Rohwer K, Rolfes R. Calculating 3D stresses in layered composite plates and shells. Mechanics of Composite Materials 1998; 34(4):355-362.
3. Rolfes R, Noack J, Taeschner M. High-performance 3D analysis of thermo-mechanically loaded composite structures. Composite Structures 1999; 46:367-379.
4. Peirce AP, Napier JAL. A spectral multipole method for efficient solution of large scale boundary element models in elastostatics. International Journal for Numerical Methods in Engineering 1995; 38:4009-4034.
5. Chenh H, Greengard L, Rokhlin V. A fast adaptive multipole algorithm in three dimensions. Journal of Computational Physics 2001; 155:468-498.
6. Popov V, Power H, Walker SP. Numerical comparison between two possible multipole alternatives for the BEM solution of 3D elasticity problems based upon Taylor series expansions. Engineering Analysis with Boundary Elements 2003; 27:521-531.
7. Wrobel LC, Aliabadi MH. The Boundary Element Method, vols. I & II. Wiley: New York, 2002.
8. Beskos D, Maier G (eds). Boundary Element Advances in Solid Mechanics. Springer: Wien, 2003.
9. Liu Y. Analysis of shell-like structures by the boundary element method based on 3-D elasticity: formulation and verification. International Journal for Numerical Methods in Engineering 1998; 41:541-558.
10. Guiggiani M, Casalini P. Direct computation of Cauchy principal value integrals in advanced boundary elements. International Journal for Numerical Methods in Engineering 1987; 24:1711-1720.
11. Lu S, Ye TQ. Direct evaluation of singular integrals in elastoplastic analysis by the boundary element method. International Journal for Numerical Methods in Engineering 1991; 32:295-311.
12. Liao H, Xu Z. A method for direct evaluation of singular integral in direct boundary element method. International Journal for Numerical Methods in Engineering 1992; 35:1473-1485.
13. Li HB, Han GM, Mang HA. A new method for evaluating for evaluating singular integrals in stress analysis of solids by the direct boundary element method. International Journal for Numerical Methods in Engineering 1985; 21:2071-2098.
14. Zhang W, Xu HR. A general and effective way for evaluating the integrals with various orders of singularity in the direct boundary element method. International Journal for Numerical Methods in Engineering 1989; 28:2059-2064.
15. Telles JCF. A self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals. International Journal for Numerical Methods in Engineering 1987; 24:959-973.
16. Telles JCF, Oliveira RF. Third degree polynomial transformation for boundary element integrals: further improvements. Engineering Analysis with Boundary Elements 1994; 13:135-141.
17. Krishnasamy G, Rizzo FJ, Liu YJ. Boundary integral equation for thin bodies. International Journal for Numerical Methods in Engineering 1994; 37:107-121.
18. Hayami K. High precision numerical integration methods for 3-D boundary element analysis. IEEE Transactions on Magnetics 1990; 26(2):603-606.
19. Hayami K, Matsumoto H. A numerical quadrature for nearly singular boundary element integrals. Engineering Analysis with Boundary Elements 1994; 13:143-154.
20. Araújo FC, Martins CJ, Mansur WJ. An efficient BE iterative-solver-based substructuring algorithm for 3D time-harmonic problems in elastodynamics. Engineering Analysis with Boundary Elements 2001; 25:795-803.
21. Araújo FC, Dors C, Mansur WJ. Dynamic cross-interaction between footings - 3D frequency-domain parallelized analysis via the BEM. Proceedings of the International Conference on Boundary Element Techniques IV, vol. I, Granada, Queen Mary, University of London, London, 2003; 253-258.
22. Araújo FC, Silva KI. The use of discontinuous boundary elements in the generic BE/BE coupling algorithm - applications to 3D potential problems. In Proceedings of the International Conference on Boundary Element Techniques V, vol. 1, Lisbon Aliabadi F, Leitão V (eds). EC Ltd.: London, 2004; 237-242.
23. Araújo FC, Dors C, Martins CJ, Mansur WJ. New developments on BE /BE multi-zone algorithms based on Krylov solvers - applications to 3D frequency - dependent problems. Journal of Brazilian Society of Mechanical Science in Engineering 2004; 26:231-248.
24. Saad Y. Iterative Methods for Sparse Linear Systems. PWS Publishing: New York, 1996.
25. van der Vorst HA. Iterative Krylov Methods for Large Linear Systems. Cambridge University Press: Cambridge, MA, 2003.
26. Araújo FC, Silva KI, Telles JCF. Generic domain decomposition and iterative solvers for 3D BEM problems. International Journal for Numerical Methods in Engineering, published online in Wiley Interscience (www.interscience.wiley.com). DOI: 10.1002/NME.1719
27. Johan Z, Hughes TJR, Shakib F. A globally convergent matrix-free algorithm for implicit time-marching schemes arising in finite element analysis of fluids. Computer Methods in Applied Mechanics and Engineering 1991; 87:281-304.
28. Baum JD, Luo H, Löhner R. Edge-based finite element scheme for Euler equations. AIAA Journal 1994; 32:1183-1190.
29. Dutto LC, Lepage CY, Habashi WG. Effect of the storage format of sparse linear systems on parallel CFD computations. Computer Methods in Applied Mechanics and Engineering 2000; 188:441-453.
30. Catabriga L, Coutinho ALGA. Implicit SUPG solution of Euler equations using edge-based data structures. Computer Methods in Applied Mechanics and Engineering 2002; 191:3477-3490.
31. Mansur WJ, Araújo FC, Malaghini JEB. Solution of BEM systems of equations via iterative techniques. International Journal for Numerical Methods in Engineering 1992; 33:1823-1841.
32. Prasad KG, Kane JH, Keyes DE, Balakrishna C. Preconditioned Krylov solvers for BEA. International Journal for Numerical Methods in Engineering 1994; 37:1651-1672.
33. Hribersek M, Skerget L. Iterative methods in solving Navier-Stokes equations by the boundary element method. International Journal for Numerical Methods in Engineering 1996; 39:115-139.
34. Leung CY, Walker SP. Iterative solution of large three-dimensional BEM elastostatic analyses using the GMRES technique. International Journal for Numerical Methods in Engineering 1997; 40:2227-2236.
35. Skerget L, Hribersek M, Kuhn G. Computational fluid dynamics by boundary-domain integral method. International Journal for Numerical Methods in Engineering 1999; 46:1291-1311.
36. Davey K, Bounds S, Rosindale I, Rasgado MTA. A coarse preconditioner for multi-domain boundary element equations. Computers and Structures 2002; 80(7-8):643-658.
37. Fang Z, Ingber MS, Martinez MJ. The solution of magnetostatic BEM systems of equations using iterative methods. Engineering Analysis with Boundary Elements 2002; 26(9):789-794.
38. Bucher HF, Wrobel LC, Mansur WJ, Magluta C. Fast solution of problems with multiple load cases by using wavelet - compressed boundary element matrices. Communications in Numerical Methods in Engineering 2003; 19(5):387-399.
39. Briceño FJ, Power H. The completed integral equation approach for the numerical solution of the motion of N solid particles in the interior of a deformable viscous drop. Engineering Analysis with Boundary Elements 2004; 28:333-344.
40. Wang H, Yao Z, Wang P. On the preconditioners for fast multipole boundary element methods for 2D multi-domain elastostatics. Engineering Analysis with Boundary Elements 2005; 29:673-688.