Implementation of a symmetric boundary element method in transient heat conduction with semi-analytical integrations

International Journal for Numerical Methods in Engineering

Volumn 46, Issue 11, 1999, Pages 1819-1843

  Carini, Angelo ^a   Diligenti, Mauro ^b   Salvadori, Alberto ^c  

^a UNIVERSITY OF BRESCIA   (Italy)

^b UNIVERSITY OF PARMA   (Italy)

^c POLITECNICO DI MILANO   (Italy)

Author keywords

Analytical integrations; Galerkin method; Heat conduction; Integral equations

Indexed keywords

BOUNDARY ELEMENT METHOD; FUNCTIONS; GALERKIN METHODS; INTEGRAL EQUATIONS; INTEGRATION; LINEAR EQUATIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; POLYNOMIALS; VARIATIONAL TECHNIQUES;

ANALYTICAL INTEGRATIONS;

HEAT CONDUCTION;

BOUNDARY ELEMENT METHOD; HEAT CONDUCTION;

EID: 0033590177     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19991220)46:11<1819::AID-NME734>3.0.CO;2-J     Document Type: Article

References (29)

1. Rizzo FJ, Shippy DH. A method of solution for certain problems of transient heat conduction. AIAA Journal 1970; 8:2004-2009.
2. Shaw RP. An integral approach to diffusion. International Journal of Heat and Mass Transfer 1974; 16:693-699.
3. Tanaka K, Tanaka M. Time space boundary elements for transient heat conduction problems. Applied Mathematical Modelling 1980; 4:331-334.
4. Roures V, Alarcon E. Transient heat conduction problems using BIEM. Computers and Structures 1983; 16: 717-730.
5. Pina MLG, Fernandez JLM. Applications in heat conduction by BEM. In Topics in Boundary Element Research, Brebbia CA (ed.). Springer: Berlin, 1984.
6. Kane JH, Balakrishna C. Symmetric Galerkin boundary formulations employing curved elements. International Journal for Numerical Methods in Engineering 1993; 36:2157-2187.
7. Balakrishna C, Gray LJ, Kane JH. Efficient analytical integration of symmetric Galerkin boundary integrals over curved elements; elasticity formulation. Computer Methods in Applied Mechanics and Engineering 1994; 117: 157-179.
8. Layton JB, Ganguly S, Balakrishna C, Kane JH. A symmetric Galerkin multi-zone boundary element formulation. International Journal for Numerical Methods in Engineering 1997; 40:2913-2931.
9. Carini A, Diligenti M, Maier G. Variational formulation of the boundary element method in transient heat conduction. Mathematical and Computer Modelling 1991; 15(3-5):71-80.
10. Carini A, Diligenti M, Maier G. Symmetric boundary integral formulations of transient heat conduction: saddle-point theorems for BE analysis and BE-FE coupling. Archives of Mechanics 1997; 49(2):253-283.
11. Sirtori S. General stress analysis by means of integral equation and boundary elements. Meccanica 1979; 14:210-218.
12. Maier G, Polizzotto C. A Galerkin approach to boundary element elastoplastic analysis. Computer Methods in Applied Mechanics and Engineering 1987; 60:175-194.
13. Polizzotto C. An energy approach to the boundary element method. Part I: Elastic solids. Computer Methods in Applied Mechanics and Engineering 1987; 60:175-194.
14. Sirtori S, Maier G, Novati G, Miccoli S. A Galerkin symmetric boundary-element method in elasticity: formulation and implementation. International Journal for Numerical Methods in Engineering 1992; 35:255-282.
15. Diligenti M, Monegato G. Integral evaluation in the BEM solution of (hyper)singular integral equations. 2D problems on polygonal domains. Journal of Computational and Applied Mathematics 1997; 81:29-57.
16. Aimi A, Diligenti M, Monegato G. New numerical integration schemes for applications of Galerkin BEM to 2-D problems. International Journal for Numerical Methods in Engineering 1997; 40:1977-1999.
17. Carslaw HS, Jaeger JC. Conduction of Heat in Solids. Oxford University Press: Oxford, 1959.
18. Sharp S, Crouch L. Heat conduction, thermoelasticity and consolidation. In Boundary Element Methods in Mechanics, Beskos DE (ed.). Elsevier: Amsterdam, 1987: 439-498.
19. Gurtin ME. Variational principles for linear initial-value problems. Quarterly Journal of Applied Mathematics 1964; 22.
20. Tonti E. On the variational formulation for linear initial value problems. Annali di Matematica Pura ed Applicata 1973; 4XCV:331-359.
21. Abramowitz M, Stegun I. Handbook of Mathematical Functions. Dover: New York, 1968.
22. Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical Recipes. Cambridge University Press: Cambridge, 1992.
23. Monegato G, Palamara Orsi A. Product formulas for Fredholm integral equations with rational kernel functions. In Numerical Integration III, Braess H, Hämmerlin G (eds.). ISNM 85. Birkhäuser: Basel, 1988: 140-156.
24. Szegö G. Orthogonal Polynomials, American Mathematical Society Colloquium, vol. 23. A.M.S: Providence, RI, 1975.
25. Elliot D, Paget DF. Product-integration rules and their occurence. BIT 1976; 16:32-40.
26. Monegato G. The numerical evaluation of hypersingular integrals. Journal of Computational and Applied Mathematics 1994; 50:9-31.
27. Mori M. Quadrature formulas obtained by variable transformation and the DE-rule. Journal of Computational and Applied Mathematics 1985; 12-13:119-130
28. Özisik MN. Boundary Value Problems of Heat Conduction. Dover: New York, 1989.
29. ABAQUS V.4.9. User's and Theory Manuals. Hibbitt Karlsson & Sorensen Inc: Rhode Island, 1991.