The scaled boundary finite element method—alias consistent infinitesimal finite element cell method—for diffusion

International Journal for Numerical Methods in EngineeringVolume 45, Issue 10 p. 1403-1431 Research Article The scaled boundary finite element method—alias consistent infinitesimal finite element cell method—for diffusion Chongmin Song, Chongmin Song Department of Civil Engineering, Institute of Hydraulics and Energy, Swiss Federal Institute of Technology, Lausanne, CH-1015 Lausanne, SwitzerlandSearch for more papers by this authorJohn P. Wolf, Corresponding Author John P. Wolf [email protected] Department of Civil Engineering, Institute of Hydraulics and Energy, Swiss Federal Institute of Technology, Lausanne, CH-1015 Lausanne, SwitzerlandDepartment of Civil Engineering, Institute of Hydraulics and Energy, Swiss Federal Institute of Technology Lausanne, CH-1015 Lausanne, SwitzerlandSearch for more papers by this author Chongmin Song, Chongmin Song Department of Civil Engineering, Institute of Hydraulics and Energy, Swiss Federal Institute of Technology, Lausanne, CH-1015 Lausanne, SwitzerlandSearch for more papers by this authorJohn P. Wolf, Corresponding Author John P. Wolf [email protected] Department of Civil Engineering, Institute of Hydraulics and Energy, Swiss Federal Institute of Technology, Lausanne, CH-1015 Lausanne, SwitzerlandDepartment of Civil Engineering, Institute of Hydraulics and Energy, Swiss Federal Institute of Technology Lausanne, CH-1015 Lausanne, SwitzerlandSearch for more papers by this author First published: 21 June 1999 https://doi.org/10.1002/(SICI)1097-0207(19990810)45:10<1403::AID-NME636>3.0.CO;2-ECitations: 54AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract The scaled boundary finite element method, alias the consistent infinitesimal finite element cell method, is developed starting from the diffusion equation. Only the boundary of the medium is discretized with surface finite elements yielding a reduction of the spatial dimension by one. No fundamental solution is necessary, and thus no singular integrals need to be evaluated. Essential and natural boundary conditions on surfaces and conditions on interfaces between different materials are enforced exactly without any discretization. The solution of the function in the radial direction is analytical. This method is thus exact in the radial direction and converges to the exact solution in the finite element sense in the circumferential directions. The semi-analytical solution inside the domain leads to an efficient procedure to calculate singularities accurately without discretization in the vicinity of the singular point. For a bounded medium symmetric steady-state stiffness and mass matrices with respect to the degrees of freedom on the boundary result without any additional assumption. Copyright © 1999 John Wiley & Sons, Ltd. REFERENCES 1 Song Ch, Wolf JP. Consistent infinitesimal finite element cell method for diffusion equation in unbounded medium. Computer Methods in Applied Mechanics and Engineering 1996; 123: 319–334. 2 Wolf JP, Song Ch. Finite-Element Modelling of Unbounded Media. Wiley: Chichester, 1996. 3 Song Ch, Wolf JP. The scaled boundary finite element method – alias consistent infinitesimal finite element cell method – for elastodynamics. Computer Methods in Applied Mechanics and Engineering 1997; 147: 329–355. 4 Song Ch, Wolf JP. The scaled boundary finite element method: analytical solution in frequency domain. Computer Methods in Applied Mechanics and Engineering 1998; 164: 249–264. 5 Patel RV, Lin Z, Misra P. Computation of stable invariant subspaces of Hamiltonian matrices. Journal of Matrix Analysis and Applications, Society of Industrial and Applied Mathematics 1994; 15: 284–298. 6 Laub AJ. A Schur method for solving algebraic Riccati equations. IEEE Transactions on Automatic Control 1979; AC-24: 913–921. 7 Nardini D, Brebbia CA. Boundary integral formulation of mass matrices for dynamic analysis. Topics in Boundary Element Research, vol. 2, Ch. 7. Springer: Berlin, 1984; 191–208. 8 Yosibashi Z. On solutions of two-dimensional linear elastostatic and heat-transfer problems in the vicinity of singular points. International Journal of Solids and Structures 1997; 34: 243–274. Citing Literature Volume45, Issue1010 August 1999Pages 1403-1431 ReferencesRelatedInformation