Abstract
In this chapter, we discuss the implicit ABCs for the exterior problem of 2-D and 3-D Poisson equations, the Helmholtz equation, and the Navier system, and for the wave equation on unbounded domains. By using artificial boundaries, the original problems are reduced to boundary or initial boundary value problems on bounded computational domains. Implicit boundary conditions on the artificial boundaries are obtained, and then the finite element or finite difference method is applied to solve the reduced problems. Some error estimates are also given.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Chen, G. and Zhou, J. (1992), Boundary Element Methods, Academic Press Limited, 1992.
Costabel, M. (1987), Symmetric methods for the coupling of finite elements and boundary elements, in Boundary Elements IX edited by Brebbia C.A. et al., Springer-Verlag, 1987.
Gatica, G.N., Gatica, L.F. and Stephan, E.P. (2003), A FEM-DtM formulation for a non-linear exterior problem in incompressible elasticity, Math. Meth. Appl. Sci., 26(2003), 151–170.
Han, H.D. (1988), Boundary integro-differential equations of elliptic boundary value problems and their numerical solutions, Scientia Sinica, Vol. 31 (1988), 1153–1165.
Han, H.D. (1990), A new class of variational formulations for the coupling of finite and boundary element methods, J. Comp. Math., 8 (1990), 223–232.
Han, H.D. (1993), The boundary integro-differential equations of boundary value problems in linear elasticity, J. Tsinghua Univ., 36 (1993), 15–25.
Han, H.D. (1994-A), The boundary integro-differential equations of three dimensional Neumann problem in linear elasticity, Numer. Math., 68(1994), 269–291.
Han, H.D. (1994-B), A boundary element procedure for the Signorini problem in three dimensional elasticity, Numer. Math. (a journal of chinese universities), 7 (1994), 104–117.
Han, H.D. (1995), A system of boundary integro-differential equations for harmonic elastic waves in R 3, Numer. Math. (a journal of chinese universities), 4 (1995), 203–621.
Johnson, C. and Nedelec, J.C. (1980), On the coupling of boundary integral and finite element methods, Math. Comp., 35(1980), 1063–1079.
Jones, D.S. (1986), Acoustic and Electromagnetic Waves, Clarendon Press, Oxford, 1986.
Kupradze, V.D. (1979), Three-Dimensional Problems of the Mathematical Thoery of Elasticity and Themoelasticity, North-Holland, Amsterdam, 1979.
Kythe, P.K. (1996), Fundamental Solutions for Differential Operators and Applications, Birkhäuser, Boston, Basel, 1996.
Meddahi, S., Gonzalez, M. and Perez, P. (2000), On a FEM-BEM formulation for an exterior quasilinear problem in the plane, SIAM J. Numer. Anal., 37(2000), 1820–1837.
Nedelec, J.C. (2001), Acoustic and Electromagnetic Equations: Integral Representations for Harmonic Problems, Springer, 2001.
Teng, Z.H. (2003), Exact boundary condition for time-depandent wave equation based on boundary integral, J. Comput. Phys., 190(2003), 398–418.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Tsinghua University Press, Beijing and Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Han, H., Wu, X. (2013). Implicit Artificial Boundary Conditions. In: Artificial Boundary Method. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35464-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-35464-9_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35463-2
Online ISBN: 978-3-642-35464-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)