From the boundary element domain decomposition methods to local trefftz finite element methods on polyhedral meshes

Lecture Notes in Computational Science and Engineering

Volumn 70 LNCSE, Issue , 2009, Pages 315-322

  Copeland, Dylan ^a   Langer, Ulrich ^a   Pusch, David ^b  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

^b ERICH SCHMID INSTITUTE OF MATERIALS SCIENCE   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRAIC MULTIGRID METHODS; BOUNDARY ELEMENTS; DISCRETIZATIONS; FINITE ELEMENT; FINITE ELEMENT DISCRETIZATIONS; HARMONIC BASIS FUNCTION; HELMHOLTZ; KRYLOV SUBSPACE ITERATIVE METHODS; POLYHEDRAL MESHES; POTENTIAL EQUATION; PRECONDITIONED CONJUGATE GRADIENT METHOD; SPARSE LINEAR SYSTEMS; SUB-DOMAINS; TREFFTZ FINITE ELEMENT METHOD; TREFFTZ METHODS;

ALGEBRA; BOUNDARY ELEMENT METHOD; CONJUGATE GRADIENT METHOD; FINITE ELEMENT METHOD; LINEAR SYSTEMS; MAXWELL EQUATIONS; OPERATIONS RESEARCH;

DOMAIN DECOMPOSITION METHODS;

EID: 78651481846     PISSN: 14397358     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-02677-5_35     Document Type: Conference Paper

References (11)

1. Brezzi, F., Lipnikov, K., Shashkov, M.: Convergence of mimetic finite difference method for diffusion problems on polyhedral meshes. SIAM J. Numer. Anal., 43(3):1872-1896, 2005. (Pubitemid 44598663)
2. Buffa, A., Ciarlet, Jr., P.: On traces for functional spaces related to Maxwell's equations. I. An integration by parts formula in Lipschitz polyhedra. Math. Methods Appl. Sci., 24:9-30, 2001.
3. Buffa, A., Hiptmair, R., von Petersdorff, T., Schwab, C.: Boundary element methods for Maxwell transmission problems in Lipschitz domains. Numer. Math., 95:459-485, 2003.
4. Copeland, D.: Boundary-element-based finite element methods for Helmholtz and Maxwell equations on general polyhedral meshes. Int. J. Appl. Math. Com-put. Sci., 5(1):60-73, 2009.
5. Hsiao, G.C., Wendland, W.L.: Domain decomposition in boundary element methods. In R. Glowinski, Y.A. Kuznetsov, G. Meurant, J. Périaux and O.B. Widlund, eds., Proceedings of the Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations, Moscow, May 21-25, 1990, pages 41-49, Philadelphia, 1991. SIAM.
6. Kuznetsov, Y., Lipnikov, K., Shashkov, M.: Mimetic finite difference method on polygonal meshes for diffusion-type problems. Comput. Geosci., 8(4):301-324, December 2004. (Pubitemid 40974198)
7. Langer, U., Steinbach, O.: Coupled finite and boundary element domain decomposition methods. In M. Schanz and O. Steinbach, eds., Boundary Element Analysis: Mathematical Aspects and Application, vol.29 of Lecture Notes in Applied and Computational Mechanics, pages 29-59, Berlin, 2007. Springer.
8. McLean, W.: Strongly elliptic systems and boundary integral equations. Cambridge University Press, Cambridge, 2000.
9. Reitzinger, S.: Algebraic Multigrid Methods for Large Scale Finite Element Equations. Reihe C -Technik und Naturwissenschaften. Universitätsverlag Rudolf Trauner, Linz, 2001.
10. Sauter, S., Schwab, C.: Randelementemethoden: Analyse, Numerik und Im-plementierung schneller Algorithmen. Teubner, Stuttgart, Leipzig, Wiesbaden, 2004.
11. Steinbach, O.: Numerical Approximation Methods for Elliptic Boundary Value Problems. Finite and Boundary Elements. Springer, New York, 2008.