Hybrid Coupled Finite-Boundary Element Methods for Elliptical Systems of Second Order
| Author(s) | Hsiao, George C. | |
| Author(s) | Schnack, E. | |
| Author(s) | Wendland, W.L. | |
| Date Accessioned | 2005-02-18T17:10:55Z | |
| Date Available | 2005-02-18T17:10:55Z | |
| Publication Date | 2000 | |
| Abstract | In this hybrid method, we consider, in addition to traditional finite elements, the Trefftz elements for which the governing equations of equilibrium are required to be satisfied a priori within the subdomain elements. If the Trefftz elements are modelled with boundary potentials supported by the individual element boundaries, this defines the so–called macro–elements. These allow one to handle in particular situations involv-ing singular features such as cracks, inclusions, corners and notches providing a locally high resolution of the desired stress fields, in combination with a traditional global varia-tional FEM analysis. The global stiffness matrix is here sparse as the one in conventional FEM. In addition, with slight modifications, the macro–elements can be incorporated into standard commercial FEM codes. The coupling between the elements is modelled by using a generalized compatibility condition in a weak sense with additional elements on the skeleton. The latter allows us to relax the continuity requirements for the global displacement field. In particular, the mesh points of the macro–elements can be chosen independently of the nodes of the FEM structure. This approach permits the combination of independent meshes and also the exploitation of modern parallel computing facilities. We present here the formulation of the method and its functional analytic setting as well as corresponding discretizations and asymptotic error estimates. For illustration, we include some computational results in two– and three–dimensional elasticity. | en |
| Sponsor | The work of G.C. Hsiao was carried out during several visits at the Universitat at Stuttgart supported by the DFG priority research programme “Boundary Element Methods” within the guest–programme We–659/19–2,3; the work of E. Schnack was supported by the DFG projects Schn–245/3–1,2,3 and Schn–245/4–1,2, by the DFG priority research programme “Boundary Element Methods” within the the projects Schn– 245/10–1,2,3, Schn–245/17–1 and the MIMD–DD–Project Schn–245/20–1; the work of W.L. Wendland was supported during several visits at the University of Delaware by the Fulbright Commission, the University of Delaware and the Delaware MURI–grant. The final version of the work was completed during G.C. Hsiao’s visit at University of Stuttgart in the summer 1997 supported by the Alexander von Humboldt–Stiftung. | en |
| Extent | 564562 bytes | |
| MIME type | application/pdf | |
| URL | http://udspace.udel.edu/handle/19716/359 | |
| Language | en_US | |
| Publisher | Department of Mathematical Sciences | en |
| Part of Series | Technical Report: 2000-05 | |
| dc.subject.classification | AMS: 73V10, 65N38, 65N30, 65N55, 65Y05 | |
| Title | Hybrid Coupled Finite-Boundary Element Methods for Elliptical Systems of Second Order | en |
| Type | Technical Report | en |