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H.-J. Payer, H.A. Mang:
"Iterative Strategies for Solving Systems of Linear, Algebraic Equations Arising in 3D BE-FE Analysis of Tunnel Drivings";
Numerical Linear Algebra with Applications, 4 (1997), 3; 239 - 268.

Simulations of excavations of tunnel can be performed by means of a coupling strategy using the boundary-element-method (BEM) and the finite-element-method (FEM). The BEM is employed for the discretization of the far-field of the tunnel, whereas the FEM is used for the interior of the tunnel and its vicinity. This strategy is based on the assumption that the influence of material non-linearities in the far-field can be neglected. The coefficient matrices of the resulting systems of linear, algebraic equations consist of a symmetric, banded, sparse part resulting from the FE subdomain and an unsymmetric, fully populated part obtained from the BE subdomain. Substantial reductions of the CPU time and the disk space required for the solution of the systems of linear, algebraic equations can be achieved by employing iteractive solvers with preconditioning and using the computer hardware intelligently. In this paper, two strategies based on such solvers are proposed and explained in detail. The convergence behaviour of the implemented iteractive solvers with regards to pure BE calculations is studied by means of solving selected numerical examples. The advantages of the two proposed methods relative to the original, direct solution strategy are demonstrated on the basis of coupled simulations. Additionally, some comments concerning the use of iteractive solvers on a vector computer are given.

http://dx.doi.org/10.1002/(SICI)1099-1506(199705/06)4:3<239::AID-NLA107>3.0.CO;2-3