Keywords: porous media, staggered method, finite element method, parallel analysis, domain decomposition, FETI.

Saturated porous media is composed of solid and fluid phase. The porous media analysis is very difficult to use the general solid mechanics theory, because saturated porous media is composed of different materials. Therefore, it is necessary to use porous theory considering solid mechanics and the fluid flow. For such reasons, the mixed finite element method is used in the saturated porous media analysis. Especially, in the case when the solid and fluid are nearly incompressible and the fluid is nearly impermeable, hence element locking problems can occur. Recently, in order to resolve this problem, the staggered method was proposed by Park and Tak [1,2]. The staggered method is composed of a multi-time step, a remeshing step and a sub-iteration step. However, the numerical efficiency is decreased because the iteration step in the staggered method is performed more than once. Thus, in order to improve the numerical efficiency, it is proposed that the method be combined with the finite element tearing and interconnecting (FETI) method and the staggered method for saturated porous media.

The FETI method is an effective domain decomposition method for parallel analysis that was introduced by Farhat [3]. This method is a domain decomposition method for parallel finite element analyses of the solution of static problems. The FETI method requires fewer interprocessor communications than traditional domain decomposition algorithms, while still offering the same amount of parallelism.

In this paper, in order to improve the numerical efficiency of the staggered method, the combined FETI method with the staggered method is used. The staggered method for the porous media is solved using the pore pressure after obtaining the displacement, so the running time for the displacement analyses is longer than for the pore pressure. In order to improve their numerical efficiency, the FETI method is applied to the calculation of the displacement and the pore pressure. First the porous media theory, then the staggered method and finally the FETI method are briefly introduced in this paper. Then the combined staggered method with the FETI method is introduced. Finally Lagrange multipliers and the conjugate gradient (CG) algorithm to solve the decomposed domain are explained, and then the proposed method is verified to be numerically efficient by using the MPI library.

1

T. Park, M. Tak, "A New Coupled Analysis for Nearly Incompressible and Impermeable Saturated Porous Media on Mixed Finite Element Method: I. Proposed Method", KSCE, 14(1), 7-16, 2010. doi:10.1007/s12205-010-0007-x

2

M. Tak, T. Park, "A New Coupled Analysis for Nearly Incompressible and Impermeable Saturated Porous Media on Mixed Finite Element Method: II. Verifications", KSCE, 14(1), 17-24, 2010. doi:10.1007/s12205-010-0017-8

3

C. Farhat, "A Method of Finite Element Tearing and Interconnecting and Its Parallel Solution Algorithm", International Journal for Numerical Methods in Engineering, 32, 1205-1277, 1991. doi:10.1002/nme.1620320604

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