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SUMMARYThe present study is aimed to overcome difficulties faced with industrial applications of multilevel iterative methods to arbitrary finite element (FE) structural analysis problems. The coarse grid concept, used in multigrid methods, is substituted with an aggregation coarse model based on the mechanical principle. On the base of this approach together with previously developed multilevel preconditioner, an efficient iterative equation solver FELAGS was developed for using in standard comprehensive finite element software systems. Numerical examples for analyses of three-dimensional (3-D) frame structures demonstrate the efficiency of the method. Comparison with incomplete Cholesky conjugate gradient (ICCG) method and direct methods is presented.

SUMMARYSome iterative multi-level approaches for solving large-scale finite-element elliptic problems are proposed. It is suggested that these approaches be used in combination with an aggregation technique. On the basis of the aggregation concept a new efficient preconditioning procedure in the inner iterative scheme of the algorithm is developed. This procedure is derived from the fundamental solution of a corresponding elliptic problem. The efficiency of the approaches is demonstrated by numerical examples.

In this paper the diffusion equation is solved in two-dimensional geometry by the dual reciprocity boundary element method (DRBEM). It is structured by fully implicit discretization over time and by weighting with the fundamental solution of the Laplace equation. The resulting domain integral of the diffusive term is transformed into two boundary integrals by using Green's second identity, and the domain integral of the transience term is converted into a finite series of boundary integrals by using dual reciprocity interpolation based on scaled augmented thin plate spline global approximation functions. Straight line geometry and constant field shape functions for boundary discretization are employed. The described procedure results in systems of equations with fully populated unsymmetric matrices. In the case of solving large problems, the solution of these systems by direct methods may be very time consuming. The present study investigates the possibility of using iterative methods for solving these systems of equations. It was demonstrated that Krylov-type methods like CGS and GMRES with simple Jacobi preconditioning appeared to be efficient and robust with respect to the problem size and time step magnitude. This paper can be considered as a logical starting point for research of iterative solutions to DRBEM systems of equations. 1998 John Wiley & Sons, Ltd.