High‐performance multilevel iterative aggregation solver for large finite‐element structural analysis problems

The 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 FEAGS 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.

[1]  V. Bulgakov,et al.  On the multi‐grid technique for solving three‐dimensional boundary value engineering problems , 1992 .

[2]  V. E. Bulgakov,et al.  Iterative aggregation technique for large-scale finite element analysis of mechanical systems , 1994 .

[3]  P. M. deZeeuw,et al.  Multigrid and conjugate gradient methods as convergence acceleration techniques , 1985 .

[4]  J. Hall,et al.  The multigrid method in solid mechanics: Part I—Algorithm description and behaviour , 1990 .

[5]  O. Axelsson,et al.  Algebraic multilevel preconditioning methods, II , 1990 .

[6]  Hans Rudolf Schwarz.  FORTRAN-Programme zur Methode der finiten Elemente , 1991 .

[7]  I. Gustafsson,et al.  Preconditioning and two-level multigrid methods of arbitrary degree of approximation , 1983 .

[8]  Vijay Sonnad,et al.  A comparison of direct and preconditioned iterative techniques for sparse, unsymmetric systems of linear equations , 1989 .

[9]  T. Manteuffel.  An incomplete factorization technique for positive definite linear systems , 1980 .

[10]  Rainald Löhner,et al.  An unstructured multigrid method for elliptic problems , 1987 .

[11]  Fast algorithms for multi-grid solvers of three-dimensional boundary value problems in structural analysis , 1992 .

[12]  V. Bulgakov.  Multi-level iterative technique and aggregation concept with semi-analytical preconditioning for solving boundary-value problems , 1993 .

[13]  M. Uschold,et al.  Methods and applications , 1953 .

[14]  R. Nicolaides,et al.  Iterative Methods for Elliptic Finite Element Equations on General Meshes , 1988 .