Large scale parallel FEM computations of far/near stress field changes in rocks

The paper describes an application of large scale finite element analysis for the assessment of stress changes in rocks induced by mining. This application allows us to illustrate efficiency of an approach based mainly on problem decomposition and parallel computing. For the main part of the computations, which is the solution of large linear systems, we use two decomposition techniques (displacement and domain decomposition). Another decomposition technique is exploited for local FE analysis of the near stress field on so called composite grids. The described methods are tested on the solution of two benchmark problems, which originate from the modelling of the effects of mining. The parallel computations are performed on a small Linux cluster.

[1]  Radim Blaheta,et al.  GPCG–generalized preconditioned CG method and its use with non‐linear and non‐symmetric displacement decomposition preconditioners , 2002, Numer. Linear Algebra Appl..

[2]  Owe Axelsson,et al.  Iterative methods for the solution of the Naviers equations of elasticity , 1977 .

[3]  A. Toselli.  Domain Decomposition Methods , 2004 .

[4]  Xiao-Chuan Cai.  The Use of Pointwise Interpolation in Domain Decomposition Methods with Nonnested Meshes , 1995, SIAM J. Sci. Comput..

[5]  Barry F. Smith,et al.  Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations , 1996 .

[6]  Radim Blaheta,et al.  Displacement decomposition - incomplete factorization preconditioning techniques for linear elasticity problems , 1994, Numer. Linear Algebra Appl..

[7]  Radim Blaheta,et al.  Nested tetrahedral grids and strengthened C.B.S. inequality , 2003, Numer. Linear Algebra Appl..

[8]  C. T. Kelley,et al.  An Aggregation-Based Domain Decomposition Preconditioner for Groundwater Flow , 2001, SIAM J. Sci. Comput..

[9]  Owe Axelsson,et al.  On iterative solvers in structural mechanics; separate displacement orderings and mixed variable methods , 1999 .

[10]  R. Blaheta,et al.  Space decomposition preconditioners and their application in geomechanics , 2003, Math. Comput. Simul..

[11]  Radim Blaheta.  Space Decomposition Preconditioners and Parallel Solvers , 2004 .

[12]  O. Axelsson.  Iterative solution methods , 1995 .

[13]  Roman Kohut,et al.  Composite Grid Finite Element Method: Implementation and Iterative Solution with Inexact Subproblems , 2002 .

[14]  Yvan Notay.  Flexible Conjugate Gradients , 2000, SIAM J. Sci. Comput..

[15]  Owe Axelsson,et al.  Two Simple Derivations of Universal Bounds for the C.B.S. Inequality Constant , 2004 .

[16]  Almerico Murli,et al.  Numerical Mathematics and Advanced Applications , 2003 .

[17]  Radim Blaheta,et al.  A multilevel method with overcorrection by aggregation for solving discrete elliptic problems , 1988 .