A multilevel method with overcorrection by aggregation for solving discrete elliptic problems
Journal of Computational and Applied Mathematics - Special issue on iterative methods for the solution of linear systems
Iterative solution methods
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Mathematics and Computers in Simulation - Special issue from IMACS sponsored conference: “Modelling '98”
The method of subspace corrections
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
An Aggregation-Based Domain Decomposition Preconditioner for Groundwater Flow
SIAM Journal on Scientific Computing
Space decomposition preconditioners and their application in geomechanics
Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
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In this paper we address the solution of large linear systems arising from the mathematical modelling in geomechanics and show an example of such modelling. The solution of linear systems is based on displacement decomposition or domain decomposition techniques with inexact solution of the arising subproblems by inner iterations. The use of inner iterations requires a generalization of the preconditioned CG method but brings additional benefits for parallel computation, possibility of reduction of the interprocessor communications and an additional tool of load balance.