Parallel High-Performance Computing in Geomechanics with Inner/Outer Iterative Procedures
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
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
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Large scale parallel FEM computations of far/near stress field changes in rocks
Future Generation Computer Systems
Mathematics and Computers in Simulation
Large scale parallel FEM computations of far/near stress field changes in rocks
Future Generation Computer Systems
Analysis and Computation of Compatible Least-Squares Methods for div-curl Equations
SIAM Journal on Numerical Analysis
Parallel schwarz methods: algebraic construction of coarse problems, implementation and testing
PPAM'05 Proceedings of the 6th international conference on Parallel Processing and Applied Mathematics
Algebraic multilevel methods with aggregations: an overview
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
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We consider theoretical and computational issues associated with an aggregation-based domain decomposition preconditioner applied to a Bi-CGSTAB iterative solver used to solve both Laplace's equation and an important nonlinear model from hydrology used to simulate unsaturated flow, Richards' equation. Theoretical results for Laplace's equation provide estimates of the condition number and the rate of convergence for a two-level Schwarz domain decomposition preconditioner. Computational results for Laplace's equation and Richards' equation show excellent scalability, although no theory is yet available to support the results for the difficult nonlinear problem.