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document
Nabben, R. (author), Vuik, C. (author)
In this paper we compare various preconditioners for the numerical solution of partial dierential equations. We compare a coarse grid correction preconditioner used in domain decomposition methods with a so-called deflation preconditioner. We prove that the effective condition number of the de ated preconditioned system is always, i.e. for all...
report 2003
document
Nabben, R. (author), Vuik, C. (author)
In this paper we compare various preconditioners for the numerical solution of partial differential equations. We compare the well-known balancing Neumann Neumann preconditioner used in domain decomposition methods with a so-called deflation preconditioner. We prove that the effective condition number of the deflated preconditioned system is...
report 2004
document
Nabben, R. (author), Vuik, C. (author)
The balancing Neumann-Neumann (BNN) and the additive coarse grid correction (BPS) preconditioner are fast and successful preconditioners within domain decomposition methods for solving partial differential equations. For certain elliptic problems these preconditioners lead to condition numbers which are independent of the mesh sizes and are...
conference paper 2006
document
Tang, J.M. (author), Nabben, R. (author), Vuik, C. (author), Erlangga, Y.A. (author)
report 2007
document
Nabben, R. (author), Vuik, C. (author)
report 2007
document
Tang, J.M. (author), MacLachlan, S.P. (author), Nabben, R. (author), Vuik, C. (author)
report 2008
document
Tang, J.M. (author), Nabben, R. (author), Vuik, C. (author), Erlangga, Y.A. (author)
For various applications, it is well-known that a multi-level, in particular two-level, preconditioned CG (PCG) method is an efficient method for solving large and sparse linear systems with a coefficient matrix that is symmetric positive definite. The corresponding two-level preconditioner combines traditional and projection-type...
journal article 2009
document
Tang, J.M. (author), MacLachlan, S.P. (author), Nabben, R. (author), Vuik, C. (author)
It is well known that two-level and multilevel preconditioned conjugate gradient (PCG) methods provide efficient techniques for solving large and sparse linear systems whose coefficient matrices are symmetric and positive definite. A two-level PCG method combines a traditional (one-level) preconditioner, such as incomplete Cholesky, with a...
journal article 2010
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