508 research outputs found
A class of nonsymmetric preconditioners for saddle point problems
For iterative solution of saddle point problems, a nonsymmetric preconditioning is studied which, with respect to the upper-left block of the system matrix, can be seen as a variant of SSOR. An idealized situation where the SSOR is taken with respect to the skew-symmetric part plus the diagonal part of the upper-left block is analyzed in detail. Since action of the preconditioner involves solution of a Schur complement system, an inexact form of the preconditioner can be of interest. This results in an inner-outer iterative process. Numerical experiments with solution of linearized Navier-Stokes equations demonstrate efficiency of the new preconditioner, especially when the left-upper block is far from symmetric
ParMooN - a modernized program package based on mapped finite elements
{\sc ParMooN} is a program package for the numerical solution of elliptic and
parabolic partial differential equations. It inherits the distinct features of
its predecessor {\sc MooNMD} \cite{JM04}: strict decoupling of geometry and
finite element spaces, implementation of mapped finite elements as their
definition can be found in textbooks, and a geometric multigrid preconditioner
with the option to use different finite element spaces on different levels of
the multigrid hierarchy. After having presented some thoughts about in-house
research codes, this paper focuses on aspects of the parallelization for a
distributed memory environment, which is the main novelty of {\sc ParMooN}.
Numerical studies, performed on compute servers, assess the efficiency of the
parallelized geometric multigrid preconditioner in comparison with some
parallel solvers that are available in the library {\sc PETSc}. The results of
these studies give a first indication whether the cumbersome implementation of
the parallelized geometric multigrid method was worthwhile or not.Comment: partly supported by European Union (EU), Horizon 2020, Marie
Sk{\l}odowska-Curie Innovative Training Networks (ITN-EID), MIMESIS, grant
number 67571
A variant of the AOR method for augmented systems
A variant of the AOR method for augmented system
ParMooN - a modernized program package based on mapped finite elements
PARMOON is a program package for the numerical solution of elliptic and
parabolic partial differential equations. It inherits the distinct features
of its predecessor MOONMD [28]: strict decoupling of geometry and finite
element spaces, implementation of mapped finite elements as their definition
can be found in textbooks, and a geometric multigrid preconditioner with the
option to use different finite element spaces on different levels of the
multigrid hierarchy. After having presented some thoughts about in-house
research codes, this paper focuses on aspects of the parallelization, which
is the main novelty of PARMOON. Numerical studies, performed on compute
servers, assess the efficiency of the parallelized geometric multigrid
preconditioner in comparison with parallel solvers that are available in
external libraries. The results of these studies give a first indication
whether the cumbersome implementation of the parallelized geometric multigrid
method was worthwhile or not
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