987 research outputs found
Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients
We present a robust and scalable preconditioner for the solution of
large-scale linear systems that arise from the discretization of elliptic PDEs
amenable to rank compression. The preconditioner is based on hierarchical
low-rank approximations and the cyclic reduction method. The setup and
application phases of the preconditioner achieve log-linear complexity in
memory footprint and number of operations, and numerical experiments exhibit
good weak and strong scalability at large processor counts in a distributed
memory environment. Numerical experiments with linear systems that feature
symmetry and nonsymmetry, definiteness and indefiniteness, constant and
variable coefficients demonstrate the preconditioner applicability and
robustness. Furthermore, it is possible to control the number of iterations via
the accuracy threshold of the hierarchical matrix approximations and their
arithmetic operations, and the tuning of the admissibility condition parameter.
Together, these parameters allow for optimization of the memory requirements
and performance of the preconditioner.Comment: 24 pages, Elsevier Journal of Computational and Applied Mathematics,
Dec 201
Modeling of Spatial Uncertainties in the Magnetic Reluctivity
In this paper a computationally efficient approach is suggested for the
stochastic modeling of an inhomogeneous reluctivity of magnetic materials.
These materials can be part of electrical machines, such as a single phase
transformer (a benchmark example that is considered in this paper). The
approach is based on the Karhunen-Lo\`{e}ve expansion. The stochastic model is
further used to study the statistics of the self inductance of the primary coil
as a quantity of interest.Comment: submitted to COMPE
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