27,450 research outputs found
Evaluating kernels on Xeon Phi to accelerate Gysela application
This work describes the challenges presented by porting parts ofthe Gysela
code to the Intel Xeon Phi coprocessor, as well as techniques used for
optimization, vectorization and tuning that can be applied to other
applications. We evaluate the performance of somegeneric micro-benchmark on Phi
versus Intel Sandy Bridge. Several interpolation kernels useful for the Gysela
application are analyzed and the performance are shown. Some memory-bound and
compute-bound kernels are accelerated by a factor 2 on the Phi device compared
to Sandy architecture. Nevertheless, it is hard, if not impossible, to reach a
large fraction of the peek performance on the Phi device,especially for
real-life applications as Gysela. A collateral benefit of this optimization and
tuning work is that the execution time of Gysela (using 4D advections) has
decreased on a standard architecture such as Intel Sandy Bridge.Comment: submitted to ESAIM proceedings for CEMRACS 2014 summer school version
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Condition number analysis and preconditioning of the finite cell method
The (Isogeometric) Finite Cell Method - in which a domain is immersed in a
structured background mesh - suffers from conditioning problems when cells with
small volume fractions occur. In this contribution, we establish a rigorous
scaling relation between the condition number of (I)FCM system matrices and the
smallest cell volume fraction. Ill-conditioning stems either from basis
functions being small on cells with small volume fractions, or from basis
functions being nearly linearly dependent on such cells. Based on these two
sources of ill-conditioning, an algebraic preconditioning technique is
developed, which is referred to as Symmetric Incomplete Permuted Inverse
Cholesky (SIPIC). A detailed numerical investigation of the effectivity of the
SIPIC preconditioner in improving (I)FCM condition numbers and in improving the
convergence speed and accuracy of iterative solvers is presented for the
Poisson problem and for two- and three-dimensional problems in linear
elasticity, in which Nitche's method is applied in either the normal or
tangential direction. The accuracy of the preconditioned iterative solver
enables mesh convergence studies of the finite cell method
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