2,140 research outputs found
High performance interior point methods for three-dimensional finite element limit analysis
The ability to obtain rigorous upper and lower bounds on collapse loads of various structures makes finite element limit analysis an attractive design tool. The increasingly high cost of computing those bounds, however, has limited its application on problems in three dimensions. This work reports on a high-performance homogeneous self-dual primal-dual interior point method developed for three-dimensional finite element limit analysis. This implementation achieves convergence times over 4.5× faster than the leading commercial solver across a set of three-dimensional finite element limit analysis test problems, making investigation of three dimensional limit loads viable. A comparison between a range of iterative linear solvers and direct methods used to determine the search direction is also provided, demonstrating the superiority of direct methods for this application. The components of the interior point solver considered include the elimination of and options for handling remaining free variables, multifrontal and supernodal Cholesky comparison for computing the search direction, differences between approximate minimum degree [1] and nested dissection [13] orderings, dealing with dense columns and fixed variables, and accelerating the linear system solver through parallelization. Each of these areas resulted in an improvement on at least one of the problems in the test set, with many achieving gains across the whole set. The serial implementation achieved runtime performance 1.7× faster than the commercial solver Mosek [5]. Compared with the parallel version of Mosek, the use of parallel BLAS routines in the supernodal solver saw a 1.9× speedup, and with a modified version of the GPU-enabled CHOLMOD [11] and a single NVIDIA Tesla K20c this speedup increased to 4.65×
Taking advantage of hybrid systems for sparse direct solvers via task-based runtimes
The ongoing hardware evolution exhibits an escalation in the number, as well
as in the heterogeneity, of computing resources. The pressure to maintain
reasonable levels of performance and portability forces application developers
to leave the traditional programming paradigms and explore alternative
solutions. PaStiX is a parallel sparse direct solver, based on a dynamic
scheduler for modern hierarchical manycore architectures. In this paper, we
study the benefits and limits of replacing the highly specialized internal
scheduler of the PaStiX solver with two generic runtime systems: PaRSEC and
StarPU. The tasks graph of the factorization step is made available to the two
runtimes, providing them the opportunity to process and optimize its traversal
in order to maximize the algorithm efficiency for the targeted hardware
platform. A comparative study of the performance of the PaStiX solver on top of
its native internal scheduler, PaRSEC, and StarPU frameworks, on different
execution environments, is performed. The analysis highlights that these
generic task-based runtimes achieve comparable results to the
application-optimized embedded scheduler on homogeneous platforms. Furthermore,
they are able to significantly speed up the solver on heterogeneous
environments by taking advantage of the accelerators while hiding the
complexity of their efficient manipulation from the programmer.Comment: Heterogeneity in Computing Workshop (2014
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