7,990 research outputs found
Preconditioned fully implicit PDE solvers for monument conservation
Mathematical models for the description, in a quantitative way, of the
damages induced on the monuments by the action of specific pollutants are often
systems of nonlinear, possibly degenerate, parabolic equations. Although some
the asymptotic properties of the solutions are known, for a short window of
time, one needs a numerical approximation scheme in order to have a
quantitative forecast at any time of interest. In this paper a fully implicit
numerical method is proposed, analyzed and numerically tested for parabolic
equations of porous media type and on a systems of two PDEs that models the
sulfation of marble in monuments. Due to the nonlinear nature of the underlying
mathematical model, the use of a fixed point scheme is required and every step
implies the solution of large, locally structured, linear systems. A special
effort is devoted to the spectral analysis of the relevant matrices and to the
design of appropriate iterative or multi-iterative solvers, with special
attention to preconditioned Krylov methods and to multigrid procedures.
Numerical experiments for the validation of the analysis complement this
contribution.Comment: 26 pages, 13 figure
A bibliography on parallel and vector numerical algorithms
This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also
Computational methods for internal flows with emphasis on turbomachinery
Current computational methods for analyzing flows in turbomachinery and other related internal propulsion components are presented. The methods are divided into two classes. The inviscid methods deal specifically with turbomachinery applications. Viscous methods, deal with generalized duct flows as well as flows in turbomachinery passages. Inviscid methods are categorized into the potential, stream function, and Euler aproaches. Viscous methods are treated in terms of parabolic, partially parabolic, and elliptic procedures. Various grids used in association with these procedures are also discussed
Status of research at the Institute for Computer Applications in Science and Engineering (ICASE)
Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science is summarized
Efficient Multigrid Preconditioners for Atmospheric Flow Simulations at High Aspect Ratio
Many problems in fluid modelling require the efficient solution of highly
anisotropic elliptic partial differential equations (PDEs) in "flat" domains.
For example, in numerical weather- and climate-prediction an elliptic PDE for
the pressure correction has to be solved at every time step in a thin spherical
shell representing the global atmosphere. This elliptic solve can be one of the
computationally most demanding components in semi-implicit semi-Lagrangian time
stepping methods which are very popular as they allow for larger model time
steps and better overall performance. With increasing model resolution,
algorithmically efficient and scalable algorithms are essential to run the code
under tight operational time constraints. We discuss the theory and practical
application of bespoke geometric multigrid preconditioners for equations of
this type. The algorithms deal with the strong anisotropy in the vertical
direction by using the tensor-product approach originally analysed by B\"{o}rm
and Hiptmair [Numer. Algorithms, 26/3 (2001), pp. 219-234]. We extend the
analysis to three dimensions under slightly weakened assumptions, and
numerically demonstrate its efficiency for the solution of the elliptic PDE for
the global pressure correction in atmospheric forecast models. For this we
compare the performance of different multigrid preconditioners on a
tensor-product grid with a semi-structured and quasi-uniform horizontal mesh
and a one dimensional vertical grid. The code is implemented in the Distributed
and Unified Numerics Environment (DUNE), which provides an easy-to-use and
scalable environment for algorithms operating on tensor-product grids. Parallel
scalability of our solvers on up to 20,480 cores is demonstrated on the HECToR
supercomputer.Comment: 22 pages, 6 Figures, 2 Table
- …