One contribution of 15 to a discussion meeting issue 'Numerical algorithms for high-performance computational science'.
Subject Areas:algorithmic information theory, computer modelling and simulation
We compare inexact Newton and coordinate descent optimization methods for improving the quality of a mesh by repositioning the vertices, where the overall quality is measured by the harmonic mean of the mean-ratio metric. The effects of problem size, element size heterogeneity, and various vertex displacement schemes on the performance of these algorithms are assessed for a series of tetrahedral meshes.
Mesh-based PDE simulation codes are becoming increasingly sophisticated and rely on advanced meshing and discretization tools. Unfortunately, it is still difficult to interchange or interoperate tools developed by different communities to experiment with various technologies or to develop new capabilities. To address these difficulties, we have developed component interfaces designed to support the information flow of mesh-based PDE simulations. We describe this information flow and discuss typical roles and services provided by the geometry, mesh, and field components of the simulation. Based on this delineation for the roles of each component, we give a high-level description of the abstract data model and set of interfaces developed by the Department of Energy's Interoperable Tools for Advanced Petascale Simulation (ITAPS) center. These common interfaces are critical to our interoperability goal, and we give examples of several services based upon these interfaces including mesh adaptation and mesh improvement.
Much of the effort required to create a new simulation code goes into developing infrastructure for mesh data manipulation, adaptive refinement, design optimization, and so forth. This infrastructure is an obvious target for code reuse, except that implementations of these functionalities are typically tied to specific data structures. In this article, we describe a software component---an abstract data model and programming interface---designed to provide low-level mesh query and manipulation support for meshing and solution algorithms. The component’s data model provides a data abstraction, completely hiding all details of how mesh data is stored, while its interface defines how applications can interact with that data. Because the component has been carefully designed to be general purpose and efficient, it provides a practical platform for implementing high-level mesh operations independently of the underlying mesh data structures. After describing the data model and interface, we provide several usage examples, each of which has been used successfully with multiple implementations of the interface functionality. The overhead due to accessing mesh data through the interface rather than directly accessing the underlying mesh data is shown to be acceptably small.
The FACETS (Framework Application for Core-Edge Transport Simulations) project began in January 2007 with the goal of providing core to wall transport modeling of a tokamak fusion reactor. This involves coupling previously separate computations for the core, edge, and wall regions. Such a coupling is primarily through connection regions of lower dimensionality. The project has started developing a component-based coupling framework to bring together models for each of these regions. In the first year, the core model will be a 1 ½ dimensional model (1D transport across flux surfaces coupled to a 2D equilibrium) with fixed equilibrium. The initial edge model will be the fluid model, UEDGE, but inclusion of kinetic models is planned for the out years. The project also has an embedded Scientific Application Partnership that is examining embedding a full-scale turbulence model for obtaining the crosssurface fluxes into a core transport code.
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