Interactive High‐Quality Visualization of Higher‐Order Finite Elements
Interactive High‐Quality Visualization of Higher‐Order Finite Elements
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DOI：
10.1111/j.1467-8659.2009.01603.x
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发表时间：
2010-05
影响因子：
2.5
通讯作者：
M. Üffinger;S. Frey;T. Ertl
中科院分区：
文献类型：
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作者：
M. Üffinger;S. Frey;T. Ertl
高阶有限元方法是一种重要的数值模拟离散方法。它们越来越多地被用于当代的数值求解器中，产生了一类必须由科学家和工程师分析的新数据。目前可用于这类数据的可视化工具要么是面向批处理的，要么限于某些单元类型和多项式次数。其他方法通过重采样来近似高阶数据，导致在交互性和质量方面进行权衡。为了克服这些限制，我们开发了一个分布式可视化系统，该系统允许对非协调非结构网格进行交互探索，该非协调非结构网格是由时空不连续Galerkin模拟产生的，其中每个单元都有自己的高阶多项式解。我们的系统使用基于GPU的光线投射来直接绘制复杂网格的体绘制，这些网格具有非凸的、变化的多项式次数的曲线单元。基于频率的自适应采样解释了沿射线的高变化。对于跨GPU集群的分布，初始对象空间分区由单元特征(如多项式次数)确定，并在运行时通过负载平衡机制进行调整。对不同的气动声学模拟中涉及激波阵面传播的性能和实用性进行了评估。
Higher‐order finite element methods have emerged as an important discretization scheme for simulation. They are increasingly used in contemporary numerical solvers, generating a new class of data that must be analyzed by scientists and engineers. Currently available visualization tools for this type of data are either batch oriented or limited to certain cell types and polynomial degrees. Other approaches approximate higher‐order data by resampling resulting in trade‐offs in interactivity and quality. To overcome these limitations, we have developed a distributed visualization system which allows for interactive exploration of non‐conforming unstructured grids, resulting from space‐time discontinuous Galerkin simulations, in which each cell has its own higher‐order polynomial solution. Our system employs GPU‐based raycasting for direct volume rendering of complex grids which feature non‐convex, curvilinear cells with varying polynomial degree. Frequency‐based adaptive sampling accounts for the high variations along rays. For distribution across a GPU cluster, the initial object‐space partitioning is determined by cell characteristics like the polynomial degree and is adapted at runtime by a load balancing mechanism. The performance and utility of our system is evaluated for different aeroacoustic simulations involving the propagation of shock fronts.