Goal-based angular adaptivity applied to a wavelet-based discretisation of the neutral particle transport equation
Goal-based angular adaptivity applied to a wavelet-based discretisation of the neutral particle transport equation
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DOI：
10.1016/j.jcp.2014.10.063
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发表时间：
2015-01
期刊：
影响因子：
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通讯作者：
Mark A. Goffin;A. Buchan;S. Dargaville;C. Pain;Paul N. Smith;R. Smedley-Stevenson
中科院分区：
文献类型：
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作者：
Mark A. Goffin;A. Buchan;S. Dargaville;C. Pain;Paul N. Smith;R. Smedley-Stevenson
提出了一种将基于目标的自适应方法应用于中性粒子输运方程角分辨的方法。该方法适用于八面体小波离散的球面角域，允许各向异性分辨率。角分辨率在空间和能量维度上都是自适应的。空间域离散使用内部元素亚网格尺度有限元法。基于目标的自适应方法优化了角度离散化，以最大限度地减少解决方案的特定泛函中的误差。基于目标的误差估计需要伴随系统的解来确定对指定泛函的重要性。误差估计和新的方法来计算它们。通过算例验证了方法的有效性。结果表明，该方法可以显着减少未知数的数量和计算时间，以获得一个给定的错误。新奇的工作是使用基于目标的自适应方法，以获得各向异性的分辨率在角域求解输运方程。
A method for applying goal-based adaptive methods to the angular resolution of the neutral particle transport equation is presented. The methods are applied to an octahedral wavelet discretisation of the spherical angular domain which allows for anisotropic resolution. The angular resolution is adapted across both the spatial and energy dimensions. The spatial domain is discretised using an inner-element sub-grid scale finite element method. The goal-based adaptive methods optimise the angular discretisation to minimise the error in a specific functional of the solution. The goal-based error estimators require the solution of an adjoint system to determine the importance to the specified functional. The error estimators and the novel methods to calculate them are described. Several examples are presented to demonstrate the effectiveness of the methods. It is shown that the methods can significantly reduce the number of unknowns and computational time required to obtain a given error. The novelty of the work is the use of goal-based adaptive methods to obtain anisotropic resolution in the angular domain for solving the transport equation.