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有效的高阶空间-角度-能量多重点不连续的加勒金有限元素对线性博尔兹曼运输的方法
Paul Houston1, Matthew E Hubbard1, Thomas J Radley1,2
1School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD UK.
概括
我们为线性博尔兹曼运输问题开发了一种新的hp版本不连续的加勒金有限元素方法 (DGFEM). 这种准确,可并行的方法可以与现有的软件一起工作,并处理复杂的几何形状.
科学领域:
- 计算物理 计算物理
- 数字分析 数字分析
- 交通运输理论 交通运输理论
背景情况:
- 线性博尔兹曼运输方程描述了各种物理系统中的粒子运输.
- 现有的数值方法,如离散坐标,在处理复杂几何和实现任意顺序准确性方面存在局限性.
- 有效和准确的解决方案对于模拟复杂的物理现象至关重要.
研究的目的:
- 为线性博尔兹曼运输问题引入一种新的hp版本的不连续的加勒金有限元素方法 (DGFEM).
- 证明该方法对任意顺序的趋同和有效的并行实现的能力.
- 为复杂的空间几何学问题提供准确的解决方案.
主要方法:
- 开发了一种统一的hp-DGFEM,可以分辨空间,角度和能量领域.
- 纳入了局部网状精细化和局部多项式度变化.
- 为了复杂的几何形状,利用了一般的多类元素.
- 进行了稳定性和hp版本的先验错误分析,包括一个新的inf-sup bound.
主要成果:
- 该hp-DGFEM提供任意顺序的收率.
- 该方法兼容标准的多组离散坐标实现,以实现高效的并行计算.
- 数值实验证实了该方法在多能和单能问题上的性能.
- 该方法有效地处理复杂的空间几何形状.
结论:
- 拟议的hp-DGFEM提供了一种高效,准确和灵活的方法来解决线性博尔兹曼运输方程.
- 这种方法允许并行使用现有软件基础设施实现高精度的解决方案.
- 它为涉及复杂几何形状和苛刻的精度要求的问题提供了显著的优势.
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