...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >On the finite volume reformulation of the mixed finite element method for elliptic and parabolic PDE on triangles
【24h】

On the finite volume reformulation of the mixed finite element method for elliptic and parabolic PDE on triangles

机译：三角形上椭圆形与抛物型PDE混合有限元方法的有限体积重构。

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

A new resolution of parabolic and elliptic partial differential equations (PDEs) based on the mixed finite element approximation on triangles has been recently developed . This new approach reduces the number of unknowns from fluxes or Lagrange multiplier defined on edges to a single unknown per element. In this paper, we analyze this transformation mathematically, and describe in details how to handle singular elements and singular edges. For these singular elements, the standard mixed method on triangles can always be made equivalent to a finite volume formulation, where the finite volumes are obtained by aggregation of finite elements across singular edges. The positive definiteness of the system matrix obtained with the new formulation is analyzed in details. A criterion is given concerning the property of this matrix which show that its conditioning is related to the shape of the triangle and the contrast in parameters from one element to the adjacent ones. Numerical experiments are performed for elliptic and parabolic PDEs. The comparisons between an iterative solver (PCG) and a direct solver (unifrontal/multifrontal) show that the direct solver is more efficient. Moreover, its performance is not correlated with the system matrix conditioning. It appears that the new formulation requires significantly less CPU time for elliptic PDEs and is competitive for parabolic PDEs. The new formulation remains also accurate enough even in nearly singular situations.
机译：最近开发了一种基于三角形混合有限元逼近的抛物线和椭圆形偏微分方程（PDE）的新分辨率。这种新方法将边上定义的通量或拉格朗日乘数的未知数减少到每个元素单个未知数。在本文中，我们对这一变换进行了数学分析，并详细描述了如何处理奇异元素和奇异边。对于这些奇异元素，始终可以使三角形的标准混合方法等效于有限体积公式，其中有限体积是通过跨奇异边缘聚合有限元素而获得的。详细分析了用新公式获得的系统矩阵的正定性。给出了有关该矩阵性质的准则，该准则表明其条件与三角形的形状以及从一个元素到相邻元素的参数对比度有关。对椭圆形和抛物线形偏微分方程进行了数值实验。迭代求解器（PCG）与直接求解器（单面/多面）之间的比较表明，直接求解器效率更高。此外，它的性能与系统矩阵调节无关。看来，新配方对椭圆形PDE所需的CPU时间大大减少，并且对于抛物线PDE具有竞争力。即使在几乎单一的情况下，新配方也仍然足够准确。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号