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相关概念视频

Differential Form of Maxwell's Equations01:17

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James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
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A line integral for a vector field is defined as the integral of the dot product of a vector function with an infinitesimal displacement vector along a prescribed path. If the prescribed path is closed, the integrals reduce to a closed-line integral. The closed-contour integral of the vector field is referred to in terms of the circulation of the vector field around the closed path. A vector with zero circulation around every closed path is called a conservative field, while one with non-zero...
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For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
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相关实验视频

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VEMcomp:一个虚拟元件MATLAB包,用于2D和3D的散装表面PDEs.

Massimo Frittelli1, Anotida Madzvamuse2,3,4,5, Ivonne Sgura1

  • 1Department of Mathematics and Physics "E. De Giorgi", Via per Arnesano, University of Salento, 73100 Lecce, Italy.

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概括

本研究介绍了VEMcomp,这是一个虚拟元素方法 (VEM) MATLAB解决器,用于部分微分方程 (PDEs). VEMcomp有效地处理复杂的几何形状和各种PDE类型,为科学计算提供了一种多功能工具.

关键词:
在散装表面的PDEs.大量表面有限元素方法.大量表面虚拟元件方法.伊梅克斯欧勒法 欧勒法在 MATLAB 中,我们可以使用 MATLAB.网格生成 网格生成 网格生成虚拟元素方法 虚拟元素方法

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科学领域:

  • 计算数学 计算数学 计算数学
  • 数字分析 数字分析
  • 科学计算科学计算

背景情况:

  • 部分微分方程 (PDEs) 在材料科学,工程和生物学领域的建模现象中是至关重要的.
  • 现有的数值方法经常面临复杂的几何形状和多种PDE配方的挑战.
  • 需要灵活和高效的解决方案,适用于广泛的科学问题.

研究的目的:

  • 介绍VEMcomp,一个虚拟元件MATLAB解决器,用于2D和3D的圆和抛物线,线性和半线性PDEs.
  • 为生成网格,计算矩阵和解决PDE问题提供统一的库.
  • 为各种 PDE 模型提供一个用户友好的界面,用于将虚拟元素方法 (VEM) 和有限元素方法 (FEM) 应用于各种 PDE 模型.

主要方法:

  • 在一般多边形和多面网格上实施最小多项式顺序 (k=1) 的虚拟元素方法 (VEM).
  • 集成用于多角形和多面体域的网格生成能力,包括对表面PDE与DistMesh的兼容性.
  • 利用IMEX Euler在短暂问题中的时间步骤,再加上VEM/FEM空间分密化.

主要成果:

  • VEMcomp成功生成了优化的网格,并计算了VEM和FEM所需的矩阵 (质量和刚度).
  • 解决器处理线性和非线性模型,包括时间依赖的批量,表面和批量-表面 PDEs.
  • 提供可选的后处理功能用于可视化和错误估计.

结论:

  • 在科学和工程领域,VEMcomp提供了一种强大而灵活的工具,用于解决广泛的PDE问题.
  • 图书馆能够处理复杂的几何形状和各种PDE类型,这使得它对研究人员非常有价值.
  • VEMcomp促进了VEM和FEM的应用,增强了对具有挑战性的问题的数值解决方案.