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首页> 外文期刊>The Astrophysical journal >MULTIDIMENSIONAL ASTROPHYSICAL STRUCTURAL AND DYNAMICAL ANALYSIS. I. DEVELOPMENT OF A NONLINEAR FINITE ELEMENT APPROACH
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MULTIDIMENSIONAL ASTROPHYSICAL STRUCTURAL AND DYNAMICAL ANALYSIS. I. DEVELOPMENT OF A NONLINEAR FINITE ELEMENT APPROACH

机译：多维天体结构和动力学分析。 I.非线性有限元方法的发展

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A new field of numerical astrophysics is introduced that addresses the solution of large multidimen- tion disks, four-dimensional spacetimes etc.), as well as rapidly evolving systems. The technique employed is the finite element method (FEM), which has been used to solve engineering structural prob- lems for more than three decades. The approach developed here has the following key features 1. The computational mesh can extend into the time dimension, as well as spacegenerally, only a few cells deep for most (flat-space) astrophysical problems, but throughout spacetime for solving Ein- stein's field equations. 2. When time is treated as a mesh dimension. virtually all equations describing the astrophysics of continuous media, including the field equations, can be written in a compact form similar to that routin- ely solved by most engineering finite element codes (albeit for nonlinear`equations in a four-dimensional spacetime instead of linear ones in two or three space dimensions) the divergence of a generalized stress tensor equals a generalized body-force vector, both of which are functions only of position, the state variables and their gradients. ` 3. The transformations that occur naturally in the four-dimensional FEM possess both coordinate and boost features, such that (A) although the computational mesh may have a complex ,nonanalytic, curvilinear structure, and may be adapted to the geometry of the problem, the physical equations still can be written in a simple coordinate system that is independent of the mesh structure, and (B) if the mesh has a complex flow v
机译：引入了数字天体物理学的新领域，该领域致力于解决大型多维磁盘，四维时空等问题以及快速发展的系统。所采用的技术是有限元方法（FEM），该技术已用于解决工程结构问题超过三十年了。这里开发的方法具有以下关键特征：1.计算网格可以扩展到时间维度，并且通常可以扩展到空间，对于大多数（平面空间）天体物理问题，只有几个单元深，但是在整个时空中都可以解决爱因斯坦的场方程。 2.将时间视为网格尺寸时。几乎所有描述连续介质天体物理学的方程式，包括场方程式，都可以用类似于大多数工程有限元代码通常解决的紧凑形式编写（尽管是在四维时空而非线性方程组中）二维应力张量的散度等于广义体力矢量，这两者都是位置，状态变量及其梯度的函数。 `3.在四维有限元法中自然发生的变换既具有坐标特征又具有增强特征，因此（A）尽管计算网格可能具有复杂的，非解析的曲线结构，并且可以适应问题的几何形状，仍然可以在独立于网格结构的简单坐标系中编写物理方程，并且（B）如果网格具有复杂的流v

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