GenASiS数学：面向对象的流形、运算和大规模物理模拟求解器
GenASiS Mathematics: Object-oriented manifolds, operations, and solvers for large-scale physics simulations
摘要：
由偏微分方程控制的物理场系统的大规模计算机模拟需要某种方法来近似连续性的数学极限。例如，守恒律经常用“有限体积”方法来处理，在这种方法中，空间被划分成大量的小“单元”，通过单元面的通量提供了一种直观的离散化，这种离散化是根据发散算子的数学定义来建模的。在这里，我们描述并提供Fortran 2003类家具可扩展的面向对象的实现简单的网格和通用的保守电流的演变，随着个人的“单元测试”程序和更大的例子问题，证明他们的使用。这些课程开创了我们正在开发的天体物理模拟代码GenASiS（通用天体物理模拟系统）的数学部分，该代码将随着时间的推移而扩展，包括额外的网格选项，数学运算，求解器类型和适用于许多多物理场应用的求解器变体。
英文摘要：
The large-scale computer simulation of a system of physical fields governed by partial differential equations requires some means of approximating the mathematical limit of continuity. For example, conservation laws are often treated with a `finite-volume' approach in which space is partitioned into a large number of small `cells,' with fluxes through cell faces providing an intuitive discretization modeled on the mathematical definition of the divergence operator. Here we describe and make available Fortran 2003 classes furnishing extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon, along with individual `unit test' programs and larger example problems demonstrating their use. These classes inaugurate the Mathematics division of our developing astrophysics simulation code GenASiS (General Astrophysical Simulation System), which will be expanded over time to include additional meshing options, mathematical operations, solver types, and solver variations appropriate for many multiphysics applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
