FESTUNG：用于不连续Galerkin方法的MATLAB / GNU Octave工具箱。第一部分：扩散算子
FESTUNG: A MATLAB / GNU Octave toolbox for the discontinuous Galerkin method. Part I: Diffusion operator
摘要：
这是一系列关于将间断Galerkin方法实现为MATLAB / GNU Octave工具箱的论文中的第一篇。主要目标是开发技术，提供优化的计算性能，结合紧凑，用户友好的界面。我们的实现依赖于完全向量化的矩阵/向量操作，并仔细记录;此外，离散化术语和代码例程之间的直接映射始终保持不变。研究了一类二维时变系数扩散方程.空间离散是基于局部不连续的Galerkin公式和局部质量守恒。基于正交多项式的零阶到四阶的近似已经被实现;代码结构可以容易地容纳任意类型和阶数的更多空间。采用隐式欧拉法进行时间离散。
英文摘要：
This is the first in a series of papers on implementing a discontinuous Galerkin method as a MATLAB / GNU Octave toolbox. The main goal is the development of techniques that deliver optimized computational performance combined with a compact, user-friendly interface. Our implementation relies on fully vectorized matrix / vector operations and is carefully documented; in addition, a direct mapping between discretization terms and code routines is maintained throughout. The present work focuses on a two-dimensional time-dependent diffusion equation with space / time-varying coefficients. The spatial discretization is based on the local discontinuous Galerkin formulation and is locally mass conservative. Approximations of orders zero through four based on orthogonal polynomials have been implemented; more spaces of arbitrary type and order can be easily accommodated by the code structure. Time discretization is performed using an implicit Euler method.
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。
