论文标题
枫木中稀疏的DAE解决者
A Sparse DAE Solver in Maple
论文作者
论文摘要
在本文中，在枫树中实现了一些自适应单步方法，例如梯形（TR），隐式中点（IMP），Euler-Backward（EB）和Radau IIA（RAD）方法，以求解INDEX-1非线性差异代数方程（DAE）。利用枫树在列表/集合中搜索的强大而有效的能力，以识别稀疏模式和分析性雅各布。发现该算法和实现对于索引-1 DAE问题是可靠的，有效的，对于有限差异/有限元元素离散化的二维模型的系统大小高达10,000个非线性DAE，并在几秒钟内求解相同。
In this paper, some adaptive single-step methods like Trapezoid (TR), Implicit-mid point (IMP), Euler-backward (EB), and Radau IIA (Rad) methods are implemented in Maple to solve index-1 nonlinear Differential Algebraic Equations (DAEs). Maple's robust and efficient ability to search within a list/set is exploited to identify the sparsity pattern and the analytic Jacobian. The algorithm and implementation were found to be robust and efficient for index-1 DAE problems and scales well for finite difference/finite element discretization of two-dimensional models with system size up to 10,000 nonlinear DAEs and solves the same in few seconds.
