论文标题
在有限元矩阵的快速组合中，并应用于非线性传热问题
On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems
论文作者
论文摘要
有限元方法是线性和非线性的部分微分方程（PDE）的数值解（PDES）的良好方法。但是，经常将有限元矩阵重复重新组合为计算中的瓶颈之一。第二个瓶颈是由使用牛顿的方法求解非线性方程系统的大型和众多线性系统。在本文中，我们将解决第一个问题。我们将看到如何使用完全无环的算法在轻度假设下重写组合过程。我们的方法导致一个小的矩阵矩阵乘法，我们可能会依靠高度优化的算法。
The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated reassemblage of finite element matrices for nonlinear PDEs is frequently pointed out as one of the bottlenecks in the computations. The second bottleneck being the large and numerous linear systems to be solved arising from the use of Newton's method to solve nonlinear systems of equations. In this paper, we will address the first issue. We will see how under mild assumptions the assemblage procedure may be rewritten using a completely loop-free algorithm. Our approach leads to a small matrix-matrix multiplication for which we may count on highly optimized algorithms.
