Bringing Trimmed Serendipity Methods to Computational Practice in Firedrake
Bringing Trimmed Serendipity Methods to Computational Practice in Firedrake
复制标题
将修剪的偶然性方法引入 Firedrake 的计算实践中
DOI：
10.1145/3490485
复制
发表时间：
2022
影响因子：
2.7
通讯作者：
Gillette, Andrew
中科院分区：
文献类型：
--
作者：
Crum, Justin;Cheng, Cyrus;Ham, David A.;Mitchell, Lawrence;Kirby, Robert C.;Levine, Joshua A.;Gillette, Andrew
我们提出了一个实现的修剪意外的有限元家庭，使用开源有限元软件包Firedrake。新的元素可以无缝地使用在软件套件中的问题，需要H1，H（旋度），或H（div）-协调元素的正方形或立方体的网格。为了测试如何以及修剪serendipity元素执行相比，传统的张量积元素，我们进行了一系列的数值实验，包括原始泊松，混合泊松，和麦克斯韦腔本征值问题。总的来说，我们发现修剪的意外元素收敛，正如预期的那样，在相同的速度作为各自的张量积元素，同时能够提供显着节省的时间或内存所需的解决某些问题。
We present an implementation of the trimmed serendipity finite element family, using the open-source finite element package Firedrake. The new elements can be used seamlessly within the software suite for problems requiringH1,H(curl), orH(div)-conforming elements on meshes of squares or cubes. To test how well trimmed serendipity elements perform in comparison to traditional tensor product elements, we perform a sequence of numerical experiments including the primal Poisson, mixed Poisson, and Maxwell cavity eigenvalue problems. Overall, we find that the trimmed serendipity elements converge, as expected, at the same rate as the respective tensor product elements, while being able to offer significant savings in the time or memory required to solve certain problems.