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Computational cost comparison between nodal and vector finite elements in the modeling of controlled source electromagnetic data using a direct solver
Computers & Geosciences ( IF 4.4 ) Pub Date : 2021-08-13 , DOI: 10.1016/j.cageo.2021.104901
Anderson Almeida da Piedade 1, 2 , Cícero Régis 1, 3 , Carlos Mateus Barriga Nunes 1 , Hilton Farias da Silva 1
Affiliation  

The Finite Element method can be implemented to model geophysical electromagnetic data using one of two methodologies called Nodal and Vector Finite Elements. This paper presents a comparison between the two approaches, emphasizing memory usage and processing time, when simulating Marine Controlled Source Electromagnetic (MCSEM) data in three-dimensional models. The study is carried out using unstructured meshes and a direct solver. Computational cost information from both methodologies are gathered from four different 3D models, each emphasizing a different aspect of the problem. The results indicate that the Vector Finite Element methodology requires less memory and processing time to calculate the same data using the same mesh. Although the nodal method generates a smaller linear system than the vector method, the vector coefficient matrix is significantly more sparse than the nodal one. The greater sparsity makes the vector approach more computationally efficient, requiring less memory and running in less time than the nodal method to generate results with the same level of accuracy.



中文翻译:

使用直接求解器对受控源电磁数据建模中节点和矢量有限元之间的计算成本比较

可以实现有限元方法以使用称为节点有限元和矢量有限元的两种方法之一对地球物理电磁数据进行建模。本文介绍了两种方法之间的比较,强调了在三维模型中模拟海洋受控源电磁 (MCSEM) 数据时的内存使用和处理时间。该研究是使用非结构化网格和直接求解器进行的。两种方法的计算成本信息都是从四个不同的 3D 模型中收集的,每个模型都强调问题的不同方面。结果表明矢量有限元方法需要更少的内存和处理时间来使用相同的网格计算相同的数据。尽管节点法生成的线性系统比矢量法更小,矢量系数矩阵明显比节点矩阵更稀疏。更大的稀疏性使向量方法在计算上更有效率,与节点方法相比,需要更少的内存和运行时间更短,以生成具有相同精度水平的结果。

更新日期:2021-08-19
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