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首页> 外文期刊>Physics of the Earth and Planetary Interiors: A Journal Devoted to Obsevational and Experimerntal Studies of the Chemistry and Physics of Planetary Interiors and Their Theoretical Interpretation >A hybrid finite difference-finite element method to incorporate topography for 2D direct current (DC) resistivity modeling
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A hybrid finite difference-finite element method to incorporate topography for 2D direct current (DC) resistivity modeling

机译：结合地形的二维混合有限差分-有限元方法，用于二维直流电阻率建模

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Finite difference (FD) and finite element (FE) approximations are two commonly used methods for solving Poisson's equation from a known electrical resistivity model. FD discretizes the model with rectangular blocks, while FE discretizes it with right triangular elements. The advantage of FD is that it requires less computational time and memory storage, while the advantage of FE is its ability to handle topography. Here we introduce a hybrid FD-FE algorithm which requires less computational resources than a typical FE algorithm but can still handle topography. The model is first discretized as FD rectangular blocks. Some of these FD rectangular blocks beneath topographical features are replaced with FE right triangular elements. A system of equations for the hybrid method is then formed according to the types of discretization used. The system is a linear combination of the FD and FE equations. All three methods are applied to several models with and without topography. Comparisons in terms of computational time, memory and accuracy show that, as expected, FD is a better choice when modeling without topography, whereas FE is more practical when modeling with topography. However, our developed hybrid FD-FE method is efficient in both circumstances. Without topography, it behaves exactly like FD. With topography, it is as accurate as FE but its speed and memory usage are slightly larger than FD. In addition, we describe a scheme for automatic mesh generation. This scheme has led to another variant method, a mixed grid hybrid method. Our hybrid scheme and the automatic grid generation can be used for slopes of up to 75° This hybrid method can be further extended and implemented for 3D DC resistivity modeling for more efficient computation.
机译：有限差分（FD）和有限元（FE）近似是从已知电阻率模型求解泊松方程的两种常用方法。 FD用矩形块离散化模型，而FE用直角三角形元素离散化模型。 FD的优势在于它需要更少的计算时间和更少的存储空间，而FE的优势在于它具有处理地形的能力。在这里，我们介绍一种混合FD-FE算法，该算法比典型的FE算法需要更少的计算资源，但仍然可以处理地形。该模型首先离散为FD矩形块。地形特征下的某些FD矩形块已替换为FE直角三角形元素。然后根据所用离散化的类型形成混合方法的方程组。该系统是FD和FE方程的线性组合。这三种方法均适用于具有和不具有地形的几种模型。在计算时间，内存和准确性方面的比较表明，不出所料，在不使用地形进行建模时，FD是更好的选择，而在使用地形进行建模时，FE更为实用。但是，我们开发的混合FD-FE方法在两种情况下都是有效的。没有地形，它的行为与FD完全相同。使用地形，它与FE一样精确，但其速度和内存使用量比FD稍大。另外，我们描述了一种自动网格生成的方案。该方案导致了另一种变型方法，混合网格混合方法。我们的混合方案和自动网格生成功能可用于高达75°的坡度。此混合方法可进一步扩展和实现用于3D DC电阻率建模，从而实现更高效的计算。

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