An adaptive method to reduce the effect of geometric approximation error on 3-D DC resistivity finite element numerical modeling

• Minimizing geometric approximation errors is a wasting-resource simulation strategy.
• Analyze the relationship between geometric approximation errors and its effect
• Propose an adaptive method to reduce the effect of geometric approximation error
• Adaptive method proposed saves grid resources in many cases.
• Adaptive method proposed enlarges the simulation capacity of unstructured mesh.

The computational area is divided into disjoint elements before 3-D DC finite element numerical simulation. If these elements cannot completely approximate the geoelectric model to be simulated, some of them have geometric approximation errors. The elements with geometric approximation errors may decrease the accuracy of the simulation. If the effect of geometric approximation errors on simulation is reduced purely by minimizing geometric approximation errors, a large number of grid resources are wasted. As a result, the corresponding simulation complexity is limited. We propose an adaptive method to reduce the effect of geometric approximation errors on 3-D DC finite element resistivity numerical modeling. This method focuses on the effect of geometric approximation errors rather than geometric approximation errors themselves. For the elements with geometric approximation errors, only those with large negative effect on simulation are refined in the adaptive process. We simulate five geoelectric models to verify the feasibility of this method. The experiments show that despite many elements with geometric approximation errors, high accuracy numerical result can be still obtained, and the element number of simulation decreases significantly. With this method, many more complex geoelectric models can be simulated using the same amount of computer resources.