无断裂的断裂：弱执行滑移方法
Discontinuities without discontinuity: The Weakly-enforced Slip Method
AI总结：
本文提出一种基于弱执行位移间断的新非 conforming 有限元方法，以解决地质逆问题中的计算效率问题。
摘要：
构造断层通常被建模为弹性介质中的Volterra或Somigliana断层。各种求解方法存在，但实际应用中常受限于计算效率而非地质准确性。典型的地质应用涉及逆问题，需检查多种断层配置，增加计算负担。实际中，这排除了传统有限元方法，因其因几何变化而具有较大的计算开销。本文提出一种基于弱执行位移间断的新非 conforming 有限元方法。弱执行间断使能够使用不依赖断层几何的逼近空间，从而实现计算组件的最优重用。此类组件重用使有限元建模成为地质应用逆问题的可行选项。对新方法的逼近性质进行了详细分析。分析由2D和3D的数值实验支持。
英文摘要：
Tectonic faults are commonly modelled as Volterra or Somigliana dislocations in an elastic medium. Various solution methods exist for this problem. However, the methods used in practice are often limiting, motivated by reasons of computational efficiency rather than geophysical accuracy. A typical geophysical application involves inverse problems for which many different fault configurations need to be examined, each adding to the computational load. In practice, this precludes conventional finite-element methods, which suffer a large computational overhead on account of geometric changes. This paper presents a new non-conforming finite-element method based on weak imposition of the displacement discontinuity. The weak imposition of the discontinuity enables the application of approximation spaces that are independent of the dislocation geometry, thus enabling optimal reuse of computational components. Such reuse of computational components renders finite-element modeling a viable option for inverse problems in geophysical applications. A detailed analysis of the approximation properties of the new formulation is provided. The analysis is supported by numerical experiments in 2D and 3D.
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