A Multigrid Multilevel Monte Carlo Method for Stokes–Darcy Model with Random Hydraulic Conductivity and Beavers–Joseph Condition

Yang, Zhipeng; Jun, Ming; Qiu, Changxin; Li, Maojun; He, Xiaoming

doi:10.1007/s10915-021-01742-2

Cited by 9 publications

(1 citation statement)

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“…These properties of the topography motivate the use of hierarchical domain refinement such that only areas around a feature are resolved in more detail, to minimize the impact on performance [17]. The selective refinement of the simulation domain is a commonly used strategy for handling practically relevant numerical simulations [18][19][20][21][22][23]. To that end and the focus of this work, a new algorithm is needed to detect the dynamic changes in the wafer surface (features) during topography simulation, enabling external fast and efficient hierarchical domain refinement.…”

Section: Introductionmentioning

confidence: 99%

A Complementary Topographic Feature Detection Algorithm Based on Surface Curvature for Three-Dimensional Level-Set Functions

et al. 2023

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The level-set method is widely used in expanding front simulations in numerous fields of computational research, such as computer graphics, physics, or microelectronics. In the latter, the level-set method is employed for topography simulations of semiconductor device fabrication processes, being driven by complicated physical and chemical models. These models tend to produce surfaces with critical points where accuracy is paramount. To efficiently increase the accuracy in regions neighboring these critical points, automatic hierarchical domain refinement is required, guided by robust feature detection. Feature detection has to be computationally efficient and sufficiently accurate to reliably detect the critical points. To that end, we present a fast parallel geometric feature detection algorithm for three-dimensional level-set functions. Our approach is based on two different, complementary curvature calculation methods of the zero level-set and an optimized feature detection parameter to detect features. For performance reasons, our algorithm can be in principal linked to different curvature calculation methods, however, as will be discussed, two particularly attractive options are available: (i) A novel extension of the standard curvature calculation method for level-set functions, and (ii) an often disregarded method for calculating the curvature due to its purported low numerical accuracy. We show, however, that the latter is still a viable option, and that our algorithm is able to reliably detect features on geometries stemming from complicated, practically relevant geometries. Our algorithm and findings are applicable to other fields of applications such as surface simplification.

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