Shared-memory block-based fast marching method for hierarchical meshes

Quell, Michael; Diamantopoulos, Georgios; Hössinger, Andreas; Weinbub, Josef

doi:10.1016/j.cam.2021.113488

Cited by 7 publications

(2 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…( 2) and to obtain the curvatures of the zero level-set, the level-set values (φ-values) are required on all grid points. This is achieved by a re-distancing step [13]. Depending on the used level-set framework, the level-set function may fulfill the signed distance property…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2023

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

et al. 2023

Self Cite

View full text Add to dashboard Cite

show abstract

“…There is already a large body of work on domain-decomposition methods for parallelizing the fast marching method [15] [24] [38] [4] [21] [39] [41] [28]. [44] first applied domain decomposition to the fast sweeping method.…”

mentioning

confidence: 99%

Exploiting Asynchronous Priority Scheduling in Parallel Eikonal Solvers

Henriksen,

You,

Pingali

2021

Preprint

View full text Add to dashboard Cite

Numerical solutions to the Eikonal equation are computed using variants of the fast marching method, the fast sweeping method, and the fast iterative method. In this paper, we provide a unified view of these algorithms that highlights their similarities and suggests a wider class of Eikonal solvers. We then use this framework to justify applying concurrent priority scheduling techniques to Eikonal solvers. We demonstrate that doing so results in good parallel performance for a problem from seismology. We explain why existing Eikonal solvers may produce different results despite using the same differencing scheme and demonstrate techniques to address these discrepancies. These techniques allow us to obtain deterministic output from our asynchronous fine-grained parallel Eikonal solver.

show abstract