Forbidden-Set Distance Labels for Graphs of Bounded Doubling Dimension

2016 ◽  
Vol 12 (2) ◽  
pp. 1-17 ◽  
Author(s):  
Ittai Abraham ◽  
Shiri Chechik ◽  
Cyril Gavoille ◽  
David Peleg
Keyword(s):  
Doubling Dimension ◽  
Forbidden Set ◽  
Set Distance

A MODIFIED SUB-CELL-FIX METHOD FOR RE-INITIALIZATION OF LEVEL-SET DISTANCE FUNCTION AND ITS DEPENDENCE TESTS ON GRID STRETCHING

2010 ◽  
Vol 24 (15) ◽  
pp. 1615-1629
Author(s):  
MING BO SUN ◽  
XUE SONG BAI ◽  
WEI DONG LIU ◽  
JIAN HAN LIANG ◽  
ZHEN GUO WANG
Keyword(s):  
Level Set ◽  
Distance Function ◽  
Second Order ◽  
Test Cases ◽  
Local Curvature ◽  
Order Accuracy ◽  
Zero Level ◽  
Numerical Errors ◽  
Satisfactory Performance ◽  
Set Distance

The sub-cell-fix (SCF) method proposed by Russo and Smereka3 computes the distance function of the cells adjacent to the zero level-set without disturbing the original zero level-set. A modified sub-cell-fix scheme independent of local curvature is developed in this paper, which makes use of a combination of the points adjacent to zero level-set surfaces and preserves the interface in a second-order accuracy. The new sub-cell-fix scheme is capable of handling large local curvature, and as a result it demonstrates satisfactory performance on several challenging test cases. The limitations of the modified scheme on stretched grids are tested and it is found that the highly stretched grid causes large numerical errors, and needs further assessment and modification.

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