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X-LIC-LOCATION:Asia/Tokyo
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TZOFFSETFROM:+0900
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DTSTAMP:20260817T171530Z
LOCATION:Hall B5 (1)\, B Block\, Level 5
DTSTART;TZID=Asia/Tokyo:20241205T145900
DTEND;TZID=Asia/Tokyo:20241205T151300
UID:siggraphasia_SIGGRAPH Asia 2024_sess133_papers_421@linklings.com
SUMMARY:Hodge decomposition of vector fields in Cartesian grids
DESCRIPTION:Zhe Su, Guowei Wei, and Yiying Tong (Michigan State University
 )\n\nWhile explicit representations of shapes such as triangular and tetra
 hedral meshes are often used for boundary surfaces and 3D volumes bounded 
 by closed surfaces, implicit representations of planar regions and volumet
 ric regions defined by level-set functions have also found widespread appl
 ications in geometric modeling and simulations. However, an important comp
 utational tool, the L2-orthogonal Hodge decomposition for scalar and vecto
 r fields defined on implicit representations under commonly used Dirichlet
 /Neumann boundary conditions with proper correspondence to the topology pr
 esents additional challenges. For instance, the projection to the interior
  or boundary of the domain is not as straightforward as in the mesh-based 
 frameworks. Thus, we introduce a comprehensive 5-component Hodge decomposi
 tion that unifies normal and tangential components in the Cartesian repres
 entation. Numerical experiments on various objects, including single-cell 
 RNA velocity,  validate the effectiveness of our approach,  confirming the
  expected rigorous L2-orthogonality and accurate cohomology.\n\nRegistrati
 on Category: Full Access, Full Access Supporter\n\nLanguage Format: Englis
 h Language\n\nSession Chair: Mirela Ben-Chen (Technion – Israel Institute 
 of Technology)\n\n
URL:https://asia.siggraph.org/2024/program/?id=papers_421&sess=sess133
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