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X-LIC-LOCATION:Asia/Tokyo
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TZOFFSETFROM:+0900
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BEGIN:VEVENT
DTSTAMP:20250110T023312Z
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:Technical Papers\n\nZhe Su, Guowei Wei, and Yiying Tong (Michi
 gan State University)\n\nWhile explicit representations of shapes such as 
 triangular and tetrahedral meshes are often used for boundary surfaces and
  3D volumes bounded by closed surfaces, implicit representations of planar
  regions and volumetric regions defined by level-set functions have also f
 ound widespread applications in geometric modeling and simulations. Howeve
 r, an important computational tool, the L2-orthogonal Hodge decomposition 
 for scalar and vector fields defined on implicit representations under com
 monly used Dirichlet/Neumann boundary conditions with proper correspondenc
 e to the topology presents additional challenges. For instance, the projec
 tion to the interior or boundary of the domain is not as straightforward a
 s in the mesh-based frameworks. Thus, we introduce a comprehensive 5-compo
 nent Hodge decomposition that unifies normal and tangential components in 
 the Cartesian representation. Numerical experiments on various objects, in
 cluding single-cell RNA velocity,  validate the effectiveness of our appro
 ach,  confirming the expected rigorous L2-orthogonality and accurate cohom
 ology.\n\nRegistration Category: Full Access, Full Access Supporter\n\nLan
 guage Format: English Language\n\nSession Chair: Mirela Ben-Chen (Technion
  – Israel Institute of Technology)
URL:https://asia.siggraph.org/2024/program/?id=papers_421&sess=sess133
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