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VERSION:2.0
PRODID:Linklings LLC
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TZID:Asia/Tokyo
X-LIC-LOCATION:Asia/Tokyo
BEGIN:STANDARD
TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:JST
DTSTART:18871231T000000
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BEGIN:VEVENT
DTSTAMP:20250110T023302Z
LOCATION:G602\, G Block\, Level 6
DTSTART;TZID=Asia/Tokyo:20241204T140000
DTEND;TZID=Asia/Tokyo:20241204T174500
UID:siggraphasia_SIGGRAPH Asia 2024_sess215_crs_101@linklings.com
SUMMARY:Mesh Quality Meets The Virtual Element Method
DESCRIPTION:Courses\n\nTommaso Sorgente (CNR-IMATI); Fabio Vicini (Politec
 nico di Torino, Dipartimento di Scienze Matematiche); and Daniela Cabiddu,
  Silvia Biasotti, and Michela Spagnuolo (CNR-IMATI)\n\nThis course emphasi
 zes the growing importance of mesh quality assessment for numerical method
 s in computer graphics, through a combination of theoretical notions and p
 ractical exercises.\n\nWe explore various approaches to define and measure
  "mesh quality". \nThe course starts with basic concepts about meshes, pol
 ytopes, and operators, then covers both common and novel quality indicator
 s and metrics for evaluating a discretization and guiding mesh generation,
  coarsening, and refinement. \nVarious local and global indicators for two
 - and three-dimensional meshes, including simplicial, quadrangular/hexahed
 ral, and generic polytopal elements, are discussed. \nA live exercise usin
 g the software PEMesh demonstrates how to compute and compare mesh quality
  using these indicators.\n\nSubsequently, we introduce the Virtual Element
  Method (VEM) for discretizing Partial Differential Equations (PDEs), focu
 sing on the second-order elliptic PDE with homogeneous boundary conditions
 , specifically Poisson's equation. \nWe discuss the advantages of VEM over
  the traditional Finite Element Method (FEM), detailing the enhanced VEM l
 ocal and global discrete space for a general polynomial degree k, and pres
 enting theoretical error estimations analogous to FEM. \nMesh requirements
  for VEM are explained, followed by a demonstration using the VEM solver i
 n PEMesh to optimize mesh quality.\n\nWe review notable mesh optimization 
 algorithms and present a specific algorithm for optimizing polygonal or po
 lyhedral meshes, utilizing the previously defined quality indicators. \nTh
 is process involves analyzing local element quality and agglomerating elem
 ents to optimize global mesh quality, with a user-set parameter controllin
 g the percentage of elements to be removed.\nPractical applications to con
 strained domains and time-dependent problems are demonstrated, culminating
  in a live PEMesh exercise comparing optimizations driven by different qua
 lity indicators.\n\nAttendees will learn which aspects of a mesh play a ro
 le in numerical simulations, how to measure the quality of a discretizatio
 n, how to solve a numerical problem with the VEM, and how to optimize the 
 quality of a mesh.\n\nRegistration Category: Full Access, Full Access Supp
 orter\n\nLanguage Format: English Language
URL:https://asia.siggraph.org/2024/program/?id=crs_101&sess=sess215
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