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PRODID:Linklings LLC
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TZID:Asia/Tokyo
X-LIC-LOCATION:Asia/Tokyo
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TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:JST
DTSTART:18871231T000000
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BEGIN:VEVENT
DTSTAMP:20260817T171538Z
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:Tommaso Sorgente (CNR-IMATI); Fabio Vicini (Politecnico di Tor
 ino, Dipartimento di Scienze Matematiche); and Daniela Cabiddu, Silvia Bia
 sotti, and Michela Spagnuolo (CNR-IMATI)\n\nThis course emphasizes the gro
 wing importance of mesh quality assessment for numerical methods in comput
 er graphics, through a combination of theoretical notions and practical ex
 ercises.\n\nWe explore various approaches to define and measure "mesh qual
 ity". \nThe course starts with basic concepts about meshes, polytopes, and
  operators, then covers both common and novel quality indicators and metri
 cs 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/hexahedral, and ge
 neric polytopal elements, are discussed. \nA live exercise using the softw
 are PEMesh demonstrates how to compute and compare mesh quality using thes
 e indicators.\n\nSubsequently, we introduce the Virtual Element Method (VE
 M) for discretizing Partial Differential Equations (PDEs), focusing on the
  second-order elliptic PDE with homogeneous boundary conditions, specifica
 lly Poisson's equation. \nWe discuss the advantages of VEM over the tradit
 ional Finite Element Method (FEM), detailing the enhanced VEM local and gl
 obal discrete space for a general polynomial degree k, and presenting theo
 retical error estimations analogous to FEM. \nMesh requirements for VEM ar
 e explained, followed by a demonstration using the VEM solver in PEMesh to
  optimize mesh quality.\n\nWe review notable mesh optimization algorithms 
 and present a specific algorithm for optimizing polygonal or polyhedral me
 shes, utilizing the previously defined quality indicators. \nThis process 
 involves analyzing local element quality and agglomerating elements to opt
 imize global mesh quality, with a user-set parameter controlling the perce
 ntage of elements to be removed.\nPractical applications to constrained do
 mains and time-dependent problems are demonstrated, culminating in a live 
 PEMesh exercise comparing optimizations driven by different quality indica
 tors.\n\nAttendees will learn which aspects of a mesh play a role in numer
 ical simulations, how to measure the quality of a discretization, how to s
 olve a numerical problem with the VEM, and how to optimize the quality of 
 a mesh.\n\nRegistration Category: Full Access, Full Access Supporter\n\nLa
 nguage Format: English Language\n\n
URL:https://asia.siggraph.org/2024/program/?id=crs_101&sess=sess215
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