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dc.contributor.authorSellán, Silviaen_US
dc.contributor.authorCheng, Herng Yien_US
dc.contributor.authorMa, Yumingen_US
dc.contributor.authorDembowski, Mitchellen_US
dc.contributor.authorJacobson, Alecen_US
dc.contributor.editorChen, Min and Benes, Bedrichen_US
dc.date.accessioned2019-03-17T09:57:04Z
dc.date.available2019-03-17T09:57:04Z
dc.date.issued2019
dc.identifier.issn1467-8659
dc.identifier.urihttps://doi.org/10.1111/cgf.13592
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf13592
dc.description.abstractMany tasks in geometry processing are modelled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh. Unfortunately, tetrahedral meshing remains an open challenge and existing methods either struggle to conform to complex boundary surfaces or require manual intervention to prevent failure. Rather than create a single volumetric mesh for the entire shape, we advocate for solid geometry processing on , where a large and complex shape is composed of overlapping solid subdomains. As each smaller and simpler part is now easier to tetrahedralize, the question becomes how to account for overlaps during problem modelling and how to couple solutions on each subdomain together . We explore how and why previous coupling methods fail, and propose a method that couples solid domains only along their boundary surfaces. We demonstrate the superiority of this method through empirical convergence tests and qualitative applications to solid geometry processing on a variety of popular second‐order and fourth‐order partial differential equations.Many tasks in geometry processing are modelled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh. Unfortunately, tetrahedral meshing remains an open challenge and existing methods either struggle to conform to complex boundary surfaces or require manual intervention to prevent failure. Rather than create a single volumetric mesh for the entire shape, we advocate for solid geometry processing on , where a large and complex shape is composed of overlapping solid subdomains. As each smaller and simpler part is now easier to tetrahedralize, the question becomes how to account for overlaps during problem modelling and how to couple solutions on each subdomain together . We explore how and why previous coupling methods fail, and propose a method that couples solid domains only along their boundary surfaces. We demonstrate the superiority of this method through empirical convergence tests and qualitative applications to solid geometry processing on a variety of popular second‐order and fourth‐order partial differential equations.en_US
dc.publisher© 2019 The Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectnumerical analysis
dc.subjectmethods and applications
dc.subject• Mathematics of computing → Discretization; Partial differential equations; Numerical differentiation
dc.titleSolid Geometry Processing on Deconstructed Domainsen_US
dc.description.seriesinformationComputer Graphics Forum
dc.description.sectionheadersArticles
dc.description.volume38
dc.description.number1
dc.identifier.doi10.1111/cgf.13592
dc.identifier.pages564-579


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