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DTSTAMP:20201212T050114Z
LOCATION:Zoom Room 3
DTSTART;TZID=Asia/Singapore:20201212T101200
DTEND;TZID=Asia/Singapore:20201212T101800
UID:siggraphasia_SIGGRAPH Asia 2020_sess119_papers_362@linklings.com
SUMMARY:Higher-Order Finite Elements for Embedded Simulation
DESCRIPTION:Technical Papers, Technical Papers Q&A\n\nHigher-Order Finite
Elements for Embedded Simulation\n\nLongva, Löschner, Kugelstadt, Fernánde
z-Fernández, Bender\n\nAs demands for high-fidelity physics-based animatio
ns increase, the need for accurate methods for simulating deformable solid
s grows. While higher-order finite elements are commonplace in engineering
due to their superior approximation properties for many problems, they ha
ve gained little traction in the computer graphics community. This may par
tially be explained by the need for finite element meshes to approximate t
he highly complex geometry of models used in graphics applications. Due to
the additional per-element computational expense of higher-order elements
, larger elements are needed, and the error incurred due to the geometry
mismatch eradicates the benefits of higher-order discretizations. One solu
tion to this problem is the embedding of the geometry into a coarser finit
e element mesh. However, to date there is no adequate, practical computati
onal framework that permits the accurate embedding into higher-order eleme
nts.\n\nWe develop a novel, robust quadrature generation method that gener
ates theoretically guaranteed high-quality sub-cell integration rules of a
rbitrary polynomial accuracy. The number of quadrature points generated is
bounded only by the desired degree of the polynomial, independent of the
embedded geometry. Additionally, we build on recent work in the Finite Cel
l Method (FCM) community so as to tackle the severe ill-conditioning cause
d by partially filled elements by adapting an Additive-Schwarz-based preco
nditioner so that it is suitable for use with state-of-the-art non-linear
material models from the graphics literature. Together these two contribut
ions constitute a general-purpose framework for embedded simulation with h
igher-order finite elements.\n\nWe finally demonstrate the benefits of our
framework in several scenarios, in which second-order hexahedra and tetra
hedra clearly outperform their first-order counterparts.\n\nRegistration C
ategory: Ultimate Supporter, Ultimate Attendee
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