Marching volume polytopes algorithm

Byfut, A.; Hellwig, Friederike; Schröder, Jörg

doi:10.1002/nme.5995

Cited by 3 publications

(6 citation statements)

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“…Such a terrain's surface is typically represented by a digital elevation model (DEM) as a heightmap. The application of the marching volume polytopes algorithm as introduced in [7] gives a piecewise linear approximation of the surface, see Fig. 3b.…”

Section: Finite Cell Methodsmentioning

confidence: 99%

A posteriori error control for the finite cell method

Stolfo

Düster

Kollmannsberger

et al. 2019

Proc Appl Math and Mech

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The paper presents some concepts of the finite cell method and discusses a posteriori error control for this approach. The focus is on the application of the dual weighted residual approach (DWR), which enables the control of the error with respect to a user-defined quantity of interest. Since both the discretization error and the quadrature error are estimated, the application of the DWR approach provides an adaptive strategy which equilibrates the error contributions resulting from discretization and quadrature. The strategy consists in refining either the finite cell mesh or its associated quadrature mesh. Numerical experiments confirm the performance of the error control and the adaptive scheme for a non-linear problem in 2D.

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Section: Finite Cell Methodsmentioning

confidence: 99%

A posteriori error control for the finite cell method

Stolfo

Düster

Kollmannsberger

et al. 2019

Proc Appl Math and Mech

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“…Note that is satisfied also for

{\overset{S}{true}}^{n} false(H false)

. In Algorithm 3, these intermediate submeshes are further refined to obtain the final submeshes

S^{n} false(H false)

H \in H^{n}

using the Marching Volume Polytopes Algorithm proposed in Byfut et al The intersections of the surface for the milling tool envelop with the edges of the intermediate submeshes

{\overset{S}{true}}^{n} false(H false)

prescribe the volume refinement pattern to obtain the sets of tetrahedrons and pyramids

scriptC false(J, {\overset{Λ}{true}}^{n} false)

for all

J \in {\overset{S}{true}}^{n} false(H false)

satisfying

J \cap \partial {\overset{Λ}{true}}^{n} \neq \emptyset

. The facets of the tetrahedrons and pyramids in

scriptC false(J, {\overset{Λ}{true}}^{n} false)

yield a piecewise linear approximation of

\partial {\overset{Λ}{true}}^{n} \cap J

.…”

Section: Discretizationmentioning

confidence: 99%

“…Illustration of the volume refinement patterns for hexahedrons as proposed in Byfut et al for the 14 basic intersection topologies with actual edge intersections assuming symmetric edge bisections…”

Section: Discretizationmentioning

confidence: 99%

“…Using the Marching Volume Polytopes Algorithm for the piecewise linear approximation of a given milled surface, re‐entrant corners will be contained in the resulting fine scale meshes. There are basically 2 situations to differentiate for a discussion of these re‐entrant corners.…”

Section: Discretizationmentioning

confidence: 99%

“…The fine scale hexahedrons at the milling path interface are further refined into pyramids and tetrahedrons to approximate that interface more accurately. For those refinements, we use refinement patterns that correspond to the interface meshes obtained for the marching cubes algorithm, see Byfut et al These fine scale elements allow for an elementwise constant definition of the characteristic function for the fictitious domain method. The ansatz functions of the finite element spaces for the fictitious domain method are defined on some coarse hexahedrons, whereas integration for the corresponding bilinear and linear forms is pursued on the fine scale hexahedrons, pyramids, and tetrahedrons.…”

Section: Introductionmentioning

confidence: 99%

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A fictitious domain method for the simulation of thermoelastic deformations in NC‐milling processes

Byfut

Schröder

2017

Numerical Meth Engineering

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Summary This paper presents a (higher‐order) finite element approach for the simulation of heat diffusion and thermoelastic deformations in NC‐milling processes. The inherent continuous material removal in the process of the simulation is taken into account via continuous removal‐dependent refinements of a paraxial hexahedron base‐mesh covering a given workpiece. These refinements rely on isotropic bisections of these hexahedrons along with subdivisions of the latter into tetrahedrons and pyramids in correspondence to a milling surface triangulation obtained from the application of the marching cubes algorithm. The resulting mesh is used for an element‐wise defined characteristic function for the milling‐dependent workpiece within that paraxial hexahedron base‐mesh. Using this characteristic function, a (higher‐order) fictitious domain method is used to compute the heat diffusion and thermoelastic deformations, where the corresponding ansatz spaces are defined for some hexahedron‐based refinement of the base‐mesh. Numerical experiments compared to real physical experiments exhibit the applicability of the proposed approach to predict deviations of the milled workpiece from its designed shape because of thermoelastic deformations in the process.

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