IEEE Trans Vis Comput Graph - A Hexahedral Multigrid Approach for Simulating Cuts in Deformable Objects.


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We present a hexahedral finite element method for simulating cuts in deformable bodies using the corotational formulation of strain at high computational efficiency. Key to our approach is a novel embedding of adaptive element refinements and topological changes of the simulation grid into a geometric multigrid solver. Starting with a coarse hexahedral simulation grid, this grid is adaptively refined at the surface of a cutting tool until a finest resolution level, and the cut is modeled by separating elements along the cell faces at this level. To represent the induced discontinuities on successive multigrid levels, the affected coarse grid cells are duplicated and the resulting connectivity components are distributed to either side of the cut. Drawing upon recent work on octree and multigrid schemes for the numerical solution of partial differential equations, we develop efficient algorithms for updating the systems of equations of the adaptive finite element discretization and the multigrid hierarchy. To construct a surface that accurately aligns with the cuts, we adapt the splitting cubes algorithm to the specific linked voxel representation of the simulation domain we use. The paper is completed by a convergence analysis of the finite element solver and a performance comparison to alternative numerical solution methods.

Resumo Limpo

present hexahedr finit element method simul cut deform bodi use corot formul strain high comput effici key approach novel embed adapt element refin topolog chang simul grid geometr multigrid solver start coars hexahedr simul grid grid adapt refin surfac cut tool finest resolut level cut model separ element along cell face level repres induc discontinu success multigrid level affect coars grid cell duplic result connect compon distribut either side cut draw upon recent work octre multigrid scheme numer solut partial differenti equat develop effici algorithm updat system equat adapt finit element discret multigrid hierarchi construct surfac accur align cut adapt split cube algorithm specif link voxel represent simul domain use paper complet converg analysi finit element solver perform comparison altern numer solut method

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