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A Unified Simplicial Model for Mixed-Dimensional and Non-Manifold Deformable Elastic Objects

Jumyung Chang, Fang Da, Eitan Grinspun, Christopher Batty
2019 Proceedings of the ACM on Computer Graphics and Interactive Techniques  
A Unified Simplicial Model for Mixed-Dimensional and Non-Manifold Deformable Elastic Objects 11:3 rod-solid (P) shell-solid (C) solid-solid (P) shell-solid (P) rod-shell (C) rod-shell (P) shell-solid (  ...  We present a unified method to simulate deformable elastic bodies consisting of mixed-dimensional components represented with potentially non-manifold simplicial meshes.  ...  We would like to thank SideFX Software for Houdini licences, and anonymous reviewers for their insightful feedback.  ... 
doi:10.1145/3340252 fatcat:hxgpdhyn5zhavkanxzyk336pp4

A mixed method for 3D nonlinear elasticity using finite element exterior calculus [article]

Bensingh Dhas, Jamun Kumar, Debasish Roy, J N Reddy
2021 arXiv   pre-print
This article discusses a mixed FE technique for 3D nonlinear elasticity using a Hu-Washizu (HW) type variational principle.  ...  Here, the deformed configuration and sections from its cotangent bundle are taken as additional input arguments.  ...  [8] have discussed a mixed finite element technique for non-linear elastic solids.  ... 
arXiv:2109.01491v1 fatcat:youwr4aehrdq5eboai7z2cpgje

A mixed variational principle in nonlinear elasticity using Cartan's moving frame and implementation with finite element exterior calculus [article]

Bensingh Dhas, Jamun Kumar N, Debasish Roy, J N Reddy
2021 arXiv   pre-print
This article offers a new perspective for the mechanics of solids using moving Cartan's frame, specifically discussing a mixed variational principle in non-linear elasticity.  ...  This discertization leads to a mixed method as it uses independent approximations for differential forms related to stress and deformation gradient.  ...  And yet, there is barely an attempt at developing a variational principle in solid mechanics to unify the posing and numerical solution of a geometrically conceived model.  ... 
arXiv:2108.13166v1 fatcat:olji6mi52bf5ha5ura5pe2ajli

Unified simulation of elastic rods, shells, and solids

Sebastian Martin, Peter Kaufmann, Mario Botsch, Eitan Grinspun, Markus Gross
2010 ACM Transactions on Graphics  
The theory and accompanying implementation do not distinguish between forms of different dimension (solids, shells, rods), nor between manifold regions and non-manifold junctions.  ...  Consequently, a single code accurately models a diverse range of elastoplastic behaviors, including buckling, writhing, cutting and merging.  ...  Acknowledgments The authors are grateful to Petr Krysl and the anonymous reviewers for their helpful comments and suggestions.  ... 
doi:10.1145/1833351.1778776 fatcat:odh65ax6uve6zotfnorwn32v6u

Parametric Contour Model In Medical Image Segmentation [chapter]

Bipul Das, Swapna Banerjee
2007 Deformable Models  
Of the model-based techniques, the deformable model is most effectively used for its ability to unify image statistics -both local and global -in a geometrically constrained framework.  ...  The model-based technique offers a unique and efficient approach toward medical image segmentation and analysis due to its power to unify image information within a physical framework.  ...  There are two main types of domain decomposition methods: non-simplicial and simplicial. Most nonsimplicial methods employ a regular tessellation of space.  ... 
doi:10.1007/978-0-387-68343-0_2 fatcat:t2vncyi6zjfrlaib7fdx2pezze

Mechanics of systems of affine bodies. Geometric foundations and applications in dynamics of structured media

J. J. Sławianowski, V. Kovalchuk, A. Martens, B. Gołubowska, E. E. Rożko
2011 Mathematical methods in the applied sciences  
Certain physical applications are possible in modelling of molecular crystals, granular media, and other physical objects.  ...  There is an essential novelty in comparison to deformation scalars of single affine bodies, i.e., there exist affinely-invariant scalars of mutual deformations.  ...  Mariano for discussions with him and for encouraging us to the work in this direction.  ... 
doi:10.1002/mma.1462 fatcat:edsijrgfkbcrfg4wrn3uhjy6bu

Emerging Challenges in Computational Topology [article]

Marshall Bern, David Eppstein, Pankaj K. Agarwal, Nina Amenta, Paul Chew, Tamal Dey, David P. Dobkin, Herbert Edelsbrunner, Cindy Grimm, Leonidas J. Guibas, John Harer, Joel Hass (+10 others)
1999 arXiv   pre-print
This report identifies important problems involving both computation and topology.  ...  Here we present the results of the NSF-funded Workshop on Computational Topology, which met on June 11 and 12 in Miami Beach, Florida.  ...  These spaces are usually high-dimensional and non-Euclidean, and hence raise some rather deep topological questions. • Topological computation.  ... 
arXiv:cs/9909001v1 fatcat:6vylpbucczf6nm45m4s236iug4

A Review of Topology Optimisation for Fluid-Based Problems

Joe Alexandersen, Casper Schousboe Andreasen
2020 Fluids  
This review paper provides an overview of the literature for topology optimisation of fluid-based problems, starting with the seminal works on the subject and ending with a snapshot of the state of the  ...  A quantititive analysis is presented with statistics covering the development of the field and presenting the distribution over subgroups.  ...  Dong and Liu [91] proposed a bi-objective formulation for the design of asymmetrical fixed-geometry microvalves for non-Newtonian flow.  ... 
doi:10.3390/fluids5010029 fatcat:6u3jnw3p2bck5oa2g2m624pxim

Reactive Flows in Deformable, Complex Media

Margot Gerritsen, Jan Martin Nordbotten, Iuliu Sorin Pop, Barbara Wohlmuth
2014 Oberwolfach Reports  
, and the key issue is to integrate the domain deformation in the multi-scale context.  ...  Such kind of problems are encountered as mathematical models in the subsurface, material science, or biological systems.The emerging mathematical models account for various processes at different scales  ...  However, in order to model more complex physical processes in the mixed-dimensional setting, the mixed-dimensional De Rham complex becomes a practical tool.  ... 
doi:10.4171/owr/2014/43 fatcat:cxkazxwlwnaqnmxamofkkhdnru

On Computing Mapping of 3D Objects

Xin Li, S. S. Iyengar
2014 ACM Computing Surveys  
Effective mapping benefits many scientific and engineering tasks that involve the modeling and processing of correlated geometric or image data.  ...  Different mapping algorithms are discussed and compared according to their formulations of objective functions, constraints, and optimization strategies.  ...  deforming n-dimensional manifolds.  ... 
doi:10.1145/2668020 fatcat:rcwzp5d4azb7xkaquyfc3l3reu

Twenty years of distributed port-Hamiltonian systems: a literature review

Ramy Rashad, Federico Califano, Arjan J van der Schaft, Stefano Stramigioli
2020 IMA Journal of Mathematical Control and Information  
We classify over a hundred and fifty studies based on different research focuses ranging from modeling, discretization, control and theoretical foundations.  ...  The theory has been successfully extended from finite-dimensional to infinite-dimensional systems through a lot of research efforts.  ...  The framework replaces the smooth structures in exterior calculus by their discrete analogues, e.g. replacing the smooth manifold by a simplicial complex and replacing the differential forms by co-chains  ... 
doi:10.1093/imamci/dnaa018 fatcat:2npd6ucypngj7gwdyhaaaqqzp4

Fourier's Method of Linear Programming and Its Dual

H. P. Williams
1986 The American mathematical monthly  
materials 74B05 Classical linear elasticity 74B10 Linear elasticity with initial stresses 74B15 Equations linearized about a deformed state (small deformations superposed on large) 74B20 Nonlinear elasticity  ...  13D05, 16E10] 18G25 Relative homological algebra, projective classes 18G30 Simplicial sets, simplicial objects (in a category) [See also 55U10] 18G35 Chain complexes [See also 18E30, 55U15] 18G40  ...  , higher-dimensional and super field theories 83E05 Geometrodynamics 83E15 Kaluza-Klein and other higher-dimensional theories 83E30 String  ... 
doi:10.2307/2322281 fatcat:yvhgyh2epbcwdoqdhuaopkcrue

Robust eXtended finite elements for complex cutting of deformables

Dan Koschier, Jan Bender, Nils Thuerey
2017 ACM Transactions on Graphics  
Most existing approaches construct a cut-aligned auxiliary mesh for integration.  ...  Left: Plate with attached objects consisting of 159k tetrahedra is cut by long, bumpy cut surface. Right: A groove is carved into the Stanford bunny (18.5k tetrahedra) rotating around a fixed axis.  ...  ACKNOWLEDGMENTS This work is supported by the ERC Starting Grant 637014 and by the German Research Foundation (DFG) under contract numbers BE 5132/4-1 and TH 2034/1-1.  ... 
doi:10.1145/3072959.3073666 fatcat:3nwvxollcrgptj3k6fxdglby5m

Twenty Female Mathematicians [article]

Hollis Williams
2021 arXiv   pre-print
In fact, the main use will probably be for a student who is coming to a new area of mathematics for the first time and needs an overview of some of the key results and references viewed through the work  ...  Changes, corrections, and additions can be suggested at the website, but the website is currently not being actively maintained, so any suggestions for corrections and changes will be made to the document  ...  Start for a class of objects and for every ordered pair of objects in the class, specify a set of morphisms which take object to object (denoted by [ , ] ).  ... 
arXiv:1910.01730v3 fatcat:2ftlzg73mncvtau6xlgu2ly264

Some Fundamental Theorems in Mathematics [article]

Oliver Knill
2022 arXiv   pre-print
This implies that there exists a generic set of ergodic and even weakly mixing (non mixing) polygons (they are then non-rational) with n vertices.  ...  Hardly anybody would consider a "lava lamp" (invented in 1963) a object of taste nowadays, even so, the fluid dynamics and motion is objectively rich and interesting, illustrating also geometric deformation  ...  With the symmetric difference as addition and the intersection as multiplication, the subsets of a given set X become a ring. This Boolean ring has the property A + A = 0 and AA = A for all sets.  ... 
arXiv:1807.08416v4 fatcat:lw7lbsxyznfrnaozilxapihmdy
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