By Daniel Sieger, Stefan Menzel, Mario Botsch (auth.), Xiangmin Jiao, Jean-Christophe Weill (eds.)

ISBN-10: 3642335721

ISBN-13: 9783642335723

ISBN-10: 364233573X

ISBN-13: 9783642335730

This quantity comprises the articles awarded on the twenty first overseas Meshing Roundtable (IMR) geared up, partly, by way of Sandia nationwide Laboratories and used to be hung on October 7–10, 2012 in San Jose, CA, united states. the 1st IMR used to be held in 1992, and the convention sequence has been held each year seeing that. every year the IMR brings jointly researchers, builders, and alertness specialists in various disciplines, from world wide, to give and speak about principles on mesh iteration and similar themes. The technical papers during this quantity current theoretical and novel principles and algorithms with functional capability, in addition to technical purposes in technology and engineering, geometric modeling, special effects, and visualization.

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Local material properties. Another advantage of elasticity-like methods is the opportunity they offer to adapt the local material properties of the mesh, especially its stiffness, according to the distortion and efforts born by each element. Following [21], the way the Jacobian of the transformation from the reference element to the current element is accounted for in the FEM matrix assembly is modified. This technique comes to locally multiply the Lam´e coefficients by a factor proportional to |K|−χ .

While (t < T els ) a) δt = Get moving mesh time step Hk , v, CF Lgeom b) Hk = Swaps optimization Hk , Qswap target , Qmax c) vopt = Vertices smoothing Hk , Qsmoothing target d) Hk+1 = Move the mesh and update vertices speed Hk , δt, v, vopt , a e) t = t + δt EndWhile EndWhile 5 Numerical Illustrations Numerous analytical examples on academic geometries have been addressed to demonstrate the feasibility of performing 3D moving mesh simulation while keeping the number of vertices constant. This means that large displacements can be handled without any remeshing using only vertices displacements and edges/faces swaps.

Therefore, a geometric parameter CF Lgeom is introduced to control the number of stages used to perform the mesh displacement between t and t + Δt. If CF Lgeom is greater than one, the mesh is authorized to cross more than one element in a single move. As each moving step is coupled with an optimization procedure, cutting a large displacement into several smaller displacements by reducing the geometric CFL enables to ease mesh movement. The moving geometric time step is given by: δtmov = CF Lgeom max Pi h(xi ) , v(xi ) where h(xi ) is the smallest altitude of all the elements in the ball of vertex Pi .

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Proceedings of the 21st International Meshing Roundtable by Daniel Sieger, Stefan Menzel, Mario Botsch (auth.), Xiangmin Jiao, Jean-Christophe Weill (eds.)

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