1,720,978 research outputs found
Degenerate tetrahedra removal
No full textStandard 3D mesh generation algorithms may produce a low quality tetrahedral mesh, i.e., a mesh where the tetrahedra have very small dihedral angles. In this paper, we propose a series of operations to recover these badly-shaped tetrahedra.
In particular, we will focus on the shape of these undesired mesh elements by proposing a novel method to distinguish and classify them. For each of these configurations, we apply a suitable sequence of operations to get a higher mesh quality. Finally, we employ a random algorithm to avoid locks and loops in the procedure.
The reliability of the proposed mesh optimization algorithm is numerically proved with several examples
A Priori Anisotropic Mesh Adaptation on Implicitly Defined Surfaces
Full text linkMesh adaptation on surfaces demands particular care due to the important role played by the surface fitting. We propose an adaptive procedure based on a new error analysis which combines a rigorous anisotropic estimator for the -norm of the interpolation error with an anisotropic heuristic control of the geometric error. We resort to a metric-based adaptive algorithm which employs local operations to modify the initial mesh according to the information provided by the error analysis. An extensive numerical validation corroborates the robustness of the error analysis as well as of the adaptive procedur
Mixed Virtual Element approximation of linear acoustic wave equation
Full text linkWe design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In the absence of external loads, the semi-discrete method exactly conserves the system energy. To integrate in time the semi-discrete problem we consider a classical \\-method scheme. We carry out the stability and convergence analysis in the energy norm for the semi-discrete problem showing an optimal rate of convergence with respect to the mesh size. We further study the property of energy conservation for the fully-discrete system. Finally, we present some verification tests as well as engineering applications of the method
A priori anisotropic mesh adaptation driven by a higher dimensional embedding
No full textWe generalize the higher embedding approach proposed in Lévy and Bonneel (2013) to generate an adapted mesh matching the intrinsic directionalities of an assigned function. In more detail, the original embedding map between the physical (lower dimensional) and the embedded (higher dimensional) setting is modified to include information associated with the function and with its gradient. Then, we set an adaptive procedure, driven by the embedded metric but performed in the lower dimensional setting, which results into an anisotropic adapted mesh of the physical domain. The effectiveness of the proposed procedure is extensively investigated on several two-dimensional test cases, involving both analytical functions and finite element approximations of differential problems. The preliminary verification in three dimensions corroborates the robustness of the method
Anisotropic finite element mesh adaptation via higher dimensional embedding
Full text linkAbstractIn this paper we provide a novel anisotropic mesh adaptation technique for adaptive finite element analysis. It is based on the concept of higher dimensional embedding, which was exploited in [1–4] to obtain an anisotropic curvature adapted mesh that fits a complex surface in R3. In the context of adaptive finite element simulation, the solution (which is an unknown function f : Ω ⊂ d → ) is sought by iteratively modifying a finite element mesh according to a mesh sizing field described via a (discrete) metric tensor field that is typically obtained through an error estimator. We proposed to use a higher dimensional embedding, Φf (x):= (x1, …, xd, s f (x1, …, xd), s ▿ f (x1, …, xd))t, instead of the mesh sizing field for the mesh adaption. This embedding contains both informations of the function f itself and its gradient. An isotropic mesh in this embedded space will correspond to an anisotropic mesh in the actual space, where the mesh elements are stretched and aligned according to the features of the function f. To better capture the anisotropy and gradation of the mesh, it is necessary to balance the contribution of the components in this embedding. We have properly adjusted Φf (x) for adaptive finite element analysis. To better understand and validate the proposed mesh adaptation strategy, we first provide a series of experimental tests for piecewise linear interpolation of known functions. We then applied this approach in an adaptive finite element solution of partial differential equations. Both tests are performed on two-dimensional domains in which adaptive triangular meshes are generated. We compared these results with the ones obtained by the software BAMG – a metric-based adaptive mesh generator. The errors measured in the L2 norm are comparable. Moreover, our meshes captured the anisotropy more accurately than the meshes of BAMG
A mesh simplification strategy for a spatial regression analysis over the cortical surface of the brain
No full textCurvature-adapted Remeshing of CAD Surfaces
Full text linkAbstractA common representation of surfaces with complicated topology and geometry is through composite parametric surfaces as is the case for most CAD modelers. A challenging problem is how to generate a mesh of such a surface that well approximates the geometry of the surface, preserves its topology and important geometric features, and contains nicely shaped elements. In this work, we present an optimization-based surface remeshing method that is able to satisfy many of these requirements simultaneously. This method is inspired by the recent work of Lévy and Bonneel (Proc. 21th International Meshing Roundtable, October 2012), which embeds a smooth surface into a high-dimensional space and remesh it uniformly in that embedding space. Our method works directly in the 3d spaces and uses an embedding space in R6 to evaluate mesh size and mesh quality. It generates a curvature-adapted anisotropic surface mesh that well represents the geometry of the surface with a low number of elements. We illustrate our approach through various examples
Mixed Virtual Element approximation of linear acoustic wave equation
No full textWe design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In the absence of external loads, the semi-discrete method exactly conserves the system energy. To integrate in time the semi-discrete problem we consider a classical θ-method scheme. We carry out the stability and convergence analysis in the energy norm for the semi-discrete problem showing an optimal rate of convergence with respect to the mesh size. We further study the property of energy conservation for the fully-discrete system. Finally, we present some verification tests as well as engineering applications of the method
The mixed virtual element method on curved edges in two dimensions
Full text linkIn this work, we propose an extension of the mixed Virtual Element Method (VEM) for bi-dimensional computational grids with curvilinear edge elements. The approximation by means of rectilinear edges of a domain with curvilinear geometrical feature, such as a portion of domain boundary or an internal interface, may introduce a geometrical error that degrades the expected order of convergence of the scheme. In the present work a suitable VEM approximation space is proposed to consistently handle curvilinear geometrical objects, thus recovering optimal convergence rates. The resulting numerical scheme is presented along with its theoretical analysis and several numerical test cases to validate the proposed approach
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