Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHexGen and Hex2Spline: Polycube-based Hexahedral Mesh Generation and Spline Modeling for Isogeometric Analysis Applications in LS-DYNA
74
0
0.0
(
0
)
Added by
Yuxuan Yu
Publication date
2020
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
In this paper, we present two software packages, HexGen and Hex2Spline, that seamlessly integrate geometry design with isogeometric analysis (IGA) in LS-DYNA. Given a boundary representation of a solid model, HexGen creates a hexahedral mesh by utilizing a semi-automatic polycube-based mesh generation method. Hex2Spline takes the output hexahedral mesh from HexGen as the input control mesh and constructs volumetric truncated hierarchical splines. Through B{e}zier extraction, Hex2Spline transfers spline information to LS-DYNA and performs IGA therein. We explain the underlying algorithms in each software package and use a rod model to explain how to run the software. We also apply our software to several other complex models to test its robustness. Our goal is to provide a robust volumetric modeling tool and thus expand the boundary of IGA to volume-based industrial applications.
rate research
Read More
In this paper, we extend our earlier polycube-based all-hexahedral mesh generation method to hexahedral-dominant mesh generation, and present the HexDom software package. Given the boundary representation of a solid model, HexDom creates a hex-dominant mesh by using a semi-automated polycube-based mesh generation method. The resulting hexahedral dominant mesh includes hexahedra, tetrahedra, and triangular prisms. By adding non-hexahedral elements, we are able to generate better quality hexahedral elements than in all-hexahedral meshes. We explain the underlying algorithms in four modules including segmentation, polycube construction, hex-dominant mesh generation and quality improvement, and use a rockerarm model to explain how to run the software. We also apply our software to a number of other complex models to test their robustness. The software package and all tested models are availabe in github (https://github.com/CMU-CBML/HexDom).
Due to the fractal nature of the domain geometry in geophysical flow simulations, a completely accurate description of the domain in terms of a computational mesh is frequently deemed infeasible. Shoreline and bathymetry simplification methods are used to remove small scale details in the geometry, particularly in areas away from the region of interest. To that end, a novel method for shoreline and bathymetry simplification is presented. Existing shoreline simplification methods typically remove points if the resultant geometry satisfies particular geometric criteria. Bathymetry is usually simplified using traditional filtering techniques, that remove unwanted Fourier modes. Principal Component Analysis (PCA) has been used in other fields to isolate small-scale structures from larger scale coherent features in a robust way, underpinned by a rigorous but simple mathematical framework. Here we present a method based on principal component analysis aimed towards simplification of shorelines and bathymetry. We present the algorithm in detail and show simplified shorelines and bathymetry in the wider region around the North Sea. Finally, the methods are used in the context of unstructured mesh generation aimed at tidal resource assessment simulations in the coastal regions around the UK.
This work proposes a rigorous and practical algorithm for generating meromorphic quartic differentials for the purpose of quad-mesh generation. The work is based on the Abel-Jacobi theory of algebraic curve. The algorithm pipeline can be summarized as follows: calculate the homology group; compute the holomorphic differential group; construct the period matrix of the surface and Jacobi variety; calculate the Abel-Jacobi map for a given divisor; optimize the divisor to satisfy the Abel-Jacobi condition by an integer programming; compute the flat Riemannian metric with cone singularities at the divisor by Ricci flow; isometric immerse the surface punctured at the divisor onto the complex plane and pull back the canonical holomorphic differential to the surface to obtain the meromorphic quartic differential; construct the motor-graph to generate the resulting T-Mesh. The proposed method is rigorous and practical. The T-mesh results can be applied for constructing T-Spline directly. The efficiency and efficacy of the proposed algorithm are demonstrated by experimental results.
This work discovers the equivalence relation between quadrilateral meshes and meromorphic quartic. Each quad-mesh induces a conformal structure of the surface, and a meromorphic differential, where the configuration of singular vertices correspond to the configurations the poles and zeros (divisor) of the meroromorphic differential. Due to Riemann surface theory, the configuration of singularities of a quad-mesh satisfies the Abel-Jacobi condition. Inversely, if a satisfies the Abel-Jacobi condition, then there exists a meromorphic quartic differential whose equals to the given one. Furthermore, if the meromorphic quadric differential is with finite, then it also induces a a quad-mesh, the poles and zeros of the meromorphic differential to the singular vertices of the quad-mesh. Besides the theoretic proofs, the computational algorithm for verification of Abel-Jacobi condition is explained in details. Furthermore, constructive algorithm of meromorphic quartic differential on zero surfaces is proposed, which is based on the global algebraic representation of meromorphic. Our experimental results demonstrate the efficiency and efficacy of the algorithm. This opens up a direction for quad-mesh generation using algebraic geometric approach.
A piecewise Chebyshevian spline space is good for design when it possesses a B-spline basis and this property is preserved under arbitrary knot insertion. The interest in piecewise Chebyshevian spline spaces that are good for design is justified by the fact that, similarly as for polynomial splines, the related parametric curves exhibit the desired properties of convex hull inclusion, variation diminution and intuitive relation between the curve shape and the location of the control points. For all good-for-design spaces, in this paper we construct a set of functions, called transition functions, which allow for efficient computation of the B-spline basis, even in the case of nonuniform and multiple knots. Moreover, we show how the spline coefficients of the representations associated with a refined knot partition and with a raised order can conveniently be expressed by means of transition functions. This result allows us to provide effective procedures that generalize the classical knot insertion and degree raising algorithms for polynomial splines. To illustrate the benefits of the proposed computational approaches, we provide several examples dealing with different types of piecewise Chebyshevian spline spaces that are good for design.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
