3 edition of **Two-dimensional mesh embedding for Galerkin B-spline methods** found in the catalog.

Two-dimensional mesh embedding for Galerkin B-spline methods

- 22 Want to read
- 15 Currently reading

Published
**1995**
by National Aeronautics and Space Administration, National Technical Information Service, distributor in [Washington, DC], [Springfield, Va
.

Written in English

- Computational grids.,
- Galerkin method.,
- Linear equations.,
- Partial differential equations.,
- Spline functions.

**Edition Notes**

Other titles | Two dimensional mesh embedding for Galerkin B-spline methods. |

Statement | Karim Shariff and Robert D. Moser. |

Series | NASA technical memorandum -- 110361. |

Contributions | Moser, Robert deLancey., United States. National Aeronautics and Space Administration. |

The Physical Object | |
---|---|

Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL18086113M |

Closed B-spline curves and surfaces usually have periodic knot vectors, and the control mesh or polygon is closed on itself. Spatiality refers to the type of geometric entity that is generated. B-spline curves have only one parametric variable and are evaluated by summing the product of the basis functions and the active control polygon. An efficient quasi-Newton method for two-dimensional steady free surface flow Demeester, T., van Brummelen, E. H. & Degroote, J., 9 Jan , In: International Journal for Numerical Methods in Fluids. Research output: Contribution to journal › Article › Academic › peer-review.

A new IsogEometric Tearing and Interconnecting (IETI) method is proposed. Exact geometry representation of IGA and solver design of FETI methods are combined. Coupling conditions for interfaces, including hanging knots, are discussed. Efficient preconditioning techniques for the interface problem are presented. Some local refinement options for IGA are by: Fig. 1 illustrates a cubic B-spline basis, where knots at the beginning and the end are repeated to make the basis interpolatory, a so-called B-spline patch with open knot vectors.A d -dimensional B-spline basis can be easily constructed by taking the tensor product of corresponding univariate B-spline basis functions (2) B i, p (ξ.

The mesh density is locally adapted to provide accuracy along these boundaries, which can be fixed or move inside the mesh. Instead of using a polygon clipping algorithm, we use the Voxel traversal algorithm coupled with a local floodfill scanline to intersect 2D or 3D . An example of B-spline basis of degree p = 1, 2 are shown in Fig. 2. One can notice that the support of a B-spline of degree p is always p + 1 knot spans and, as a consequence, each p-th degree function has p − 1 continuous derivatives across the element boundaries (i.e. across the knots) if they are not repeated. Repetition of knots can be Author: Schoeps.

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Get this from a library. Two-dimensional mesh embedding for Galerkin B-spline methods. [Karim Shariff; Robert deLancey Moser; United States. National Aeronautics and Space Administration.]. Two-Dimensional Mesh Embedding for B-spline Methods arbitrary orders of accuracy and high resolving powers similar to those of compact schemes.

Furthermore, if one uses a Galerkin scheme one gets, in addition to conservation of the discretized quantities, conservation of quadratic invariants such as energy. the ability to treat semi Cited by: The Galerkin B-spline method has a number of useful properties (Moser et al.

[31): (i) Thanks to the high degree of continuity of the B-splines, the scheme has high resolution similar to compact finite-differences (Lele [2]) without the need to separately construct numerical boundary schemes.

Abstract In this paper, the bi-quintic B-spline base functions have been modified on a general two dimensional problem. A special form of the two dimensional problem has been considered as its application and has been solved by the Galerkin finite element method using the modified bi-quintic B-spline base functions.

The first one is the divergenece-free Galerkin method of Kravchenko et al. () for LES of turbulent flow past a circular cylinder, which employs the embedded meshing of the "Mesh embedding or. Using an explicit displacement-based formulation in mesh-free computations, high-resolution shear-band formations are obtained in both two-dimensional (2-D) and three-dimensional (3-D) simulations.

creasing order of splines [12, 13]. The dispersion analysis of B-spline Galerkin based FEM has been studied in [12, 14] for one-dimensional case and in [15] for two-dimensional case.

The eﬀect of inhomogeneity of spline shape func-tions and of parameterization of the. The dispersion analysis of B-spline Galerkin based FEM has been studied in, for one-dimensional case and in for two-dimensional case.

The effect of inhomogeneity of spline shape functions and of parameterization of the B-spline representation on the dispersion and Cited by: 8. The interpolation by two-dimensional cubic B-spline of a network data with mesh m×n and uniform ∆x and ∆y requires 2(m+n+2) more equations in order to satisfy the uniqueness of the governing system of equations.

However, it relates to the degree of polynomial B-spline considered. For reverse engineering, nonuniform rational B-spline (NURBS) surfaces expressed by the tensor product are fitted to measured coordinates of points. To estimate the unknown control points, the lofting or skinning method by cross-sectional curve fits leads to efficient computations.

Its numerical complexity for estimating k 2 control points is O(k 3), while simultaneously estimating the control Cited by: The finite element procedure consists in finding an approximate solution in the form of piecewise linear functions, piecewise quadratic, etc.

For two-dimensional problems, one of the most frequently used approaches is to triangulate the domain and find the approximate solution which is Cited by: Wavelet Galerkin Methods for Boundary Integral Equations and the Coupling with Finite Element Methods.

Wavelet Transforms and Time-Frequency Signal Analysis, SIAM Journal on Numerical AnalysisOn the generation Cited by: Abstract. This paper examines the role of continuity of the basis in the computation of turbulent flows.

We compare standard finite elements and non-uniform rational B-splines (NURBS) discretizations that are employed in Isogeometric Analysis (Hughes et al. in Comput Methods Appl Mech Eng, –, ).Cited by: Morphing Rational B-spline Curves and Surfaces Using Mass Distributions Tao Ju1 and Ron Goldman1 1 Department of Computer Science, Rice University, Houston, Texas, USA Abstract A rational B-spline curve or surface is a collection of points associated with a mass (weight) distribution.

TheseFile Size: 1MB. Shouyu Cai, Weihong Zhang, Jihong Zhu and Tong Gao, Stress constrained shape and topology optimization with fixed mesh: A B-spline finite cell method combined with level set function, Computer Methods in Applied Mechanics and Engineering, /,(), ().

The shape functions for a 2D quadratic and a 3D quadratic B spline element can be expressed as, (3 8) A two dimensional cubic B spline element is shown in Figure 3 6. The basis functions of a two dimensional cubic B spline elem ent are constructed as a product of the basis functions of a.

Wolfgang Dahmen, Gitta Kutyniok, Wang-Q Lim, Christoph Schwab and Gerrit Welper, Adaptive anisotropic Petrov–Galerkin methods for first order transport equations, Journal of Computational and Applied Mathematics, /,(), ().Cited by: Thomas P.

Wihler, Béatrice Rivière, Discontinuous Galerkin Methods for Second-Order Elliptic PDE with Low-Regularity Solutions, Journal of Scientific Computing, v n.2, p, February Peng Di, Jingling Xue, Model-driven tile size selection for DOACROSS loops on GPUs, Proceedings of the 17th international conference on Parallel Cited by: An adaptable curved quadrilateral element based on quadratic B‐splines is developed for finite element analysis of membrane vibration problems.

The approximated displacement field in each element is divided into corners, edges and internal modes. The number of knots on the edges of elements are distinct in any integer power of 2.

The elements of different resolutions can be thus connected. Two-dimensional fracture mechanics analyses using the wavelet Galerkin method and extended finite element method, International Journal for Numerical Methods in Engineering, 93,A wavelet Galerkin method employing B-spline bases for solid mechanics problems without the use of a fictitious domain, Computational Mechanics.

The convergence of Galerkin and collocation methods with splines for pseudodifferential equations on closed curves; Z. Anal.\ Anwendungen; 3; ; ; %SchmidtHess % carl 7sep95 \rhl{S} \refJ Schmidt, Jochen W.B-spline surfaces are tensor products of B-spline curves that maintain the advantages of smoothness and sparsity.

Figure illustrates how a conventional wing-body-tail aircraft geometry can be constructed with 4-sided B-spline surfaces Figure Conventional configuration geometry (a), final structural mesh (Courtesy of Hwang & Martins).Mesh Generation in CFD Ideen Sadrehaghighi, Ph.D.

Cyliner Head (Polyhedral cells) ISSN –, UDK JIA Huana, SUN Qin b, “A Comparison of Two Dynamic Mesh Methods in Fluid –Structure interaction”, School of Aeronautics, Northwestern Polytechnic University, Xi‘an china. 2nd International Conference on Electronic.