3 edition of **Algebraic grid generation using tensor product b-splines** found in the catalog.

Algebraic grid generation using tensor product b-splines

- 254 Want to read
- 28 Currently reading

Published
**1985** by National Aeronautics and Space Administration, Langley Research Center, For sale by the National Technical Information Service in Hampton, Va, [Springfield, Va .

Written in English

- Numerical grid generation (Numerical analysis),
- Fluid dynamics.

**Edition Notes**

Statement | Bonita V. Saunders. |

Series | NASA contractor report -- 177968., NASA contractor report -- NASA CR-177968. |

Contributions | Langley Research Center. |

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

Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL15276800M |

The tensor product b-spline basis functions are constructed so that the basis functions and their first partials are continuous on the parameter space. The coordinate functions inherit this smoothness: a grid computed by evaluating the coordinate functions along constant parameter lines leads to smooth grid lines with smoothly varying tangents. Introduction. B-splines were investigated as early as the nineteenth century by Nikolai term "B-spline" was coined by Isaac Jacob Schoenberg [1] and is short for basis spline. [2] A spline function is a piecewise polynomial function of degree k in a variable places where the pieces meet are known as knots. A self-explanatory, pictorial view of the algorithm of algebraic adaptive grid generation is shown in Fig. 1. The grid and solution will be transferred from the flow solver if the solution is good enough to apply grid adaptation. The criterion of good solution can be the pressure L2 residue or another prop-. Welcome to our online library. Here you can find thousands of eBooks in a variety of genres in PDF, Epub and Mobi formats. Convenient search and writers directory. New releases and classics, popular and not - all of your favorite books and authors can be found on our website.

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Algebraic grid generation using tensor product b-splines by bonita valerie saunders b.a., maycollege of william and mary m.s., mayuniversity of virginia a dissertation submitted to the faculty of old dominion university in partial fulfillment of the Cited by: 3.

Tensor Product B-Spline Mesh Generation 2 x 0 2 4 Ν 0 5 10 Fig Plot of Struve function Lν illustrating bad clipping and poor resolution of poles design allowed us to write more efﬁcient code to implement the interactive capabilitiesCited by: 1. The treatment of structured grid generation starts with basic geometry and tensor analysis before moving on to identify the variety of approaches that can be employed in the generation of structured grids.

The book then introduces unstructured grid generation by explaining the basics of Delaunay triangulation and advancing front by: We discuss the use of tensor product B-spline meshes to design accurate three dimensional graphs of high level B.V.: Algebraic grid generation using tensor product B-splines, NASA CR Wang Q.

() Tensor Product B-Spline Mesh Generation for Accurate Surface Visualizations in the NIST Digital Library of Mathematical Functions. Cited by: 1. Topological considerations in structuring the grid generation mapping are discussed.

The concept of the degree Algebraic grid generation using tensor product b-splines book a mapping and how it can be used to determine what requirements are necessary if a mapping is to produce a suitable grid is examined.

The grid generation algorithm uses a mapping composed of bicubic : B. Saunders. • Bonita V. Saunders, Algebraic Grid Generation Using Tensor Product B-Splines, Ph.D. dissertation, Old Dominion University, Also, NASA contractor report: NASA CRSeptember Selected Talks Invited Lectures • B-Spline Mesh Generation, 3D Web Graphics, and the NIST Digital Library of MathematicalFile Size: KB.

The existence of a limiting grid (termed the “grid at infinity”) is demonstrated for Alternative II; it is shift invariant, and its form is not a tensor product. Finally, a way to exploit the translation property of such algebraic methods using the direct variational method is given.

This paper discusses an algebraic mapping which uses tensor product B-splines to produce such a grid given the boundary description. Abstract--The development of an algebraic grid generation system to track a Algebraic grid generation using tensor product b-splines book interface during directional solidification of a binary alloy is discussed.

A single mapping, constructed with tensor product B-splines, is proposed for calculations of both shallow and deep solidification cells. The. The title, The Poor Man’s Introduction to Tensors, is a reference to Gravitation by Misner, Thorne and Wheeler, which characterizes simplified approaches to a problem as “the poor man’s way to do X.” Originally, these notes were.

directions, such a quantity is called Tensor. The stress at a point of an elastic solid is an example of a Tensor which depends on two directions one normal to the area and other that of the force on it.

Tensors have their applications to Riemannian Geometry, Mechanics, Elasticity, Theory of Relativity,File Size: 1MB. Get this from a library. Algebraic grid generation using tensor product b-splines. [Bonita V Saunders; Langley Research Center.].

We have proposed a new algebraic grid generation method based on tensor product functions on sub-regions. The control points involved in the method are used to control the grid quality by optimal locations of some of them.

This is achieved by using some optimization strategies based on grid Cited by: 2. tensor analysis. Many exercises are included in each volume. However, it is likely that teachers will wish to generate additional exercises. Several times during the preparation of this book we taught a one semester course to students with a very limited background in linear algebra and no background in tensor File Size: 1MB.

Algebraic grid generation is the direct expression of a physical coordinate system as a function of a uniform grid in a rectangular computational coordinate system.

Bonita Saunders and Qiming Wang, "Tensor Product Grid Generation for Complex Surface Visualizations in a Digital Library of Mathematical Functions," 11th International Society for Grid Generation (ISGG) Conference, Montreal, Canada, MayBonita V.

Saunders, Boundary Fitted Grid Generation Using Tensor Product B-splines, Numerical Methods for Fluid Dynamics, Oxford University Press (). B.T. Murray, G.B. McFadden, S.R. Coriell, and A.A. Wheeler, Bonita V. Saunders, The Effect of Gravity Modulation on Thermosolutal Convection in an Infinite Layer of Fluid, Physical Fluids.

Construct the algebraic grid through the following steps: compute the orthogonal directions φ 3, φ 4, ψ 3, ψ 4 by means of and, compute the control points {Q ij} i,j=1 m p,n p with the strategy in. compute the knots of the B-splines as in, use to generate the mixed algebraic surface X(ξ,η) Cited by: 7.

algebraic grid surfaces by means of a re-parametrization procedure combined with the use of quality parameters for grid surfaces.

The re-parametrization phase is based on a tensor product transformation following given directions. The free parameters in the tensor product are set by solving an optimization problem that uses objective functions.

The present book, a valuable addition to the English-language literature on linear algebra and tensors, constitutes a lucid, eminently readable and completely elementary introduction to this field of mathematics.

A special merit of the book is its free use of tensor notation, in particular the Einstein summation convention/5(3). Multivariate Tensor Product Splines Introduction to Multivariate Tensor Product Splines. The toolbox provides (polynomial) spline functions in any number of variables, as tensor products of univariate splines.

These multivariate splines come in both standard forms, the B-form and the ppform, and their construction and use parallels entirely that of the univariate splines discussed in previous. The algorithm uses an algebraic grid generation system deﬁned by a mapping T from the unit square I2 to a physical domain of arbitrary shape.

(ξ,η), (1) 4 B. Saunders and Q. Wang where 0 ≤ ξ,η ≤ 1 and each Bij is the tensor product of cubic B-splines. Hence, Bij(ξ,η) = Bi(ξ)Bj(η) where Bi and Bj are elements of cubic B-spline.

satisfactory grid without a more systematic approach. In particular, the application of general interpolation techniques provides a more formal approach toward the generation of grids using algebraic methods.

Smith and Weigel () developed a flexible method of directly providing grids using interpolation between Size: 1MB. Let V⊗n denote the tensor product of n copies of V and let T(V) = ⊕∞ n=0V ⊗n. Deﬁne the associative multiplication on T(V) via tensor product. T(V) is called tensor algebra. If {vi} is a basis of V, then T(V) is a free associative algebra with generators {vi}.

(Symmetric algebra.) Let S(V) be the quotient of T(V) by the ideal I. ALGEBRAIC GRID GENERATION USING TENSOR PRODUCT B-SPLINES Bonita Valerie Saunders Old Dominion University, Director: Dr.

Philip W. Smith In general, finite difference methods are more success-ful if the accompanying grid has lines which are smooth and nearly orthogonal.

This thesis discusses the develop. Approximation by Tensor Product Splines. Because the toolbox can handle splines with vector coefficients, it is easy to implement interpolation or approximation to gridded data by tensor product splines, as the following illustration is meant to show.

You can also run the example “Bivariate Tensor Product Splines”. Grid generation codes represent an indispensable tool for solving field prob lems in nearly all areas of applied mathematics.

The use of these grid codes significantly enhances the productivity and reliability of the numerical analy sis of problems with complex geometry and complicated solutions. The science of grid generation is rather young and is still growing fast; new developments are 3/5(2).

This seminorm becomes a norm on modulo the appropriate subspace, and its completion is denoted and is called the projective tensor product of and. We also have. so is a Banach *-algebra. But it fails to satisfy the C*-axiom (): It turns out that representations on and allow us to define norms on that make it a C*-algebra.

Definition 1. Does the tensor product commute with the exterior product. Ask Question (A \otimes_{R} S)$. I was trying to use the universal properties of the exterior algebra and the tensor product, but without much success.

Thank you in advance for your help. linear-algebra ring-theory modules. We present algebraic techniques, named Transfinite Interpolation, for mesh generation.

Various transfinite interpolation techniques are derived from 1D projection operators. Many geological formations such as the Utsira formation and the Snøhvit gas field can be divided into layers or blocks based on the geometrical or lithological properties Author: Sanjay Kumar Khattri.

The treatment of structured grid generation starts with basic geometry and tensor analysis before moving on to identify the variety of approaches that can be employed in the generation of structured grids. The book then introduces unstructured grid generation by explaining the basics of Delaunay triangulation and advancing front techniques.

In mathematics, the tensor algebra of a vector space V, denoted T(V) or T • (V), is the algebra of tensors on V (of any rank) with multiplication being the tensor is the free algebra on V, in the sense of being left adjoint to the forgetful functor from algebras to vector spaces: it is the "most general" algebra containing V, in the sense of the corresponding universal property.

The tensor product of commutative algebras is of constant use in algebraic geometry. For affine schemes X, Y, Z with morphisms from X and Z to Y, so X = Spec(A), Y = Spec(B), and Z = Spec(C) for some commutative rings A,B,C, the fiber product scheme is the affine scheme corresponding to the tensor product of algebras.

Since we are aiming on 3‐D models we discuss 1‐D series expansions in terms of polynomial B splines and trigonometric B splines in sections and The tensor product approach [ Schmidt, ] is used to derive the 2‐D spline model in Subsection which means an alternative to the spherical harmonic by: I'm looking to generate a C-grid for an airfoil using Matlab with clustering at the surface and wake region.

I've looked at a book called Computational Techniques for Fluid Dynamics Vol. 2 and it does a decent job of explaining it and has a code but the language is in Fortran and I have no experience with that programming language at all. InSpaltenstein showed in ("Resolutions of unbounded complexes", Compositio Math.

65 (), no. 2, –) that one can use unbounded homotopically flat resolutions of sheaves to get a derived tensor product of unbounded complexes. Similarly, you may use homotopically injective resolutions of sheaves to derive functors on the right. Book Description.

Handbook of Grid Generation addresses the use of grids (meshes) in the numerical solutions of partial differential equations by finite elements, finite volume, finite differences, and boundary elements. Four parts divide the chapters: structured grids.

A fully categorical approach that emphasizes the universal properties of the tensor product,as well as a great deal of multilinear algebra, can be found in 's Module Theory:An Approach to Linear Algebra. There's also a discussion in Steven Roman's Advanced Linear Algebra,but the presentation in Blyth's book isn't as dry and formal.

Orthogonal block structured surface grids; Surface grid generation with a linkage to geometric generation; Boundary fitted grid generation using tensor product B-splines ; Grid convergence for adaptive methods; Grid quality: an interplay of grid and solver; Body capturing using adaptive cartesian grids; In the mathematical subfield of numerical analysis, a B-spline or basis spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition.

Any spline function of given degree can be expressed as a linear combination of B-splines of that degree. Cardinal B-splines have knots that are equidistant from each other. A strategy to construct a grid conforming to the boundaries of a prescribed domain by using transfinite interpolation methods is discussed.

A transfinite interpolation procedure is combined with a B-spline tensor product scheme defined by using suitable control points.The tensor product B-spline basis functions are constructed so that the basis functions and their first partials are continuous on the computational domain for the block.

The coordinate functions inherit this smoothness: a grid computed by evaluating the coordinate function along constant parameter lines leads to smooth grid lines with smoothly.Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.

It only takes a minute to sign up. Definition of tensor product for modules. Ask Question Asked 3 years, 5 months ago. Browse other questions tagged linear-algebra vector-spaces modules definition tensor.