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Toshniwal D. - One of the best experts on this subject based on the ideXlab platform.
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A General Class of C1 Smooth Rational Splines: Application to Construction of Exact Ellipses and Ellipsoids
'Elsevier BV', 2021Co-Authors: Speleers Hendrik, Toshniwal D.Abstract:In this paper, we describe a general class of C1 smooth rational splines that enables, in particular, exact descriptions of ellipses and ellipsoids — some of the most important primitives for CAD and CAE. The univariate rational splines are assembled by transforming multiple sets of NURBS basis functions via so-called design-through-analysis compatible extraction matrices; different sets of NURBS are allowed to have different polynomial Degrees and weight functions. Tensor products of the univariate splines yield multivariate splines. In the bivariate setting, we describe how similar design-through-analysis compatible transformations of the tensor-product splines enable the construction of smooth surfaces containing one or two polar singularities. The material is self-contained, and is presented such that all tools can be easily implemented by CAD or CAE practitioners within existing software that support NURBS. To this end, we explicitly present the matrices (a) that describe our splines in terms of NURBS, and (b) that help refine the splines by performing (local) Degree Elevation and knot insertion. Finally, all C1 spline constructions yield spline basis functions that are locally supported and form a convex partition of unity.Delft Institute of Applied MathematicsNumerical Analysi
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Isogeometric discrete differential forms: Non-uniform Degrees, Bezier extraction, polar splines and flows on surfaces: Non-uniform Degrees, Bézier extraction, polar splines and flows on surfaces
'Elsevier BV', 2021Co-Authors: Toshniwal D., Hughes ThomasAbstract:Spaces of discrete differential forms can be applied to numerically solve the partial differential equations that govern phenomena such as electromagnetics and fluid mechanics. Robustness of the resulting numerical methods is complemented by pointwise satisfaction of conservation laws (e.g., mass conservation) in the discrete setting. Here we present the construction of isogeometric discrete differential forms, i.e., differential form spaces built using smooth splines. We first present an algorithm for computing Bézier extraction operators for univariate spline differential forms that allow local Degree Elevation. Then, using tensor-products of the univariate splines, a complex of discrete differential forms is built on meshes that contain polar singularities, i.e., edges that are singularly mapped onto points. We prove that the spline complexes share the same cohomological structure as the de Rham complex. Several examples are presented to demonstrate the applicability of the proposed methodology. In particular, the splines spaces derived are used to simulate generalized Stokes flow on arbitrarily curved smooth surfaces and to numerically demonstrate (a) optimal approximation and inf–sup stability of the spline spaces; (b) pointwise incompressible flows; and (c) flows on deforming surfaces.Numerical Analysi
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Isogeometric discrete differential forms: Non-uniform Degrees, Bezier extraction, polar splines and flows on surfaces: Non-uniform Degrees, Bézier extraction, polar splines and flows on surfaces
'Elsevier BV', 2021Co-Authors: Toshniwal D., Hughes ThomasAbstract:Spaces of discrete differential forms can be applied to numerically solve the partial differential equations that govern phenomena such as electromagnetics and fluid mechanics. Robustness of the resulting numerical methods is complemented by pointwise satisfaction of conservation laws (e.g., mass conservation) in the discrete setting. Here we present the construction of isogeometric discrete differential forms, i.e., differential form spaces built using smooth splines. We first present an algorithm for computing Bézier extraction operators for univariate spline differential forms that allow local Degree Elevation. Then, using tensor-products of the univariate splines, a complex of discrete differential forms is built on meshes that contain polar singularities, i.e., edges that are singularly mapped onto points. We prove that the spline complexes share the same cohomological structure as the de Rham complex. Several examples are presented to demonstrate the applicability of the proposed methodology. In particular, the splines spaces derived are used to simulate generalized Stokes flow on arbitrarily curved smooth surfaces and to numerically demonstrate (a) optimal approximation and inf–sup stability of the spline spaces; (b) pointwise incompressible flows; and (c) flows on deforming surfaces
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A General Class of C1 Smooth Rational Splines: Application to Construction of Exact Ellipses and Ellipsoids
'Elsevier BV', 2021Co-Authors: Speleers Hendrik, Toshniwal D.Abstract:In this paper, we describe a general class of C1 smooth rational splines that enables, in particular, exact descriptions of ellipses and ellipsoids — some of the most important primitives for CAD and CAE. The univariate rational splines are assembled by transforming multiple sets of NURBS basis functions via so-called design-through-analysis compatible extraction matrices; different sets of NURBS are allowed to have different polynomial Degrees and weight functions. Tensor products of the univariate splines yield multivariate splines. In the bivariate setting, we describe how similar design-through-analysis compatible transformations of the tensor-product splines enable the construction of smooth surfaces containing one or two polar singularities. The material is self-contained, and is presented such that all tools can be easily implemented by CAD or CAE practitioners within existing software that support NURBS. To this end, we explicitly present the matrices (a) that describe our splines in terms of NURBS, and (b) that help refine the splines by performing (local) Degree Elevation and knot insertion. Finally, all C1 spline constructions yield spline basis functions that are locally supported and form a convex partition of unity.
Mazure Marie-laurence - One of the best experts on this subject based on the ideXlab platform.
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Quantum Lorentz Degrees of Polynomials and a Pólya Theorem for Polynomials Positive on q-Lattices
'Elsevier BV', 2021Co-Authors: Ait-haddou Rachid, Goldman Ron, Mazure Marie-laurenceAbstract:International audienceWe establish the uniform convergence of the control polygons generated by repeated Degree Elevation of q-Bézier curves (i.e., polynomial curves represented in the q-Bernstein bases of increasing Degrees) on [0, 1], q > 1, to a piecewise linear curve with vertices on the original curve. A similar result is proved for q < 1, but surprisingly the limit vertices are not on the original curve, but on the 1/q-Bézier curve with control polygon taken in the reverse order. We introduce a q-deformation (quantum Lorentz Degree) of the classical notion of Lorentz Degree for polynomials and we study its properties. As an application of our convergence results, we introduce a notion of q-positivity which guarantees that the q-Lorentz Degree is finite. We also obtain upper bounds for the quantum Lorentz Degrees. Finally, as a by-product we provide a generalization to polynomials positive on q-lattices of the univariate Pólya theorem concerning polynomials positive on the non-negative axis
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Dimension Elevation is not always corner-cutting
'Elsevier BV', 2020Co-Authors: Beccari, Carolina Vittoria, Casciola Giulio, Mazure Marie-laurenceAbstract:International audienceDegree Elevation is a typical corner-cutting algorithm. It refers to the process transforming control polygons when embedding a polynomial space of some Degree into any polynomial space of higher Degree.Dimension Elevation similarly refers to the transformation of control polygons when embedding an Extended Chebyshev space possessing a Bernstein basis into another one, of higher dimension. Unlike Degree Elevation, this cannot always be split into successive (corner-cutting) steps elevating the dimension by one. What happens when it is not possible is investigated here. We shall see that the new control points can even be located outside the initial control polygons, giving evidence that dimension Elevation is not always corner-cutting
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Quantum Lorentz Degrees of Polynomials and a Pólya Theorem for Polynomials Positive on q-Lattices
HAL CCSD, 2020Co-Authors: Ait-haddou Rachid, Goldman Ron, Mazure Marie-laurenceAbstract:We establish the uniform convergence of the control polygons generated by repeated Degree Elevation of q-Bézier curves (i.e., polynomial curves represented in the q-Bernstein bases of increasing Degrees) on [0, 1], q > 1, to a piecewise linear curve with vertices on the original curve. A similar result is proved for q < 1, but surprisingly the limit vertices are not on the original curve, but on the 1/q-Bézier curve with control polygon taken in the reverse order. We introduce a q-deformation (quantum Lorentz Degree) of the classical notion of Lorentz Degree for polynomials and we study its properties. As an application of our convergence results, we introduce a notion of q-positivity which guarantees that the q-Lorentz Degree is finite. We also obtain upper bounds for the quantum Lorentz Degrees. Finally, as a by-product we provide a generalization to polynomials positive on q-lattices of the univariate Pólya theorem concerning polynomials positive on the non-negative axis
Thomas J R Hughes - One of the best experts on this subject based on the ideXlab platform.
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isogeometric discrete differential forms non uniform Degrees bezier extraction polar splines and flows on surfaces
Computer Methods in Applied Mechanics and Engineering, 2021Co-Authors: Deepesh Toshniwal, Thomas J R HughesAbstract:Abstract Spaces of discrete differential forms can be applied to numerically solve the partial differential equations that govern phenomena such as electromagnetics and fluid mechanics. Robustness of the resulting numerical methods is complemented by pointwise satisfaction of conservation laws (e.g., mass conservation) in the discrete setting. Here we present the construction of isogeometric discrete differential forms, i.e., differential form spaces built using smooth splines. We first present an algorithm for computing Bezier extraction operators for univariate spline differential forms that allow local Degree Elevation. Then, using tensor-products of the univariate splines, a complex of discrete differential forms is built on meshes that contain polar singularities, i.e., edges that are singularly mapped onto points. We prove that the spline complexes share the same cohomological structure as the de Rham complex. Several examples are presented to demonstrate the applicability of the proposed methodology. In particular, the splines spaces derived are used to simulate generalized Stokes flow on arbitrarily curved smooth surfaces and to numerically demonstrate (a) optimal approximation and inf–sup stability of the spline spaces; (b) pointwise incompressible flows; and (c) flows on deforming surfaces.
Deepesh Toshniwal - One of the best experts on this subject based on the ideXlab platform.
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isogeometric discrete differential forms non uniform Degrees bezier extraction polar splines and flows on surfaces
Computer Methods in Applied Mechanics and Engineering, 2021Co-Authors: Deepesh Toshniwal, Thomas J R HughesAbstract:Abstract Spaces of discrete differential forms can be applied to numerically solve the partial differential equations that govern phenomena such as electromagnetics and fluid mechanics. Robustness of the resulting numerical methods is complemented by pointwise satisfaction of conservation laws (e.g., mass conservation) in the discrete setting. Here we present the construction of isogeometric discrete differential forms, i.e., differential form spaces built using smooth splines. We first present an algorithm for computing Bezier extraction operators for univariate spline differential forms that allow local Degree Elevation. Then, using tensor-products of the univariate splines, a complex of discrete differential forms is built on meshes that contain polar singularities, i.e., edges that are singularly mapped onto points. We prove that the spline complexes share the same cohomological structure as the de Rham complex. Several examples are presented to demonstrate the applicability of the proposed methodology. In particular, the splines spaces derived are used to simulate generalized Stokes flow on arbitrarily curved smooth surfaces and to numerically demonstrate (a) optimal approximation and inf–sup stability of the spline spaces; (b) pointwise incompressible flows; and (c) flows on deforming surfaces.
Funda Kuyurtar - One of the best experts on this subject based on the ideXlab platform.
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review of the methods to prevent femoral arteriotomy complications and contrast nephropathy in patients undergoing cardiac catheterization cardiac catheterization and care approaches in turkey
Journal of Cardiovascular Nursing, 2007Co-Authors: Meral Altiok, Sabire Yurtsever, Funda KuyurtarAbstract:BACKGROUND AND RESEARCH OBJECTIVE: There are different care and treatment approaches to prevent femoral arteriotomy complications and contrast nephropathy in patients undergoing cardiac catheterization. The purpose of our study was to identify approaches widely used in Turkey to prevent femoral arteriotomy complications and contrast nephropathy in patients undergoing cardiac catheterization. MATERIALS AND METHODS: The study was a descriptive study. A questionnaire was mailed to 36 university medical faculty hospitals that have active interventional cardiology units. Twenty-nine universities (80.5%) responded. RESULTS AND CONCLUSIONS: In general in Turkey, only manual pressure is used to achieve initial hemostasis at the femoral insertion site, with a pressure dressing and sandbag added to maintain hemostasis. Arterial closure devices are rarely used. In general, after the procedure, patients are required to lie flat with, at most, a 15- to 30-Degree Elevation during bed rest. To prevent contrast nephropathy in patients at risk, intravenous saline solutions are started before the procedure and continued afterward. In other patients, only oral fluid replacement is used. Traditional approaches in the management of femoral artery insertion site continue, and practices used in the prevention of contrast nephropathy are similar to current practices.