The Stable Evaluation of B-Splines and Splines

Boor, Carl de

doi:10.1007/978-1-4612-6333-3_10

Cited by 162 publications

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“…In order to enhance the accuracy, a third order polynomial (cubic spline) interpolation was employed. 39 Thus, each interval image is the computational result of nearby four images directly obtained from calibration. Figure 7 shows the measured results at five different points in the range of 0-10 psi.…”

Section: Resultsmentioning

confidence: 99%

Optofluidic membrane interferometer: An imaging method for measuring microfluidic pressure and flow rate simultaneously on a chip

Song

2011

Biomicrofluidics

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We present a novel image-based method to measure the on-chip microfluidic pressure and flow rate simultaneously by using the integrated optofluidic membrane interferometers (OMIs). The device was constructed with two layers of structured polydimethylsiloxane (PDMS) on a glass substrate by multilayer soft lithography. The OMI consists of a flexible air-gap optical cavity which upon illumination by monochromatic light generates interference patterns that depends on the pressure. These interference patterns were captured with a microscope and analyzed by computer based on a pattern recognition algorithm. Compared with the previous techniques for pressure sensing, this method offers several advantages including low cost, simple fabrication, large dynamic range, and high sensitivity. For pressure sensing, we demonstrate a dynamic range of 0-10 psi with an accuracy of 62% of full scale. Since multiple OMIs can be integrated into a single chip for detecting pressures at multiple locations simultaneously, we also demonstrated a microfluidic flow sensing by measuring the differential pressure along a channel. Thanks to the simple fabrication that is compatible with normal microfluidics, such OMIs can be easily integrated into other microfluidic systems for in situ fluid monitoring.

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Section: Resultsmentioning

confidence: 99%

Optofluidic membrane interferometer: An imaging method for measuring microfluidic pressure and flow rate simultaneously on a chip

Song

2011

Biomicrofluidics

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“…Furthermore, define the p-th order B-spline basis as de Boor;2001;Shen et al;, and let G = G (p−2) be the space spanned by B p (u).…”

Section: Estimation Methodsmentioning

confidence: 99%

Partially linear single index models for repeated measurements

Liang

Tsai

2014

Journal of Multivariate Analysis

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“…For univariate basis functions, the corresponding extrapolation weights e i,j are generally defined by the so-called de Boor-Fix or dual functional (see e.g. [6,23,25]). In addition, a simplified formula can be derived for uniform parameter spaces [22,24].…”

Section: Stable Basis For Trimmed Geometriesmentioning

confidence: 99%

Integration of Design and Analysis Through Boundary Integral Equations

Marussig

Zechner

Beer

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. The direct integration of Computer Aided Geometric Design (CAGD) models into a numerical simulation improves the accuracy of the geometrical representation of the problem as well as the efficiency of the overall analysis process.In this work, the complementary features of isogeometric analysis and boundary integral equations are combined to obtain a coalescence of design and analysis which is based on a boundary-only discretization. Following the isogeometric concept, the functions used by CAGD are employed for the simulation. An independent field approximation is applied to obtain a more flexible and efficient formulation. In addition, a procedure is presented which allows a stable analysis of trimmed geometries and a straightforward positioning of collocation points.Several numerical examples demonstrate the characteristics and benefits of the proposed approach. In particular, the independent field approximation improves the computational efficiency and reduces the storage requirements without any loss of accuracy. The proposed methodology permits a seamless integration of the most common design models into an analysis of linear elasticity problems. 6526Benjamin Marussig, Jürgen Zechner, Gernot Beer, and Thomas-Peter Fries INTRODUCTIONIsogeometric analysis aims to close the existing gap between the design process and analysis such that a simulation can be performed without generating a mesh. Consequently, the accuracy and efficiency of the overall simulation process is improved, since meshing is timeconsuming [1, 2] and introduces additional (geometrical) approximation errors. In addition, the basis functions used by design models, i.e. NURBS, provide further benefits such as high continuity [3,4].However, during the last years, it has become clear that a true integration of design and analysis is far from trivial due to several reasons: first of all, most engineering design models are based on a boundary representation (B-Rep) rather than a volume description. Secondly, three dimensional B-Rep models are usually defined by a non-conforming partition of NURBS surfaces, i.e. their mathematical parametrizations have no explicit relation to each other. Thirdly, each boundary surface is based on a tensor product structure which is a very efficient representation but has limitations due to its four sided nature. As a result, almost all NURBS based design models use trimming procedures to increase the flexibility of tensor product surfaces. This means that only a certain area of a surface is visualized while the underlying mathematical parametrization remains unchanged.In this work, a coherent framework is presented which allows a seamless integration of trimmed NURBS models into an analysis. In general, the governing equations of the problem are expressed by means of boundary integral equations which are discretized by a numerical approximation method. Here, the boundary element method (BEM) is used since it is the most versatile approach. However, it should be pointed out that other schemes like the Nyst...

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The Stable Evaluation of B-Splines and Splines

Cited by 162 publications

References 0 publications

Optofluidic membrane interferometer: An imaging method for measuring microfluidic pressure and flow rate simultaneously on a chip

Optofluidic membrane interferometer: An imaging method for measuring microfluidic pressure and flow rate simultaneously on a chip

Partially linear single index models for repeated measurements

Integration of Design and Analysis Through Boundary Integral Equations

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