PetIGA-MF: a multi-field high-performance toolbox for structure-preserving B-splines spaces

Sarmiento, A. F.; Côrtes, A.M.A.; García, Daniel; Dalcín, Lisandro; Collier, Nathaniel O.; Calo, Victor M.

doi:10.48550/arxiv.1602.08727

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2017

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“…Isogeometric analysis based on NURBS (Non-Uniform Rational B-Splines) has been described in a number of papers (e.g. [12,24,25,41]) and the efficient implementation of the method in open source software has been discussed in [26,29,54,57]. Isogeometric analysis employs piecewise polynomial curves composed of linear combinations of Bspline basis functions.…”

Section: Problem Statementmentioning

confidence: 99%

Dispersion-optimized quadrature rules for isogeometric analysis: Modified inner products, their dispersion properties, and optimally blended schemes

Puzyrev

Deng

Calo

2017

Computer Methods in Applied Mechanics and Engineering

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This paper introduces optimally-blended quadrature rules for isogeometric analysis and analyzes the numerical dispersion of the resulting discretizations. To quantify the approximation errors when we modify the inner products, we generalize the Pythagorean eigenvalue theorem of Strang and Fix. The proposed blended quadrature rules have advantages over alternative integration rules for isogeometric analysis on uniform and nonuniform meshes as well as for different polynomial orders and continuity of the basis. The optimally-blended schemes improve the convergence rate of the method by two orders with respect to the fully-integrated Galerkin method. The proposed technique increases the accuracy and robustness of isogeometric analysis for wave propagation problems.

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