@InCollection{    Gravesen_2014aa,
  abstract      = {Before isogeometric analysis can be applied to solving a partial differential equation posed over some physical domain, one needs to construct a valid parametrization of the geometry. The accuracy of the analysis is affected by the quality of the parametrization. The challenge of computing and maintaining a valid geometry parametrization is particularly relevant in applications of isogemetric analysis to shape optimization, where the geometry varies from one optimization iteration to another. We propose a general framework for handling the geometry parametrization in isogeometric analysis and shape optimization. It utilizes an expensive non-linear method for constructing/updating a high quality reference parametrization, and an inexpensive linear method for maintaining the parametrization in the vicinity of the reference one. We describe several linear and non-linear parametrization methods, which are suitable for our framework. The non-linear methods we consider are based on solving a constrained optimization problem numerically, and are divided into two classes, geometry-oriented methods and analysis-oriented methods. Their performance is illustrated through a few numerical examples.},
  author        = {Gravesen, Jens and Evgrafov, Anton and Nguyen, Dang-Manh and Nørtoft, Peter},
  booktitle     = {Mathematical Methods for Curves and Surfaces},
  doi           = {10.1007/978-3-642-54382-1_11},
  editor        = {Floater, Michael and Lyche, Tom and Mazure, Marie-Laurence and Mørken, Knut and Schumaker, LarryL.},
  file          = {Gravesen_2014aa.pdf},
  isbn          = {978-3642543814},
  keywords      = {isogeometric,optimization,parametrization},
  langid        = {english},
  pages         = {189--212},
  publisher     = {Springer Berlin Heidelberg},
  series        = {Lecture Notes in Computer Science},
  title         = {Planar Parametrization in Isogeometric Analysis},
  volume        = {8177},
  year          = {2014}
}

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It utilizes an expensive non-linear method for constructing/updating a high quality reference parametrization, and an inexpensive linear method for maintaining the parametrization in the vicinity of the reference one. We describe several linear and non-linear parametrization methods, which are suitable for our framework. The non-linear methods we consider are based on solving a constrained optimization problem numerically, and are divided into two classes, geometry-oriented methods and analysis-oriented methods. 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The accuracy of the analysis is affected by the quality of the parametrization. The challenge of computing and maintaining a valid geometry parametrization is particularly relevant in applications of isogemetric analysis to shape optimization, where the geometry varies from one optimization iteration to another. We propose a general framework for handling the geometry parametrization in isogeometric analysis and shape optimization. It utilizes an expensive non-linear method for constructing/updating a high quality reference parametrization, and an inexpensive linear method for maintaining the parametrization in the vicinity of the reference one. We describe several linear and non-linear parametrization methods, which are suitable for our framework. The non-linear methods we consider are based on solving a constrained optimization problem numerically, and are divided into two classes, geometry-oriented methods and analysis-oriented methods. 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