Isogeometric Analysis Based Shape Optimization.
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We solve shape optimization problems involving partial differential equations. The latter are discretized and solved using isogeometric analysis. B-splines and non uniform rational B-splines are introduced, along with both theory and implementation aspects of the numerical method. We solve a chemical reaction problem that is governed by a system of non-linearly coupled Laplace equations, which is only one of numerous possible application areas of isogeometric analysis based shape optimization.