Isogeometric analysis on implicit domains using weighted extended PHT-splines

Abstract The urging quest for diminishing the gap between finite element methods and computer-aided design is growing every day. Isogeometric analysis is driving that search a step forward in contrast with traditional finite element methods. One of the areas that need more investigation is using isogeometric analysis on domains that contain singularities. In this case, the parameterization process is occasionally non-trivial, and some of the inherited basis functions are not well defined producing rough solutions. Moreover, NURBS basis functions are not the best choice to perform local refinement since adaptivity is indispensable. In this study, a new approach that serves as a generalization for some of the ideas in both the isogeometric analysis and the WEB method is introduced. Isogeometric analysis on implicit domains replaces mesh generation with implicit spline weight function generation and construct weighted extended PHT-splines for analysis. The geometry and the analysis both are built starting from the same function space avoiding parameterization. The PHT-splines are adaptive and allow local refinement naturally leading to a higher accuracy while dealing with singularities. An illustration with numerical examples demonstrates the efficiency and performance of the proposed method.

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