Local Refinement for Isogeometric Analysis
During the last chapter several aspects of isogeometric analysis were discussed. This chapter will focus on the main topic of this thesis: adaptivity. Adaptive simulation is essential for simulating complex problems and using the available resources where they are needed. The uniform refinement techniques presented in the previous chapter turns out not to be flexible enough. In this chapter we will strongly rely on the previous section about isogeometric analysis and expand the concepts introduced therein to introduce an effective method for local refinement. The approach we propose is based on function spaces from CAGD, which were not especially designed for this purpose. We transform this idea to isogeometric analysis by adjusting it to create a basis with desirable properties, but also add an element concept that is suitable for the simulation setting and extendable to more advanced techniques like error estimation. It is very crucial at this point that we have taken both aspects, applied geometry and numerical analysis, into account.
KeywordsBasis Function Active Element Reference Element Spline Space Isogeometric Analysis
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