Isogeometric Analysis: Higher-Order Differential Equations

Abstract

This thesis introduces Isogeometric Analysis as a potentional bridge between the Finite Element Analysis (FEA) and Computer Aided Design (CAD) communities. An introduction to B-splines and B-spline-based Isogeometric Analysis is given. Then an implemented Isogeometric Analysis solver is used to solve both the Poisson problem and the higher order Biharmonic equation on the unit square. The significant convergence results for Isogeometric Analysis is verified in both cases. Lastly, the highly non-linear, and stiff, Cahn-Hilliard equation is studied. The implemented solver is used to show good results, particularily in the Dirichlet boundary condition case. This demonstrates a major advantage of Isogeometric Analysis over traditional Finite Element Method, in that higher order partial differential equations can be solved without any major workarounds or adjustments to the solver by increasing the continuity of the basis.