An IGA Framework for PDE-Based Planar Parameterization on Convex Multipatch Domains

The first step towards applying isogeometric analysis techniques to solve PDE problems on a given domain consists in generating an analysis-suitable mapping operator between parametric and physical domains with one or several patches from no more than a description of the boundary contours of the physical domain. A subclass of the multitude of...

Preconditioning for Linear Systems Arising from IgA Discretized Incompressible Navier-Stokes Equations

We deal with efficient techniques for numerical simulation of the incompressible fluid flow based on the Navier–Stokes equations discretized using the isogeometric analysis approach. Typically, the most time-consuming part of the simulation is solving the large saddle-point type linear systems arising from the discretization. These systems can...

Efficient p-Multigrid Based Solvers for Isogeometric Analysis on Multipatch Geometries

Isogeometric Analysis can be considered as the natural extension of the Finite Element Method (FEM) to higher-order spline based discretizations simplifying the treatment of complex geometries with curved boundaries. Finding a solution of the resulting linear systems of equations efficiently remains, however, a challenging task. Recently, p...