Robust multigrid methods for biharmonic problem problems with application to PDE-constrained optimization using IGA

MSc Jarle Sogn

Nov. 9, 2021, 3:30 p.m. S3 048

In this talk we present multigrid methods for the second biharmonic pro-
blem with a scalable lower-order term in the context of isogeometric analysis
(IgA). We prove a multigrid convergence estimate using the Bramble frame-
work. This estimate is independent of the scale of the lower-order term, the
spline degree and with only a logarithmic dependence on the grid-size. In con-
trast to other works, these estimates does not require that the underlying
grids are equidistant. Numerical experiments are provided which illustrate the
convergence theory and the efficiency of the proposed multigrid approaches.