Efficient preconditioning strategies in Isogeometric analysis

Monica Montardini

Oct. 9, 2018, 3:30 p.m. S2 054

Isogeometric analysis is a high-order numerical method used to solve Partial Differential
Equations (PDEs). In this talk I will focus on the k-method, that consists of using splines of
degree p and regularity p-1, i.e. the maximal regularity allowed. The cost of the k-method
is essentially concentrated into two processes: the formation of the linear system and its
numerical solution. I will focus on the second computational challenge, i.e. the solution of
the system, and I will present some efficient and robust preconditioning methods suited to
solve different kind of PDEs, also in the multipatch setting. The basis of all the strategies
is the Fast Diagonalization method, a fast solver for Sylvester-like equations. Starting from
the Poisson problem, I will then consider Stokes system and, finally, I will give a special
attention to space-time solving strategies for the heat equation.