Space-time Galerkin isogeometric method and efficient solver for parabolic problem

In this work we focus on the preconditioning of a Galerkin space-time isogeometric discretization of the heat equation. Exploiting the tensor product structure of the basis functions, we propose a preconditioner that is the sum of Kronecker products of matrices and that can be efficiently applied thanks to an extension of the classical fast diagonalization method. The preconditioner is robust w.r.t. polynomial degree and the time required for the application is almost proportional to the number of degrees-of-freedom, for a serial execution. By incorporating some information on the geometry parametrization and on the coefficients, we keep high efficiency with non-trivial geometry parametrization of the domain.