Description
Chair: Michele Benzi
We explore preconditioning strategies for solving non-symmetric linear systems arising from PDE discretizations. In particular, we analyze the performance of Krylov subspace methods when applied to normal equations. We introduce the idea of cross-eyed preconditioning and discuss its advantages in cases involving convection-diffusion equations. By leveraging physical insights from PDEs, we...
We consider a large class of arbitrarily high-order evolutionary PDEs, including phase-field models and polyharmonic reaction-diffusion problems on rectangular domains with Neumann boundary conditions. We propose a matrix-oriented approach that, after full discretisation, requires the solution of a sequence of algebraic matrix equations of Lancaster type. To this end, we apply lumped finite...
Large block-structured matrices with Toeplitz-type blocks of different sizes frequently arise in various applications, but pose computational issues when solving the associated linear systems. In our setting, the matrices $A_n$ are composed of (block rectangular) unilevel Toeplitz blocks defined by rectangular $s \times t$ matrix-valued generating functions. Under mild assumptions on the block...
