Due Giorni di Algebra Lineare Numerica e Applicazioni

Session

Morning Session II

20 Jan 2025, 11:10

Building E (Aula Magna "Fratelli Pontecorvo", Building E, Polo Fibonacci. Pisa)

Description

Chair: Michele Benzi

49. Cross-eyed preconditioning for normal equations arising from PDEs

Umberto Zerbinati (University of Oxford)

20/01/2025, 11:10

Talk

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...

41. Matrix-oriented discretisations of phase-field and high-order diffusion problems

Massimo Frittelli (University of Salento, Department of Mathematics and Physics "E. De Giorgi")

20/01/2025, 11:30

Talk

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...

9. Scalable approximation and solvers for ionic electrodiffusion in cellular geometries

Pietro Benedusi

20/01/2025, 11:50

Talk

The activity and dynamics of excitable cells are fundamentally regulated and moderated by extracellular and intracellular ion concentrations and their electric potentials. The increasing availability of dense reconstructions of excitable tissue at extreme geometric detail pose a new and clear scientific computing challenge for computational modelling of ion dynamics and transport. We present a...

10. Blocking structures, approximation, and preconditioning

Valerio Loi (Università degli studi dell'Insubria)

20/01/2025, 12:10

Talk

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...