Our colleagues at the University of Pisa have released a new preprint advancing work on augmented Lagrangian (AL) preconditioners for fictitious domain methods, building on their previous publication in CMAME.
This follow-up focuses on elliptic interface problems with jump coefficients, a common challenge in multiphysics simulations with heterogeneous materials or domains. Using the Fictitious Domain with Distributed Lagrange Multipliers formulation, the proposed preconditioners improve convergence of the Flexible GMRES (FGMRES) method even in the presence of large coefficient jumps.
To enhance efficiency, the team also introduces a block-triangular variant that significantly reduces computational cost while maintaining robustness. Theoretical analysis demonstrates eigenvalue clustering for the ideal preconditioner and characterises the spectrum behaviour for the modified version.
Extensive numerical tests on various immersed geometries confirm mesh-independent iteration counts, robustness across large coefficient jumps, and substantial reductions in wall-clock time.
This preprint highlights dealiiX’s ongoing efforts to provide high-performance, scalable numerical solvers for complex multiphysics and biomedical simulations.
Read the full preprint here: https://arxiv.org/pdf/2603.12993
Congratulations to Michele Benzi, Marco Feder, Luca Heltai, and Federica Mugnaioni for this outstanding advancement!