Research School: Digital Twins of the Human Body

Session

IN-DEPTH ALGORITHMIC SESSION

Dec 10, 2025, 2:00 PM

Room 128-129 (SISSA Main Building)

Conveners

IN-DEPTH ALGORITHMIC SESSION: Accelerating Numerical Simulations in CFD by Model Reduction with Scientific and Physics-Informed Machine Learning for Digital Twin(s)

• Gianluigi Rozza (SISSA, International School for Advanced Studies)

IN-DEPTH ALGORITHMIC SESSION: Polytopic mesh methods: recent developments and deal.II-based implementation

• Andrea Cangiani (SISSA)
• Pasquale Claudio Africa

IN-DEPTH ALGORITHMIC SESSION: High-performance finite element algorithms with matrix-free implementations

• Martin Kronbichler (Ruhr University Bochum)

IN-DEPTH ALGORITHMIC SESSION: Scalable and optimal preconditioners for coupled multiphysics problems

• Luca Heltai (University of Pisa)

IN-DEPTH ALGORITHMIC SESSION: Recent advances on MUMPS: MUltifrontal Massively Parallel Solver for the direct solution of sparse linear equations

• Patrick Amestoy (MUMPS Technologies)

16. Accelerating Numerical Simulations in CFD by Model Reduction with Scientific and Physics-Informed Machine Learning for Digital Twin(s)

Prof. Rozza, Gianluigi (SISSA, International School for Advanced Studies)

12/10/25, 2:00 PM

Partial differential equations (PDEs) are invaluable tools for modeling complex physical phenomena. However, only a limited number of PDEs can be solved analytically, leaving the majority of them requiring computationally expensive numerical approximations. To address this challenge, reduced order models (ROMs) have emerged as a promising field in computational sciences, offering efficient...

27. Polytopic mesh methods: recent developments and deal.II-based implementation

Cangiani, Andrea (SISSA), Africa, Pasquale Claudio

12/10/25, 2:45 PM

The efficient and accurate resolution of multiphysics problems posed on intricate geometries typically requires time-consuming meshing, and the accurate representation of the geometry and solutions features with standard meshes may require excessive computational power.
Polytopic meshes can be used for complexity reduction for multi-physics problems posed on intricate geometries. For...

21. High-performance finite element algorithms with matrix-free implementations

Kronbichler, Martin (Ruhr University Bochum)

12/11/25, 9:00 AM

The objective of my talk is the efficient implementation of solvers for linear systems arising from the discretization of partial differential equations (PDEs) with higher-order finite element methods. The classical workflow is to first construct a sparse matrix and a right-hand side through the evaluation of element integrals in one part of the code. The matrix and vector are then passed to a...

24. Scalable and optimal preconditioners for coupled multiphysics problems

Heltai, Luca (University of Pisa)

12/11/25, 9:45 AM

We introduce augmented Lagrangian preconditioning strategies for solving linear systems arising from coupled problems. In particular we explore in details finite element discretizations of fictitious domain formulations with Lagrange and distributed Lagrange multipliers. The presentation focuses on two- and three-block structures appearing in Poisson, Stokes, and elliptic interface problems,...

22. Recent advances on MUMPS: MUltifrontal Massively Parallel Solver for the direct solution of sparse linear equations

Amestoy, Patrick (MUMPS Technologies)

12/11/25, 11:00 AM

The scientific library MUMPS (for MUltifrontal Massively Parallel Solver) solves large systems of sparse linear equations, AX=B, in a robust and efficient way on high performance computers. The matrix A is a large square matrix and X and B are vectors or matrices whose sparsity can also be exploited. MUMPS is an open source software, distributed under the CeCILL C licence which can be...