ALcHyMiA

ALcHyMiA: Advanced Structure Preserving Lagrangian schemes for novel first order Hyperbolic Models: towards General Relativistic Astrophysics

ERC Starting Grant funded under the Horizon Europe programme, grant agreement No 101114995.
Period: 01/04/2024 -- 31/03/2029.

Budget: 1.500.000 euros.

Abstract & Objectives
ALcHyMiA will make substantial progress in applied mathematics, targeting long-time stable and self-consistent simulations in general relativity and high energy density problems, via the development of new and effective structure preserving numerical methods with provable mathematical properties. We will devise innovative schemes for hyperbolic partial differential equations (PDE) which at the discrete level exactly preserve all the invariants of the continuous problem, such as equilibria, involutions and asymptotic limits. Next to fluids and magnetohydrodynamics, key for benchmarks and valuable applications on Earth, we target a new class of first order hyperbolic systems that unifies fluid and solid mechanics and gravity theory. This allows to study gravitational waves, binary neutron stars and accretion disks around black holes that require the coupled evolution of matter and spacetime. Here, high resolution and minimal dissipation at shocks and moving interfaces are crucial and will be achieved by groundbreaking direct Arbitrary-Lagrangian-Eulerian (ALE) methods on moving Voronoi meshes with changing topology. These are necessary to maintain optimal grid quality even when following rotating compact objects, complex shear flows or metric torsion. They also ensure rotational invariance, entropy stability and Galilean invariance in the Newtonian limit. The breakthrough of our new Finite Volume and Discontinuous Galerkin ALE schemes lies in the geometrical understanding and high order PDE integration over 4D spacetime manifolds. The high-risk high-gain challenge is the design of smart DG schemes with bound-preserving function spaces, taking advantage of the Voronoi properties. Finally, it is an explicit mission of ALcHyMiA to grow a solid scientific community, sharing know-how by tailored dissemination activities from top-level schools to carefully organized international events revolving around personalized interactions.

Group members
✔ Elena Gaburro   (Principal Investigator)
✔ Elena Bernardelli   (PhD Student)
✔ Stefano Muzzolon   (PhD Student)
✔ Matej Klima   (Post doctoral researcher)
✔ Mauro Bonafini   (Tenure track RTT researcher, partially involved in the project)
✔ Maurizio Tavelli   (Tenure track RTT researcher, partially involved in the project)

Open call: expression of interest for a PhD position - University of Verona, Italy:

Deadline: interested candidates are kindly invited to contact elena.gaburro@univr.it as soon as possible. The PhD call opens at the beginning of May 2025.

Topic: Development of novel Advanced Structure Preserving Lagrangian methods for the solution of hyperbolic equations on unstructured meshes

Salary: 1350 EUR net per month.

The work modality can be agreed with the selected candidate:
- The exact research topic can be decided together;
- Smart working and output-oriented approach are possible;
- Participation to international conferences will be funded and encouraged;
- Research periods abroad in patner institutions can also be funded.

Starting date: November 2025.

If you would like to apply, or if you need any further information, please contact me by email (elena.gaburro@univr.it).

Available soon: call for a Postdoctoral position - University of Verona, Italy:

Starting date: from October 2025 to March 2026.
(Consider that up to 4 months may be necessary from the first contact to the complete set up of the contract.)

Title: Development of novel numerical methods for the solution of hyperbolic equations on unstructured meshes

Salary and duration:
- Groos annual salary: from 43.000 to 50.000 euros, depending on the expected experience;
- Duration: 2 years with the possibility of being renewed.

The work modality can be agreed with the selected candidate:
- The exact research topic can be decided together;
- Smart working and output-oriented approach are welcomed;
- Participation to international conferences will be funded and encouraged;
- Research periods abroad in patner institutions can also be funded.

If you would like to apply, or if you need any further information, please contact me by email (elena.gaburro@univr.it).

--> Available on demand: 3 to 6 months internships and 2 years Post Doctoral positions

People interested in not yet open positions should send an email to elena.gaburro@univr.it, including a detailed CV.

Possible research topics include: lagrangian schemes on moving meshes with topology changes (for example: parallelization, moving boundaries, adaptive mesh refinement, new applications, 3D extension ...) and well balancing for general relativity (using simplified or complete models, in 1D, 2D or 3D, with a theoretical and/or a numerical approach).

Publications:

[4] E. Gaburro.
High order Well-Balanced Arbitrary-Lagrangian-Eulerian ADER discontinuous Galerkin schemes on general polygonal moving meshes.
Submitted, 2025. Preprint: ArXiv link.

[3] E. Gaburro, W. Boscheri, S. Chiocchetti and M. Ricchiuto.
Discontinuous Galerkin schemes for hyperbolic systems in non-conservative variables: Quasi-conservative formulation with subcell finite volume corrections.

Computer Methods in Applied Mechanics and Engineering, 2025. DOI: 10.1016/j.cma.2024.117311.
Preprint: ArXiv link.

[2] M. Ciallella, S. Clain, E. Gaburro and M. Ricchiuto.
Very high order treatment of embedded curved boundaries in compressible flows: ADER discontinuous Galerkin with a space-time Reconstruction for Off-site data.
Computers and Mathematics with Applications, 2024. DOI: 10.1016/j.camwa.2024.08.02.
Preprint: ArXiv link.

[1] M. Dumbser, O. Zanotti, E. Gaburro and I. Peshkov.
A well-balanced discontinuous Galerkin method for the first–order Z4 formulation of the Einstein–Euler system.
Journal of Computational Physics, 2024.
DOI: 10.1016/j.jcp.2024.112875. Preprint: ArXiv link.

Figures:

Coming soon ...