[Dottorcomp] Seminari di Matematica Applicata, 20/05/2025, Muhammad Hassan, Paola Goatin

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

Martedì 20 Maggio 2025, alle *ore 15 precise*, presso la sala conferenze
dell'IMATI di Pavia,

Muhammad Hassan (Paul Scherrer Institute, Svizzera)
terrà un seminario dal titolo:

The Numerical Analysis of the Coupled Cluster Method in Quantum Chemistry,
e alle *ore 16 precise*,

Paola Goatin (Université Côte d’Azur, Inria)

terrà un seminario dal titolo:

Non-local flow models with time delay: analysis and numerical experiments.

Abstract (Hassan): A central problem in quantum chemistry is the
computation of the lowest eigenvalue of the electronic Hamiltonian, an
unbounded, self-adjoint operator acting on a Hilbert space of antisymmetric
functions. The main difficulty in the resolution of this problem is the
very high dimensionality of the eigenfunctions, being functions of 3N
variables where N denotes the number of electrons in the system. A popular
strategy to deal with this complexity is to use a low-rank, non-linear
representation of the sought-after eigenfunction. Examples include the
tensor-train-based DMRG algorithm and the coupled cluster method in which
the ansatz is an exponential cluster operator acting on a
judiciously-chosen reference state.

The goal of this talk is to present a recently-developed well-posedness and
error analysis for the single-reference coupled cluster method. Under the
minimal assumption that the sought-after eigenvalue is non-degenerate and
the associated eigenfunction is not orthogonal to a chosen reference, we
prove that the continuous coupled cluster equations are locally well-posed.
Under some additional structural assumptions on the associated
discretisation spaces, we prove that several classes of discrete coupled
cluster equations are also locally well-posed, and we derive a priori and
residual-based a posteriori error estimates.

This is joint-work with Yvon Maday and Yipeng Wang (LJLL, Sorbonne
Université).

Abstract (Goatin): We prove the well-posedness of entropy weak solutions of
a (multi-class) non-local traffic flow model with time delay. Existence is
obtained by convergence of finite volume approximate solutions constructed
by Hilliges-Weidlich scheme, while the L^1 stability with respect to the
initial data and the delay parameter relies on a Kruzkov-type doubling of
variable technique. Numerical tests are provided to illustrate the model
characteristics, as well as the solution dependence on the delay and
look-ahead parameters. Also, applications to the modeling of mixed
autonomous / human driven traffic are presented.

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https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/