I am a PhD student at Laboratoire Jacques-Louis Lions in Paris, under the supervision of prof. Yvon Maday.

More information about my research activity, the classes I teach and details about my education can be found in the dedicated pages. See also the pdf version of my CV and my contact page.

My main research theme is the development of an hP discontinuous Galerkin method to approximate the solution to problems arising in quantum chemistry. In particular, we consider all-electron potentials, which give rise to wavefunctions belonging to weighted Sobolev spaces.
In many real world problems in quantum chemistry, we are mainly concerned with the computation of the *ground state energy* of a system. We consider non linear eigenvalue problems of the form
\begin{equation}
\label{eq:hartree-fock}
\mathcal{F}u = \lambda u
\end{equation}
where \(\mathcal{F}\) is a self adjoint elliptic operator (depending on \(u\)) containing a potential \(V\) with singularities in a set of isolated points \(\mathcal{C}\).
The solutions to this problem belong to the *countably normed Sobolev space*
\begin{equation}
\mathcal{K}^{\infty,\gamma} = \left\{ u \in \mathcal{D}':\; d(x, \mathcal{C})^{|\alpha|-\gamma}\partial^\alpha u\in L^2,\, |\alpha|=s,\, \forall s\in \mathbb{N}\right\} .
\end{equation}
The interest of hP methods is that the numerical solution \(u_\delta\) *converges exponentially* to the exact solution
\begin{equation}
\lVert u- u_\delta \rVert_\mathrm{DG} \leq C \inf_{v_\delta\in X_\delta}\lVert u -v_\delta \rVert_\mathrm{DG}\leq C \exp\left(-bN^{1/(d+1)}\right).
\end{equation}

Office 326, corridor 15-25

4 place Jussieu

75005 Paris, France

marcati (at) ljll.math.upmc.fr