25 citations · 26 across the 8 of their papers we have counts for
9 papers
A diffusion-free multi-layer neural-network method for multidimensional nonlinear hyperbolic equations
Emmanuel Lorin, Arian Novruzi
This paper is devoted to the non-diffusive computation of solutions to -dimensional hyperbolic systems of conservation laws (HCL) and more specifically the accurate approximatio…
The structure of the solution to the generalized Stokes equations and a new method for solving them
Arian Novruzi
We show that the velocity solution to the generalized Stokes equations with Dirichlet boundary conditions in dimension two and three is the superposition of two divergence-free…
Non-diffusive neural network method for hyperbolic conservation laws
Emmanuel Lorin, Arian Novruzi
In this paper we develop a non-diffusive neural network (NDNN) algorithm for accurately solving weak solutions to hyperbolic conservation laws. The principle is to construct these…
Polygons as maximizers of Dirichlet energy or first eigenvalue of Dirichlet-Laplacian among convex planar domains
Jimmy Lamboley, Arian Novruzi, Michel Pierre
In this paper we prove that solutions to several shape optimization problems in the plane, with a convexity constraint on the admissible domains, are polygons. The main terms of th…
A gradient method in a Hilbert space with an optimized inner product: achieving a Newton-like convergence
Arian Novruzi, Bartosz Protas
In this paper we introduce a new gradient method which attains quadratic convergence in a certain sense. Applicable to infinite-dimensional unconstrained minimization problems pose…
Estimates of First and Second Order Shape Derivatives in Nonsmooth Multidimensional Domains and Applications
Jimmy Lamboley, Arian Novruzi, Michel Pierre
In this paper we investigate continuity properties of first and second order shape derivatives of functionals depending on second order elliptic PDE's around nonsmooth domains, ess…