100 citations · 495 across the 18 of their papers we have counts for
4 papers · 1 filter
Schwarz Waveform Relaxation Physics-Informed Neural Networks for Solving Advection-Diffusion-Reaction Equations
Emmanuel Lorin, Xu Yang
This paper develops a physics-informed neural network (PINN) based on the Schwarz waveform relaxation (SWR) method for solving local and nonlocal advection-diffusion-reaction equat…
Pseudospectral computational methods for the time-dependent Dirac equation in static curved spaces
Xavier Antoine, François Fillion-Gourdeau, Emmanuel Lorin +1
Pseudospectral numerical schemes for solving the Dirac equation in general static curved space are derived using a pseudodifferential representation of the Dirac equation along wit…
Domain Decomposition Method for the -body Time-Independent and Time-Dependent Schrödinger Equation
E. Lorin
This paper is devoted to the derivation of a pleasingly parallel Galerkin method for the time-independent -body Schrödinger equation, and its time-dependent version modeling mol…
Efficient determination of critical parameters of nonlinear Schrödinger equation with point-like potential using generalized polynomial chaos methods
Debananda Chakraborty, Jae-Hun Jung, Emmanuel Lorin
We consider the nonlinear Schrödinger equation with a point-like source term. The soliton interaction with such a singular potential yields a critical solution behavior. That is, f…