4 citations · 4 across the 8 of their papers we have counts for
9 papers
A Two-Stage Learning PINN Approach for Solving the Inverse Problem of the 1D Porous Medium Equation
Noura Al Helwani, Sophie Moufawad, Nabil Nassif
The Porous Medium Equation (PME), given by for , is a degenerate nonlinear parabolic partial differential equation that arises in various physical application…
Direct Problem for Gas Diffusion in Polar Firn with Variable Coefficients
Sophie Moufawad, Nabil Nassif, Faouzi Triki
We consider the mathematical model of gas trapping in deep polar ice (firns), which consists of a parabolic partial differential equation, that can degenerate at one boundary extre…
Solving Inverse PDE Problems using Minimization Methods and AI
Noura Al Helwani, Sophie Moufawad, Georges Sakr
Many physical and engineering systems require solving direct problems to predict behavior and inverse problems to determine unknown parameters from measurement. In this work, we st…
Data-Driven Models for studying the Dynamics of the COVID-19 Pandemics
Rawan H. Madi, Sophie M. Moufawad, Nabil R. Nassif
This paper seeks to study the evolution of the COVID-19 pandemic based on daily published data from Worldometer website, using a time-dependent SIR model. Our findings indicate tha…
Flexibly Enlarged Conjugate Gradient Methods
Sophie M. Moufawad
Enlarged Krylov subspace methods and their s-step versions were introduced [7] in the aim of reducing communication when solving systems of linear equations Ax = b. These enlarged…
Direct and Inverse Problem for Gas Diffusion in Polar Firn
Sophie M. Moufawad, Nabil R. Nassif, Faouzi Triki
Simultaneous use of partial differential equations in conjunction with data analysis has proven to be an efficient way to obtain the main parameters of various phenomena in differe…
Newton Type Methods for solving a Hasegawa-Mima Plasma Model
Sophie M. Moufawad, Nabil R. Nassif
In [1], the non-linear space-time Hasegawa-Mima plasma equation is formulated as a coupled system of two linear PDE's, a solution of which is a pair (u, w). The first equation is o…
A Finite-Element Model for the Hasegawa-Mima Wave Equation
Hagop Karakazian, Sophie Moufawad, Nabil Nassif
In a recent work, two of the authors have formulated the non-linear space-time Hasegawa-Mima plasma equation as a coupled system of two linear PDEs, a solution of which is a pair $…
Numerical Stability of s-step Enlarged Krylov Subspace Conjugate Gradient Methods
Sophie Moufawad
Recently, enlarged Krylov subspace methods, that consists of enlarging the Krylov subspace by a maximum of t vectors per iteration based on the domain decomposition of the graph of…