arXiv subjects

Rabia Djellouli

Publications and source records attributed to Rabia Djellouli.

3 recordsLinked to original sources

arXiv2025

MOR-T L : A Novel Model Order Reduction Method for Parametrized Problems with Application to Seismic Wave Propagation

This paper presents an efficient strategy for constructing Reduced-Order Model (ROM) bases using Taylor polynomial expansions and Fr{é}chet derivatives with respect to model parameters. The proposed approach enables the construction of ROM bases with minimal additional computational cost. By exploiting Fr{é}chet derivatives -solution to the same problem with distinct right-hand sides -the method introduces a streamlined multiple-right-hand-side (RHS) strategy for ROM bases construction. This approach not only reduces overall computational expenses but also improves accuracy during model parameter updates. Numerical experiments on a two-dimensional wave problem demonstrate significant efficiency gains and enhanced performance, highlighting the potential of the proposed method to advance computational cost-effectiveness, particularly in seismic inversion applications.

math.NA↗

arXiv2024

Polar Jet Stream Fluctuations in an Energy Balance Model

We investigate the effect of increased longwave radiative forcing (a proxy for increased greenhouse gas concentration) on the zonally averaged location of the eddy-driven jet stream in a latitude dependent, two-layer Energy Balance Model. The model includes separate terms for atmospheric and surface albedos, and takes into account reflections of shortwave radiation between the surface and atmospheric layers. We introduce the notion of a cloud factor function, which depends on temperature gradients, to simulate the eddy-driven jet. An increase in longwave radiative forcing initially results in a poleward movement of the jet stream's mean latitude, but as the forcing increases, the location of the jet stream becomes quasi-periodic and its mean location moves equatorward.

physics.ao-ph↗

arXiv2024

Legendre Expansions of Products of Functions with Applications to Nonlinear Partial Differential Equations

Given the Fourier-Legendre expansions of $f$ and $g$, and mild conditions on $f$ and $g$, we derive the Fourier-Legendre expansion of their product in terms of their corresponding Fourier-Legendre coefficients. In this way, expansions of whole number powers of $f$ may be obtained. We establish upper bounds on rates of convergence. We then employ these expansions to solve semi-analytically a class of nonlinear PDEs with a polynomial nonlinearity of degree 2. The obtained numerical results illustrate the efficiency and performance accuracy of this Fourier-Legendre based solution methodology for solving an important class of nonlinear PDEs.

math.NA↗