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Pooya Zakian

Pooya Zakian

Academic rank: Associate Professor
ORCID: https://orcid.org/0000-0002-7252-9531
Education: PhD.
ScopusId: 55570851100
Faculty: Engineering
Address: Arak University
Phone: 086-32265320

Research

Title
A stochastic spectral finite element method for wave propagation analyses with medium uncertainties
Type
JournalPaper
Keywords
Stochastic Spectral Finite element method; Karhunen–Loève Expansion; Polynomial Chaos Expansion; Random media; Uncertainty quantification; Wave propagation.
Year
2018
Journal Applied Mathematical Modelling
DOI
Researchers Pooya Zakian

Abstract

A stochastically enriched spectral finite element method (StSFEM) is developed to solve wave propagation problems in random media. This method simultaneously includes all features of spectral finite element and stochastic finite element methods, which leads to excellent accuracy and convergence by implementing Gauss–Lobatto–Legendre collocation points permitting to generate coarser meshes. In addition, the proposed StSFEM leads to diagonal mass matrices, which accelerates temporal integration schemes and provides de- sirable accuracy. Furthermore, it numerically solves the Fredholm integral equation arising from Karhunen–Loève Expansion with favorable accuracy and computing time. Here, the StSFEM is examined and developed to stochastic wave propagation phenomena through several numerical simulations. Results demonstrate successful performance of the StSFEM in the solved problems so that one can accomplish uncertainty quantification of time do- main wave propagation within random continua by incorporating the StSFEM.