Publications by Doghonay Arjmand

An Elliptic Local Problem With Exponential Decay Of The Resonance Error For Numerical Homogenization

Assyr Abdulle, Edoardo Paganoni, Doghonay Arjmand

Numerical multiscale methods usually rely on some coupling between a macroscopic and a microscopic model. The macroscopic model is incomplete as effective quantities, such as the homogenized material coefficients or fluxes, are missing in the model. These ...

SIAM PUBLICATIONS2023

A parabolic local problem with exponential decay of the resonance error for numerical homogenization

Assyr Abdulle, Edoardo Paganoni, Doghonay Arjmand

This paper aims at an accurate and efficient computation of effective quantities, e.g. the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods are based on a m ...

WORLD SCIENTIFIC PUBL CO PTE LTD2021

Modelling long-range interactions in multiscale simulations of ferromagnetic materials

Doghonay Arjmand

Atomistic-continuum multiscale modelling is becoming an increasingly popular tool for simulating the behaviour of materials due to its computational efficiency and reliable accuracy. In the case of ferromagnetic materials, the atomistic approach handles th ...

SPRINGER2020

Temporal upscaling in micromagnetism via heterogeneous multiscale methods

Doghonay Arjmand

We consider a multiscale strategy addressing the disparate scales in the Landau-Lifschitz equations in micromagnetism. At the microscopic scale, the dynamics of magnetic moments are driven by a high frequency field. On the macroscopic scale we are interest ...

ELSEVIER SCIENCE BV2019

Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems

Assyr Abdulle, Edoardo Paganoni, Doghonay Arjmand

EMS publishing house2019

Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems

Assyr Abdulle, Edoardo Paganoni, Doghonay Arjmand

This paper presents two new approaches for finding the homogenized coefficients of multiscale elliptic PDEs. Standard approaches for computing the homogenized coefficients sufer from the so-called resonance error, originating from a mismatch between the tr ...

ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER2019

Atomistic-continuum multiscale modelling of magnetisation dynamics at non-zero temperature

Doghonay Arjmand

2018

An Equation-Free Approach For Second Order Multiscale Hyperbolic Problems In Non-Divergence Form

Doghonay Arjmand

The present study concerns the numerical homogenization of second order hyperbolic equations in non-divergence form, where the model problem includes a rapidly oscillating coefficient function. These small scales influence the large scale behavior, hence t ...

INT PRESS BOSTON, INC2018