1 citations · 1 across the 8 of their papers we have counts for
12 papers
Solving elliptic PDEs in unbounded domains
Doghonay Arjmand, Filip Marttala
An accurate approximation of solutions to elliptic problems in infinite domains is challenging from a computational point of view. This is due to the need to replace the infinite d…
A hybrid boundary integral-PDE approach for the approximation of the demagnetization potential in micromagnetics
Doghonay Arjmand, Victor Martinez Calzada
The demagnetization field in micromagnetism is given as the gradient of a potential which solves a partial differential equation (PDE) posed in R^d. In its most general form, this…
Efficient low rank approximations for parabolic control problems with unknown heat source
Doghonay Arjmand, Maksat Ashyraliyev
An inverse problem of finding an unknown heat source for a class of linear parabolic equations is considered. Such problems can typically be converted to a direct problem with non-…
Analytical and numerical study of a modified cell problem for the numerical homogenization of multiscale random fields
Assyr Abdulle, Doghonay Arjmand, Edoardo Paganoni
A central question in numerical homogenization of partial differential equations with multiscale coefficients is the accurate computation of effective quantities, such as the homog…
An elliptic local problem with exponential decay of the resonance error for numerical homogenization
Assyr Abdulle, Doghonay Arjmand, Edoardo Paganoni
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 h…
A parabolic local problem with exponential decay of the resonance error for numerical homogenization
Assyr Abdulle, Doghonay Arjmand, Edoardo Paganoni
This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equatio…
Modelling long-range interactions in multiscale simulations of ferromagnetic materials
Doghonay Arjmand, Mikhail Poluektov, Gunilla Kreiss
Atomistic-continuum multiscale modelling is becoming an increasingly popular tool for simulating the behaviour of materials due to its computational efficiency and reliable accurac…
Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems
Assyr Abdulle, Doghonay Arjmand, Edoardo Paganoni
This paper presents two new approaches for finding the homogenized coefficients of multiscale elliptic PDEs. Standard approaches for computing the homogenized coefficients suffer f…
An Equation-Free Approach for Second Order Multiscale Hyperbolic Problems in Non-Divergence Form
Doghonay Arjmand, Gunilla Kreiss
The present study concerns the numerical homogenization of second order hyperbolic equations in non-divergence form, where the model problem includes a rapidly oscillating coeffici…
Atomistic-continuum multiscale modelling of magnetisation dynamics at non-zero temperature
Doghonay Arjmand, Mikhail Poluektov, Gunilla Kreiss
In this article, a few problems related to multiscale modelling of magnetic materials at finite temperatures and possible ways of solving these problems are discussed. The discussi…
Estimates for the upscaling error in heterogeneous multiscale methods for wave propagation problems in locally periodic media
Doghonay Arjmand, Olof Runborg
This paper concerns the analysis of a multiscale method for wave propagation problems in microscopically nonhomogeneous media. A direct numerical approximation of such problems is…
Temporal upscaling in micro magnetism via heterogeneous multiscale methods
Doghonay Arjmand, Stefan Engblom, Gunilla Kreiss
We consider a multiscale strategy addressing the disparate scales in the Landau-Lifschitz equations in micro-magnetism. At the microscopic scale, the dynamics of magnetic moments a…