Picture of blood cells

Open Access research which pushes advances in bionanotechnology

Strathprints makes available scholarly Open Access content by researchers in the Strathclyde Institute of Pharmacy & Biomedical Sciences (SIPBS) , based within the Faculty of Science.

SIPBS is a major research centre in Scotland focusing on 'new medicines', 'better medicines' and 'better use of medicines'. This includes the exploration of nanoparticles and nanomedicines within the wider research agenda of bionanotechnology, in which the tools of nanotechnology are applied to solve biological problems. At SIPBS multidisciplinary approaches are also pursued to improve bioscience understanding of novel therapeutic targets with the aim of developing therapeutic interventions and the investigation, development and manufacture of drug substances and products.

Explore the Open Access research of SIPBS. Or explore all of Strathclyde's Open Access research...

Effective transmission conditions for domain decomposition methods applied to the time-harmonic curl-curl Maxwell's equations

Dolean, Victorita and Gander, Martin J. and Lanteri, Stephane and Lee, Jin-Fa and Peng, Zhen (2015) Effective transmission conditions for domain decomposition methods applied to the time-harmonic curl-curl Maxwell's equations. Journal of Computational Physics, 280. pp. 232-247. ISSN 0021-9991

[img]
Preview
Text (Dolean-etal-JCP-20158-Effective-transmission-conditions-for-domain-decomposition-methods)
Dolean_etal_JCP_20158_Effective_transmission_conditions_for_domain_decomposition_methods.pdf
Accepted Author Manuscript
License: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 logo

Download (2MB)| Preview

    Abstract

    The time-harmonic Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental for the simulation of many modern devices we have become used to in everyday life. The numerical solution of these equations is hampered by two fundamental problems: first, in the high frequency regime, very fine meshes need to be used in order to avoid the pollution effect well known for the Helmholtz equation, and second the large scale systems obtained from the vector valued equations in three spatial dimensions need to be solved by iterative methods, since direct factorizations are not feasible any more at that scale. As for the Helmholtz equation, classical iterative methods applied to discretized Maxwell equations have severe convergence problems.We explain in this paper a family of domain decomposition methods based on well chosen transmission conditions. We show that all transmission conditions proposed so far in the literature, both for the first and second order formulation of Maxwell's equations, can be written and optimized in the common framework of optimized Schwarz methods, independently of the first or second order formulation one uses, and the performance of the corresponding algorithms is identical. We use a decomposition into transverse electric and transverse magnetic fields to describe these algorithms, which greatly simplifies the convergence analysis of the methods. We illustrate the performance of our algorithms with large scale numerical simulations.