Picture of athlete cycling

Open Access research with a real impact on health...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by Strathclyde researchers, including by researchers from the Physical Activity for Health Group based within the School of Psychological Sciences & Health. Research here seeks to better understand how and why physical activity improves health, gain a better understanding of the amount, intensity, and type of physical activity needed for health benefits, and evaluate the effect of interventions to promote physical activity.

Explore open research content by Physical Activity for Health...

Analysis of iterative sub-structuring techniques for boundary element approximation of the hypersingular operator in three dimensions

Ainsworth, M. and Guo, B. (2002) Analysis of iterative sub-structuring techniques for boundary element approximation of the hypersingular operator in three dimensions. Applicable Analysis, 81 (2). pp. 241-280. ISSN 0003-6811

Full text not available in this repository. Request a copy from the Strathclyde author

Abstract

The article deals with the analysis of Additive Schwarz preconditioners for the h-version of the boundary element method for the hypersingular integral equation on surfaces in three dimensions. The first preconditioner consists of decomposing into local spaces associated with the subdomain interiors, supplemented with a wirebasket space associated with the subdomain interfaces. The wirebasket correction only involves the inversion of a diagonal matrix, while the interior correction consists of inverting the sub-blocks of the stiffness matrix corresponding to the interior degrees of freedom on each subdomain. It is shown that the condition number of the preconditioned system grows at most as max K Hm1 (1 + log H/hK)2 where H is the size of the quasi-uniform subdomains and hK is the size of the elements in subdomain K. A second preconditioner is given that incorporates a coarse space associated with the subdomains. This improves the robustness of the method with respect to the number of subdomains: theoretical analysis shows that growth of the condition number of the preconditioned system is now bounded by max K (1 + log H/hK)2.