Diwan, G.C. and Mohamed, M.S. and Seaid, M. and Trevelyan, J. and Laghrouche, O. (2015) 'Mixed enrichment for the finite element method in heterogeneous media.', International journal for numerical methods in engineering., 101 (1). pp. 54-78.
Problems of multiple scales of interest or of locally nonsmooth solutions may often involve heterogeneous media. These problems are usually very demanding in terms of computations with the conventional finite element method. On the other hand, different enriched finite element methods such as the partition of unity, which proved to be very successful in treating similar problems, are developed and studied for homogeneous media. In this work, we present a new idea to extend the partition of unity finite element method to treat heterogeneous materials. The idea is studied in applications to wave scattering and heat transfer problems where significant advantages are noted over the standard finite element method. Although presented within the partition of unity context, the same enrichment idea can also be extended to other enriched methods to deal with heterogeneous materials.
|Keywords:||Finite element method, Partition of unity method, Acoustic wave scattering, Transient heat transfer, Composite materials, Heterogeneous media, Multiscale.|
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||http://dx.doi.org/10.1002/nme.4795|
|Publisher statement:||This is the accepted version of the following article: Diwan G. C., Mohamed M. S., Seaid M., Trevelyan J., and Laghrouche O. (2014), Mixed enrichment for the finite element method in heterogeneous media, International Journal for Numerical Methods in Engineering, 101 (1): 54-78, which has been published in final form at http://dx.doi.org/10.1002/nme.4795. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.|
|Date accepted:||23 August 2014|
|Date deposited:||28 October 2014|
|Date of first online publication:||01 October 2014|
|Date first made open access:||No date available|
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