Kirkup, S ORCID: 0000-0002-9680-7778, Yazdani, J ORCID: 0000-0001-5273-0951, Aspey, R and Badheka, R (2014) The inverse solution of the atomic mixing equations by an operator-splitting method. Applied Mathematical Modelling, 38 (7-8). pp. 2214-2223. ISSN 0307-904X
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Official URL: http://dx.doi.org/10.1016/j.apm.2013.10.034
Abstract
The quantification problem of recovering the original material distribution from secondary ion mass spectrometry (SIMS) data is considered in this paper. It is an inverse problem, is ill-posed and hence it requires a special technique for its solution. The quantification problem is essentially an inverse diffusion or (classically) a backward heat conduction problem. In this paper an operator-splitting method (that is proposed in a previous paper by the first author for the solution of inverse diffusion problems) is developed for the solution of the problem of recovering the original structure from the SIMS data. A detailed development of the quantification method is given and it is applied to typical data to demonstrate its effectiveness.
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