Computational solution of the atomic mixing equations

Kirkup, Stephen Martin; Wadsworth, M.; Armour, D.G.; Badheka, R.; Berg, Jan-Albert van den

doi:10.1002/(sici)1099-1204(199807/08)11:4<189::aid-jnm301>3.0.co;2-a

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Statement Of the Quantification Problem In Operator Notation1

The Mathematical and Computational Model For Atomic Mixing1

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2014

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Cited by 4 publications

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“…A computational simulation based on this model, known as IMPETUS, has also been developed. The IMPETUS code is based on modelling the concentrations by a set of convection-diffusion partial differential equations and solving them by finite difference methods [5][6][7].…”

Section: Statement Of the Quantification Problem In Operator Notationmentioning

confidence: 99%

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The inverse solution of the atomic mixing equations by an operator-splitting method

Kirkup

Yazdani

Aspey

et al. 2014

Applied Mathematical Modelling

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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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Section: Statement Of the Quantification Problem In Operator Notationmentioning

confidence: 99%

“…The partial differential equations (2) are parabolic diffusion-convection equations. A detailed description of the methods employed to compute the energy and range functions, the sputter yield and the recession speed are given in references Badheka [5] and Kirkup et al [6][7].…”

Section: The Mathematical and Computational Model For Atomic Mixingmentioning

confidence: 99%