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

Stephen Kirkup*, Javad Yazdani, Robin Aspey, Ranjan Badheka

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)2214-2223
Number of pages10
JournalApplied Mathematical Modelling
Volume38
Issue number7-8
DOIs
StatePublished - Jan 1 2014

Keywords

  • Atomic mixing
  • Inverse diffusion
  • Inverse problem
  • Quantification
  • SIMS

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics

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