Source Identification for the Smoluchowski Equation Using an Ensemble of Adjoint Equation Solutions

A. V. Penenko, A. B. Salimova

Research output: Contribution to journalArticlepeer-review

Abstract

A source identification algorithm for systems of nonlinear ordinarydifferential equations of production-destruction type is applied to aninverse problem for a discretized Smoluchowski equation. An unknownsource function is estimated by time series of measurements of particleconcentrations of a specific size. Based on an ensemble of adjointequation solutions, a sensitivity operator is constructed that relatesperturbations of the sought-for model parameters with perturbations ofthe measured values. This reduces the inverse problem to a family ofquasilinear operator equations. To solve the equations, an algorithm ofthe Newton–Kantorovich type with r-pseudoinversematrices is used. The efficiency and properties of the algorithm arestudied numerically.

Original languageEnglish
Pages (from-to)152-164
Number of pages13
JournalNumerical Analysis and Applications
Volume13
Issue number2
DOIs
Publication statusPublished - 1 Jun 2020

Keywords

  • adjoint equations
  • inverse source problem
  • Newton--Kantorovich method
  • sensitivity operator
  • Smoluchowski equation

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