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

Standard

Source Identification for the Smoluchowski Equation Using an Ensemble of Adjoint Equation Solutions. / Penenko, A. V.; Salimova, A. B.

In: Numerical Analysis and Applications, Vol. 13, No. 2, 01.06.2020, p. 152-164.

Research output: Contribution to journal › Article › peer-review

Harvard

Penenko, AV & Salimova, AB 2020, 'Source Identification for the Smoluchowski Equation Using an Ensemble of Adjoint Equation Solutions', Numerical Analysis and Applications, vol. 13, no. 2, pp. 152-164. https://doi.org/10.1134/S1995423920020068

APA

Penenko, A. V., & Salimova, A. B. (2020). Source Identification for the Smoluchowski Equation Using an Ensemble of Adjoint Equation Solutions. Numerical Analysis and Applications, 13(2), 152-164. https://doi.org/10.1134/S1995423920020068

Vancouver

Penenko AV, Salimova AB. Source Identification for the Smoluchowski Equation Using an Ensemble of Adjoint Equation Solutions. Numerical Analysis and Applications. 2020 Jun 1;13(2):152-164. doi: 10.1134/S1995423920020068

Author

Penenko, A. V. ; Salimova, A. B. / Source Identification for the Smoluchowski Equation Using an Ensemble of Adjoint Equation Solutions. In: Numerical Analysis and Applications. 2020 ; Vol. 13, No. 2. pp. 152-164.

BibTeX

@article{9e15df1d225946d1b00ef6d2c1a489de,

title = "Source Identification for the Smoluchowski Equation Using an Ensemble of Adjoint Equation Solutions",

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.",

keywords = "adjoint equations, inverse source problem, Newton--Kantorovich method, sensitivity operator, Smoluchowski equation",

author = "Penenko, {A. V.} and Salimova, {A. B.}",

year = "2020",

month = jun,

day = "1",

doi = "10.1134/S1995423920020068",

language = "English",

volume = "13",

pages = "152--164",

journal = "Numerical Analysis and Applications",

issn = "1995-4239",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "2",

}

RIS

TY - JOUR

T1 - Source Identification for the Smoluchowski Equation Using an Ensemble of Adjoint Equation Solutions

AU - Penenko, A. V.

AU - Salimova, A. B.

PY - 2020/6/1

Y1 - 2020/6/1

N2 - 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.

AB - 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.

KW - adjoint equations

KW - inverse source problem

KW - Newton--Kantorovich method

KW - sensitivity operator

KW - Smoluchowski equation

UR - http://www.scopus.com/inward/record.url?scp=85086900065&partnerID=8YFLogxK

U2 - 10.1134/S1995423920020068

DO - 10.1134/S1995423920020068

M3 - Article

AN - SCOPUS:85086900065

VL - 13

SP - 152

EP - 164

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 2

ER -

ID: 24615497