EFFICIENT SOLUTION OF PARAMETER IDENTIFICATION PROBLEMS WITH H1 REGULARIZATION

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10490704" target="_blank" >RIV/00216208:11320/24:10490704 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ZKoOmR9bxx" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ZKoOmR9bxx</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/22M1520591" target="_blank" >10.1137/22M1520591</a>

Jazyk výsledku

angličtina

Název v původním jazyce

EFFICIENT SOLUTION OF PARAMETER IDENTIFICATION PROBLEMS WITH H1 REGULARIZATION

Popis výsledku v původním jazyce

We consider the identification of spatially distributed parameters under H 1 regularization. Solving the associated minimization problem by Gauss--Newton iteration results in linearized problems to be solved in each step that can be cast as boundary value problems involving a low-rank modification of the Laplacian. Using an algebraic multigrid as a fast Laplace solver, the Sherman-Morrison--Woodbury formula can be employed to construct a preconditioner for these linear problems which exhibits excellent scaling w.r.t. the relevant problem parameters. We first develop this approach in the functional setting, thus obtaining a consistent methodology for selecting boundary conditions that arise from the H 1 regularization. We then construct a method for solving the discrete linear systems based on combining any fast Poisson solver with the Woodbury formula. The efficacy of this method is then demonstrated with scaling experiments. These are carried out for a common nonlinear parameter identification problem arising in electrical resistivity tomography.

Název v anglickém jazyce

EFFICIENT SOLUTION OF PARAMETER IDENTIFICATION PROBLEMS WITH H1 REGULARIZATION

Popis výsledku anglicky

We consider the identification of spatially distributed parameters under H 1 regularization. Solving the associated minimization problem by Gauss--Newton iteration results in linearized problems to be solved in each step that can be cast as boundary value problems involving a low-rank modification of the Laplacian. Using an algebraic multigrid as a fast Laplace solver, the Sherman-Morrison--Woodbury formula can be employed to construct a preconditioner for these linear problems which exhibits excellent scaling w.r.t. the relevant problem parameters. We first develop this approach in the functional setting, thus obtaining a consistent methodology for selecting boundary conditions that arise from the H 1 regularization. We then construct a method for solving the discrete linear systems based on combining any fast Poisson solver with the Woodbury formula. The efficacy of this method is then demonstrated with scaling experiments. These are carried out for a common nonlinear parameter identification problem arising in electrical resistivity tomography.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

SIAM Journal of Scientific Computing

ISSN

1064-8275

e-ISSN

1095-7197

Svazek periodika

46

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

26

Strana od-do

"A1160"-"A1185"

Kód UT WoS článku

001291134400005

EID výsledku v databázi Scopus

2-s2.0-85191579856