An inverse problem in an elastic domain with a crack : a fictitious domain approach

被引：2

作者：

Bodart, Oliver ^{[1
]}

Cayol, Valerie ^{[2
]}

Dabaghi, Farshid ^{[3
]}

Koko, Jonas ^{[4
]}

机构：

[1] Univ Jean Monnet St Etienne, Inst Camille Jordan, CNRS, UMR 5208, F-42023 St Etienne, France

[2] Univ Clermont Auvergne, Lab Magmas & Volcans, OPGC, CNRS,IRD, F-63000 Clermont Ferrand, France

[3] Univ Jean Monnet, Inst Camille Jordan, F-42023 St Etienne, France

[4] Univ Clermont Auvergne, UMR 6158, LIMOS, CNRS, Campus Cezeaux,BP 10448, F-63173 Aubiere, France

来源：

COMPUTATIONAL GEOSCIENCES | 2022年 / 26卷 / 02期

关键词：

Inverse problem; Crack; Fictitious domain; Linear elasticity; Conjugate gradient; FINITE-ELEMENT-METHOD; WEAK DISCONTINUITIES; LAGRANGE MULTIPLIERS; BOUNDARY; PROPAGATION; SIMULATION; SLIP;

D O I：

10.1007/s10596-021-10121-7

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

An inverse problem applied to volcanology is studied. It consists in the determination of the variable pressure applied to a crack in order to fit observed ground displacements. The deformation of the volcano is assumed to be governed by linear elasticity. The direct problem is solved via a fictitious domain method, using a finite element discretization of XFEM type. The ground misfit is minimized using a combination of a domain decomposition and optimatily conditions. The gradient of the cost function is derived from a sensitivity analysis. Discretization of the problem is studied. Numerical tests (in 2D and 3D) are presented to illustrate the effectiveness of the proposed approach. In particular, we find that a quasi-Newton method is more efficient than a conjugate gradient method for solving the optimization problem.

引用

页码：423 / 435

页数：13

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