scholarly journals Uniqueness on recovery of piecewise constant conductivity and inner core with one measurement

2018 ◽  
Vol 12 (3) ◽  
pp. 733-743
Author(s):  
Xiaoping Fang ◽  
◽  
Youjun Deng ◽  
Keyword(s):  
Inner Core ◽  
Piecewise Constant ◽  
Piecewise Constant Conductivity

Shape and parameter reconstruction for the Robin transmission inverse problem

2016 ◽  
Vol 24 (6) ◽  
Author(s):  
Antoine Laurain ◽  
Houcine Meftahi
Keyword(s):  
Inverse Problem ◽  
Shape Optimization ◽  
Saddle Point Problem ◽  
Point Problem ◽  
Optimization Approach ◽  
Reconstruction Method ◽  
Piecewise Constant ◽  
Piecewise Constant Conductivity ◽  
Level Set Approach ◽  
Parameter Reconstruction

AbstractIn this paper we consider the inverse problem of simultaneously reconstructing the interface where the jump of the conductivity occurs and the Robin parameter for a transmission problem with piecewise constant conductivity and Robin-type transmission conditions on the interface. We propose a reconstruction method based on a shape optimization approach and compare the results obtained using two different types of shape functionals. The reformulation of the shape optimization problem as a suitable saddle point problem allows us to obtain the optimality conditions by using differentiability properties of the min-sup combined with a function space parameterization technique. The reconstruction is then performed by means of an iterative algorithm based on a conjugate shape gradient method combined with a level set approach. To conclude we give and discuss several numerical examples.

scholarly journals A numerical method for the determination of a piecewise-constant conductivity

2008 ◽  
Vol 135 ◽  
pp. 012038
Author(s):  
A El Badia ◽  
J Giroire ◽  
C Hollandts-Lechevalier
Keyword(s):  
Numerical Method ◽  
Piecewise Constant ◽  
Piecewise Constant Conductivity

scholarly journals On mild and weak solutions for stochastic heat equations with piecewise-constant conductivity

2020 ◽  
Vol 159 ◽  
pp. 108682 ◽  
Author(s):  
Yuliya Mishura ◽  
Kostiantyn Ralchenko ◽  
Mounir Zili
Keyword(s):  
Weak Solutions ◽  
Heat Equations ◽  
Piecewise Constant ◽  
Piecewise Constant Conductivity ◽  
Stochastic Heat Equations

scholarly journals Forward Field Computation with OpenMEEG

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Alexandre Gramfort ◽  
Théodore Papadopoulo ◽  
Emmanuel Olivi ◽  
Maureen Clerc
Keyword(s):  
Inverse Problem ◽  
Electrical Impedance ◽  
Numerical Solutions ◽  
Physiological Modeling ◽  
Impedance Tomography ◽  
Piecewise Constant ◽  
The Core ◽  
Piecewise Constant Conductivity ◽  
Electric Potentials ◽  
Quasistatic Regime

To recover the sources giving rise to electro- and magnetoencephalography in individual measurements, realistic physiological modeling is required, and accurate numerical solutions must be computed. We present OpenMEEG, which solves the electromagnetic forward problem in the quasistatic regime, for head models with piecewise constant conductivity. The core of OpenMEEG consists of the symmetric Boundary Element Method, which is based on an extended Green Representation theorem. OpenMEEG is able to provide lead fields for four different electromagnetic forward problems: Electroencephalography (EEG), Magnetoencephalography (MEG), Electrical Impedance Tomography (EIT), and intracranial electric potentials (IPs). OpenMEEG is open source and multiplatform. It can be used from Python and Matlab in conjunction with toolboxes that solve the inverse problem; its integration within FieldTrip is operational since release 2.0.

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