scholarly journals Effect of Torso Non-Homogeneities in the quasi-static inverse problems arising in electrocardiology

2019 ◽  
Vol 5 (2) ◽  
pp. 235-250
Author(s):  
BedrEddine Ainseba ◽  
Mostafa Bendahmane ◽  
Alejandro Lopez
Keyword(s):  
Finite Element Method ◽  
Inverse Problem ◽  
Existence And Uniqueness ◽  
Numerical Experiments ◽  
Stationary Problem ◽  
Electrical Potentials ◽  
Torso Model ◽  
Primal And Dual Problems ◽  
Primal And Dual ◽  
Element Method

AbstractIn the present paper, an homogeneous and non-homogeneous inverse problem constrained by the stationary problem in electrocardiology representing the heart, lungs surfaces, and torso model is investigated. Our goal is to reconstruct the electrical potentials on the surface of the heart from the information obtained non invasively on the torso surface. The existence and uniqueness of solution for the heart-torso problem and the related inverse problem is assessed, and the primal and dual problems are discretized using a finite element method. We present some preliminary numerical experiments using an efficient implementation of the proposed scheme in homogeneous and non-homogeneous cases. Finally, we demonstrate the effect of the non-homogeneity on the reconstructed epicardial potential and show that the inverse ECG problem cannot be solved by the classical BEM (boundary element method).

Approximation of the Vibration Modes of a Plate and Shells Coupled With a Fluid

2006 ◽  
Vol 73 (6) ◽  
pp. 1005-1010 ◽  
Author(s):  
E. Hernández
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Compressible Fluid ◽  
Numerical Experiments ◽  
Vibration Modes ◽  
Solid Interface ◽  
Thin Structure ◽  
Fluid Equations ◽  
Element Method

We consider a method to compute the vibration modes of an elastic thin structure (shell or plate) in contact with a compressible fluid. For the structure, the classical Naghdi equations, based on the Reissner–Mindlin hypothesis, are considered and its approximation using the mixed interpolation of tensorial component 4 finite element method. The fluid equations are discretized by using Raviart–Thomas elements, and a non-conforming coupling is used on the fluid-solid interface. Numerical experiments are reported, assessing the efficiency of this coupled scheme.

scholarly journals A Least-Squares FEM for the Direct and Inverse Rectangular Cavity Scattering Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Enxi Zheng ◽  
Fuming Ma ◽  
Yujie Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Numerical Experiments ◽  
Bessel Functions ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Rectangular Cavity ◽  
Total Field ◽  
Element Method

This paper is concerned with the scattering problem of a rectangular cavity. We solve this problem by a least-squares nonpolynomial finite element method. In the method, we use Fourier-Bessel functions to capture the behaviors of the total field around corners. And the scattered field towards infinity is represented by a combination of half-space Green functions. Then we analyze the convergence and give an error estimate of the method. By coupling the least-squares nonpolynomial finite element method and the Newton method, we proposed an algorithm for the inverse scattering problem. Numerical experiments are presented to show the effectiveness of our method.

Numerical experiments in quantum physics: Finite‐element method

1988 ◽  
Vol 56 (5) ◽  
pp. 444-448 ◽  
Author(s):  
Debra J. Searles ◽  
Ellak I. von Nagy‐Felsobuki
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Experiments ◽  
Quantum Physics ◽  
Element Method

scholarly journals CONVECTIVE AND RADIATIVE THERMAL TRANSFER WITH MULTIPLE REFLECTIONS: ANALYSIS AND APPROXIMATION BY A FINITE ELEMENT METHOD

2001 ◽  
Vol 11 (02) ◽  
pp. 229-262 ◽  
Author(s):  
J. MONNIER ◽  
J. P. VILA
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Existence And Uniqueness ◽  
Multiple Reflections ◽  
Convection Diffusion ◽  
Thermal Transfer ◽  
Uniqueness Of The Solution ◽  
Nonlinear Integrodifferential System ◽  
Account Heat ◽  
Element Method

We study a 3D steady-state thermal model taking into account heat transfer by convection, diffusion and radiation with multiple reflections (grey bodies). This model is a nonlinear integrodifferential system which we solve numerically by a finite element method. Some results of existence and uniqueness of the solution are proved, the numerical analysis is detailed, error estimates are given and two-dimensional numerical results of thermal exchanges under a car bonnet are presented.

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