scholarly journals Magnetocardiogram forward problem based on personalized three-dimensional heart-torso model

2019 ◽  
Vol 68 (17) ◽  
pp. 178702
Author(s):  
Wei-Wei Xu ◽  
Ming-Zhu Bai ◽  
Qiang Lin ◽  
Zheng-Hui Hu
Keyword(s):  
Three Dimensional ◽  
Forward Problem ◽  
Torso Model

scholarly journals Solving the magnetocardiography forward problem in a realistic three-dimensional heart-torso model

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Zhenghui Hu ◽  
Kaikai Ye ◽  
Mingzhu Bai ◽  
Zekuan Yang ◽  
Qiang Lin
Keyword(s):  
Three Dimensional ◽  
Forward Problem ◽  
Torso Model

scholarly journals PDE based determination of piezoelectric material tensors

2006 ◽  
Vol 17 (4) ◽  
pp. 383-416 ◽  
Author(s):  
BARBARA KALTENBACHER ◽  
TOM LAHMER ◽  
MARCUS MOHR ◽  
MANFRED KALTENBACHER
Keyword(s):  
Inverse Problem ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Forward Problem ◽  
System Of Equations ◽  
Material Tensor ◽  
Infinite Dimensional ◽  
Material Parameters ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

The exact numerical simulation of piezoelectric transducers requires the knowledge of all material tensors that occur in the piezoelectric constitutive relations. To account for mechanical, dielectric and piezoelectric losses, the material parameters are assumed to be complex. The issue of material tensor identification is formulated as an inverse problem: As input measured impedance values for different frequency points are used, the searched-for output is the complete set of material parameters. Hence, the forward operator F mapping from the set of parameters to the set of measurements, involves solutions of the system of partial differential equations arising from application of Newton's and Gauss' law to the piezoelectric constitutive relations. This, via two or three dimensional finite element discretisation, leads to an indefinite system of equations for solving the forward problem. Well-posedness of the infinite dimensional forward problem is proven and efficient solution strategies for its discretized version are presented. Since unique solvability of the inverse problem may hardly be verified, the system of equations we have to solve for recovering the material tensor entries can be rank deficient and therefore requires application of appropriate regularisation strategies. Consequently, inversion of the (nonlinear) parameter-to-measurement map F is performed using regularised versions of Newton's method. Numerical results for different piezoelectric specimens conclude this paper.

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