Abstract
Tissue stiffness is one of the qualitative properties to distinguish abnormal tissues from normal tissues, and the stiffness changes are generally described in terms of the Lamé coefficient. In this paper, an all-at-once Lagrange-Newton-Krylov-Schwarz algorithm is developed to solve the inverse problem of recovering the Lamé coefficient in biological tissues. Specifically, we propose and study a multiplicative two-level domain decomposition preconditioner in the inexact Newton step. Numerical experiments are presented to show the efficiency and scalability of the algorithm on supercomputers.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
X.-C. Cai, S. Liu, and J. Zou. Parallel overlapping domain decomposition methods for coupled inverse elliptic problems. Commun. Appl. Math. Comput. Sci., 4:1–26, 2009.
S. Catheline, M. Tanter, F. Wu, and M. Fink. Diffraction field of a low frequency vibrator in soft tissues using transient elastography. IEEE Trans. Ultrason. Ferroelectn. Freq. Control, 46(4):1013–1019, 1999.
L. Ji and J. McLaughlin. Recovery of the Lamé parameter μ in biological tissues. Inverse Probl., 20(1):1–24, 2004.
J. McLaughlin and D. Renzi. Shear wave speed recovery in transient elastography and supersonic imaging using propagating fronts. Inverse Probl., 22(2):681–706, 2006.
L. Sandrin, M. Tanter, S. Catheline, and M. Fink. Shear modulus imaging with 2-d transient elastography. IEEE Trans. Ultrason. Ferroelectn. Freq. Control, 49(4):426–435, 2002.
A. Toselli and O. Widlund. Domain Decomposition Methods—Algorithms and Theory, volume 34 of Springer Series in Computational Mathematics. Springer, Berlin, 2005.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liu, S., Cai, XC. (2011). Two-Level Multiplicative Domain Decomposition Algorithm for Recovering the Lamé Coefficient in Biological Tissues. In: Huang, Y., Kornhuber, R., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XIX. Lecture Notes in Computational Science and Engineering, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11304-8_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-11304-8_17
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11303-1
Online ISBN: 978-3-642-11304-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)