Two-Level Multiplicative Domain Decomposition Algorithm for Recovering the Lamé Coefficient in Biological Tissues

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.