UN CO RR EC TE D PR O O F 1 A Simultaneous Augmented Lagrange Approach for AQ 1 2 the Simulation of Soft Biological Tissue 3

In this paper, we consider the elastic deformation of arterial walls as occurring, 12 e.g., in the process of a balloon angioplasty, a common treatment in the case of atherosclero13 sis. Soft biological tissue is an almost incompressible material. To account for this property 14 in finite element simulations commonly used free energy functions contain terms penalizing 15 volumetric changes. The incorporation of such penalty terms can, unfortunately, spoil the con16 vergence of the nonlinear iteration scheme, i.e., of Newton’s method, as well as of iterative 17 solvers applied for the solution of the linearized systems of equations. We show that the aug18 mented Lagrange method can improve the convergence of the linear and nonlinear iteration 19 schemes while, at the same time, implementing a guaranteed bound for the volumetric change. 20 Our finite element model of an atherosclerotic arterial segment, see Fig. 1, is constructed from 21 intravascular ultrasound images; for details see [4]. 22