Premium
Preconditioned augmented Lagrangian formulation for nearly incompressible cardiac mechanics
Author(s) -
Campos Joventino Oliveira,
Santos Rodrigo Weber,
Sundnes Joakim,
Rocha Bernardo Martins
Publication year - 2018
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.2948
Subject(s) - augmented lagrangian method , solver , preconditioner , mathematics , compressibility , multigrid method , computer science , iterative method , mathematical optimization , partial differential equation , mechanics , mathematical analysis , physics
Computational modeling of the heart is a subject of substantial medical and scientific interest, which may contribute to increase the understanding of several phenomena associated with cardiac physiological and pathological states. Modeling the mechanics of the heart have led to considerable insights, but it still represents a complex and a demanding computational problem, especially in a strongly coupled electromechanical setting. Passive cardiac tissue is commonly modeled as hyperelastic and is characterized by quasi‐incompressible, orthotropic, and nonlinear material behavior. These factors are known to be very challenging for the numerical solution of the model. The near‐incompressibility is known to cause numerical issues such as the well‐known locking phenomenon and ill‐conditioning of the stiffness matrix. In this work, the augmented Lagrangian method is used to handle the nearly incompressible condition. This approach can potentially improve computational performance by reducing the condition number of the stiffness matrix and thereby improving the convergence of iterative solvers. We also improve the performance of iterative solvers by the use of an algebraic multigrid preconditioner. Numerical results of the augmented Lagrangian method combined with a preconditioned iterative solver for a cardiac mechanics benchmark suite are presented to show its improved performance.