Zusammenfassung
The non-linear elasticity equations of heart mechanics are solved
while emulating the effects of a propagating activation wave. The
dynamics of a 1 cm(3) slab of active cardiac tissue was simulated
as the electrical wave traversed the muscular heart wall transmurally.
The regular Newton (Newton-Raphson) method was compared to two modified
Newton approaches, and also to a third approach that delayed update
only of some selected Jacobian elements. In addition, the impact
of changing the time step (0.01, 0.1 and 1 ms) and the relative non-linear
convergence tolerance (10(-4), 10(-3) and 10(-2)) was investigated.
Updating the Jacobian only when slow convergence occurred was by
far the most efficient approach, giving time savings of 83-96\%.
For each of the four methods, CPU times were reduced by 48-90\% when
the time step was increased by a factor 10. Increasing the convergence
tolerance by the same factor gave time savings of 3-71\%. Different
combinations of activation wave speed, stress rate and bulk modulus
revealed that the fastest method became relatively even faster as
stress rate and bulk modulus was decreased, while the activation
speed had negligible influence in this respect.
Nutzer