Parallel inexact Newton–Krylov and quasi-Newton solvers for nonlinear elasticity

In this work, we address the implementation and performance of inexact Newton-Krylov quasi-Newton algorithms, more specifically BFGS method, for solution nonlinear elasticity equations, compare them to a standard method. This is done through systematic analysis solvers with respect problem size, magnitude data number processors in both almost incompressible mechanics. We consider three test cases: Cook's membrane (static, incompressible), twist incompressible) cardiac model (complex material, time dependent, incompressible). Our results suggest that methods should be preferred compressible mechanics, whereas problems. show these claims are also backed up by convergence methods. any case, all present adequate performance, provide significant speed-up over CPU reduction exceeding 50% best cases.