2 research outputs found
A robust and efficient iterative method for hyper-elastodynamics with nested block preconditioning
We develop a robust and efficient iterative method for hyper-elastodynamics
based on a novel continuum formulation recently developed. The numerical scheme
is constructed based on the variational multiscale formulation and the
generalized- method. Within the nonlinear solution procedure, a block
factorization is performed for the consistent tangent matrix to decouple the
kinematics from the balance laws. Within the linear solution procedure, another
block factorization is performed to decouple the mass balance equation from the
linear momentum balance equations. A nested block preconditioning technique is
proposed to combine the Schur complement reduction approach with the fully
coupled approach. This preconditioning technique, together with the Krylov
subspace method, constitutes a novel iterative method for solving
hyper-elastodynamics. We demonstrate the efficacy of the proposed
preconditioning technique by comparing with the SIMPLE preconditioner and the
one-level domain decomposition preconditioner. Two representative examples are
studied: the compression of an isotropic hyperelastic cube and the tensile test
of a fully-incompressible anisotropic hyperelastic arterial wall model. The
robustness with respect to material properties and the parallel performance of
the preconditioner are examined
A projected super-penalty method for the -coupling of multi-patch isogeometric Kirchhoff plates
This work focuses on the development of a super-penalty strategy based on the
-projection of suitable coupling terms to achieve -continuity between
non-conforming multi-patch isogeometric Kirchhoff plates. In particular, the
choice of penalty parameters is driven by the underlying perturbed saddle point
problem from which the Lagrange multipliers are eliminated and is performed to
guarantee the optimal accuracy of the method. Moreover, by construction, the
method does not suffer from locking also on very coarse meshes. We demonstrate
the applicability of the proposed coupling algorithm to Kirchhoff plates by
studying several benchmark examples discretized by non-conforming meshes. In
all cases, we recover the optimal rates of convergence achievable by B-splines
where we achieve a substantial gain in accuracy per degree-of-freedom compared
to other choices of the penalty parameters