  We present the application of simultaneous diagonalization and minimum energy
(SDME) high-order finite element modal bases for simulation of transient
non-linear elastodynamic problem, including impact cases with neo-hookean
hyperelastic materials. The bases are constructed using procedures for
simultaneous diagonalization of the internal modes and Schur complement of the
boundary modes from the standard nodal and modal bases, constructed using
Lagrange and Jacobi polynomials, respectively. The implementation of these
bases in a high-order finite element code is straightforward, since the
procedure is applied only to the one-dimensional expansion bases. Non-linear
transient structural problems with large deformation, hyperelastic materials
and impact are solved using the obtained bases with explicit and implicit time
integration procedures. Iterative solutions based on preconditioned conjugate
gradient methods are considered. The performance of the proposed bases in terms
of the number of iterations of pre-conditioned conjugate gradient methods and
computational time are compared with the standard nodal and modal bases. Our
numerical tests obtained speedups up to 41 using the considered bases when
compared to the standard ones.
