  In smoothed particle hydrodynamics (SPH) method, the particle-based
approximations are implemented via kernel functions, and the evaluation of
performance involves two key criteria: numerical accuracy and computational
efficiency. In the SPH community, the Wendland kernel reigns as the prevailing
choice due to its commendable accuracy and reasonable computational efficiency.
Nevertheless, there exists an urgent need to enhance the computational
efficiency of numerical methods while upholding accuracy. In this paper, we
employ a truncation approach to limit the compact support of the Wendland
kernel to 1.6h. This decision is based on the observation that particles within
the range of 1.6h to 2h make negligible contributions, practically approaching
zero, to the SPH approximation. To address integration errors stemming from the
truncation, we incorporate the Laguerre-Gauss kernel for particle relaxation
due to the fact that this kernel has been demonstrated to enable the attainment
of particle distributions with reduced residue and integration errors
\cite{wang2023fourth}. Furthermore, we introduce the kernel gradient correction
to rectify numerical errors from the SPH approximation of kernel gradient and
the truncated compact support. A comprehensive set of numerical examples
including fluid dynamics in Eulerian formulation and solid dynamics in total
Lagrangian formulation are tested and have demonstrated that truncated and
standard Wendland kernels enable achieve the same level accuracy but the former
significantly increase the computational efficiency.
