Relative increase or decrease of the δρ_err (top), E₀ (middle), and E₁ (bottom) of the hydrostatic glass when relaxed for different kernels in respect to the corresponding error of the C₂ kernel. The simulations here were performed with only the GDSPH method. The terms N32, N64, N128, and N256 refer to the number of neighbors: N_smooth = 32,64,128,256, respectively. The δρ_err, E₀ and E₁ of the C2 kernel for each N_smooth is δρ_err = 5.539 × 10⁻³,3.747 × 10⁻³,1.243 × 10⁻³,5.860 × 10⁻⁴, E₀ = 2.763 × 10⁻³,2.024 × 10⁻³, 6.797 × 10⁻⁴,4.253 × 10⁻⁴, and E₁ = 2.210 × 10⁻²,1.484 × 10⁻²,2.557 × 10⁻³,8.305 × 10⁻⁴. The optimized kernels can in general be seen to drastically reduce the E₁ error relative to the C2 kernel. For the glass optimized kernel’s we can also see a general decrease in both δρ and E₀ for their given N_smooth.