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For comparison, we also give the numerical results of the spectral gradient method (denoted by SGM) in [9], the conjugate gradient method (denoted by CGM) in [16].
We conduct experiments to compare the prediction performance of our CRF-based method (denoted by CRF) with a heuristic method (denoted by Heuristic).
We establish a new two-dimensional Riemann solver based on the HLLC method (denoted by the ALE HLLC-2D).
A multi-dimensional Riemann solver based on the HLLC method (denoted by HLLC-2D solver) is established.
In all our experiments, we perform histogram-level concatenation of two types of features: encoded HOG and HOF descriptors for interest point method (denoted by "STIP") and encoded MBHx and MBHy descriptors for the trajectory-based method (denoted by 'iDT').
To enable the analysis of the theoretical performance limits of the backtracking version of the proposed algorithm, a method denoted by Tree: Dec. + BT* is additionally evaluated.
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In order to analyze the behavior of the effective one-step error (in the discrete l2 (R h ) norm) of the θ-method, denoted by Estep, we must consider in system (7) the "source" vector w as w ≡ w n = I + Δ t ( 1 - θ ) A ( u n ) u n + Δ t ( 1 - θ ) b ( u n ) + Δ t ( θ s n + 1 + ( 1 - θ ) s n ). with u n = {u(x i, y j, t n )} and t n = tn+1- Δ t.
One of the methods denoted by P2H was introduced by the first author and collaborator for the case of homogeneous and isotropic media.
The total utility values achieved by the naive method, the uniform method, and the proposed method are denoted by Xnaive, Xuni, and Xopt, respectively.
The displacement and acceleration response curves of dropping shock process by Ren-He's method (denoted RHM) are compared with those by the Runge-Kutta method (denoted R-K) as shown in Figures 1 and 2, respectively.
We denote this method by 2D-FE, while our method is denoted by 3D-FE.
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