In this paper, we propose a new parallel ordering method to vectorize and parallelize the sparse triangular solver, which is called hierarchical block multi-color ordering. In this method, the parallel forward and backward substitutions can be vectorized while preserving the advantages of block multi-color ordering, that is, fast convergence and fewer thread synchronizations. To evaluate the proposed method in a parallel ICCG (Incomplete Cholesky Conjugate Gradient) solver, numerical tests were conducted using seven test matrices on three types of computational nodes. The numerical results indicate that the proposed method outperforms the conventional block and nodal multi-color ordering methods in 18 out of 21 test cases, which confirms the effectiveness of the method.
Algebraic block multi-color ordering is known as a parallelization method for a sparse triangular solver. In the previous work, we confirmed the effectiveness of the method in a multi-threaded ICCG solver for a linear system with a symmetric coefficient matrix. In this study, we enhance the method so as to deal with an unsymmetric coefficient matrix. We develop a multi-threaded ILU-GMRES solver based on the enhanced method and evaluate its performance in terms of both the runtime and the number of iterations.
A full-wavefield imaging detection method is developed and then applied to reveal the defects in the highway embankment. This testing system integrates the point-source/point-receiver scheme with the multi-directional imaging technique to achieve the effect like scanning. It is equipped with an impacting hammer, a series of three-component velocity transducers and a signal capturing unit. To evaluate the feasibility of this system for detecting defect of highway embankment, a full-scaled highway embankment model test with pre-setting defection is conducted. And a 3-D numerical simulation using FEM are performed for comparison and mechanism study. It is paid special attention on the propagation characteristics of full wave field in the model. The characteristics of spectral characteristics derived from Fourier transform are analyzed. Experimental results show agreement with the numerical ones on the processed scanning images. It is concluded that the full-wavefield imaging detection method exhibits high potential in inspecting the defects of highway embankment by imaging.
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