To speed up three-dimensional (3D) DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method (AGMG). We first discretize the differential equation of the secondar...To speed up three-dimensional (3D) DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method (AGMG). We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner (AGMG-CG) to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling (3DDCXH). In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.展开更多
This paper firstly introduces the structure and working principle of DSP-based parallel system, parallel accelerating board and SHARC DSP chip. Then it pays attention to investigating the system’s programming charact...This paper firstly introduces the structure and working principle of DSP-based parallel system, parallel accelerating board and SHARC DSP chip. Then it pays attention to investigating the system’s programming characteristics, especially the mode of communication, discussing how to design parallel algorithms and presenting a domain-decomposition-based complete multi-grid parallel algorithm with virtual boundary forecast (VBF) to solve a lot of large-scale and complicated heat problems. In the end, Mandelbrot Set and a non-linear heat transfer equation of ceramic/metal composite material are taken as examples to illustrate the implementation of the proposed algorithm. The results showed that the solutions are highly efficient and have linear speedup.展开更多
In this paper, the author presents a class of stationary ternary 4-point approximating symmetrical subdivision algorithm that reproduces cubic polynomials. By these subdivision algorithms at each refinement step, new ...In this paper, the author presents a class of stationary ternary 4-point approximating symmetrical subdivision algorithm that reproduces cubic polynomials. By these subdivision algorithms at each refinement step, new insertion control points on a finer grid are computed by weighted sums of already existing control points. In the limit of the recursive process, data is defined on a dense set of point, The objective is to find an improved subdivision approximating algorithm which has a smaller support and a higher approximating order. The author chooses a ternary scheme because the best way to get a smaller support is to pass from the binary to ternary or complex algorithm and uses polynomial reproducing propriety to get higher approximation order. Using the cardinal Lagrange polynomials the author has proposed a 4-point approximating ternary subdivision algorithm and found that a higher regularity of limit function does not guarantee a higher approximating order. The proposed 4-point ternary approximation subdivision family algorithms with the mask a have the limit function in C2 and have approximation order 4. Also the author has demonstrated that in this class there is no algorithm whose limit function is in C3. It can be seen that this stationary ternary 4-point approximating symmetrical subdivision algorithm has a lower computational cost than the 6-point binary approximation subdivision algorithm for a greater range of points.展开更多
This paper studies the algorithm of the adaptive grid and fuzzy interacting multiple model (AGFIMM) for maneuvering target tracking, while focusing on the problems of the fixed structure multiple model (FSMM) algo...This paper studies the algorithm of the adaptive grid and fuzzy interacting multiple model (AGFIMM) for maneuvering target tracking, while focusing on the problems of the fixed structure multiple model (FSMM) algorithm's cost-efficiency ratio being not high and the Markov transition probability of the interacting multiple model (IMM) algorithm being difficult to determine exactly. This algorithm realizes the adaptive model set by adaptive grid adjustment, and obtains each model matching degree in the model set by fuzzy logic inference. The simulation results show that the AGFIMM algorithm can effectively improve the accuracy and cost-efficiency ratio of the multiple model algorithm, and as a result is suitable for enineering apolications.展开更多
基金supported by the Natural Science Foundation of China(Nos.41404057,41674077 and 411640034)the Nuclear Energy Development Project of China,and the‘555’Project of Gan Po Excellent People
文摘To speed up three-dimensional (3D) DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method (AGMG). We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner (AGMG-CG) to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling (3DDCXH). In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.
基金Project (No. 60173046) supported by the National Natural ScienceFoundation of China
文摘This paper firstly introduces the structure and working principle of DSP-based parallel system, parallel accelerating board and SHARC DSP chip. Then it pays attention to investigating the system’s programming characteristics, especially the mode of communication, discussing how to design parallel algorithms and presenting a domain-decomposition-based complete multi-grid parallel algorithm with virtual boundary forecast (VBF) to solve a lot of large-scale and complicated heat problems. In the end, Mandelbrot Set and a non-linear heat transfer equation of ceramic/metal composite material are taken as examples to illustrate the implementation of the proposed algorithm. The results showed that the solutions are highly efficient and have linear speedup.
文摘In this paper, the author presents a class of stationary ternary 4-point approximating symmetrical subdivision algorithm that reproduces cubic polynomials. By these subdivision algorithms at each refinement step, new insertion control points on a finer grid are computed by weighted sums of already existing control points. In the limit of the recursive process, data is defined on a dense set of point, The objective is to find an improved subdivision approximating algorithm which has a smaller support and a higher approximating order. The author chooses a ternary scheme because the best way to get a smaller support is to pass from the binary to ternary or complex algorithm and uses polynomial reproducing propriety to get higher approximation order. Using the cardinal Lagrange polynomials the author has proposed a 4-point approximating ternary subdivision algorithm and found that a higher regularity of limit function does not guarantee a higher approximating order. The proposed 4-point ternary approximation subdivision family algorithms with the mask a have the limit function in C2 and have approximation order 4. Also the author has demonstrated that in this class there is no algorithm whose limit function is in C3. It can be seen that this stationary ternary 4-point approximating symmetrical subdivision algorithm has a lower computational cost than the 6-point binary approximation subdivision algorithm for a greater range of points.
基金Foundation item: Supported by the National Nature Science Foundation of China (No. 61074053, 61374114) and the Applied Basic Research Program of Ministry of Transport of China (No. 2011-329-225 -390).
文摘This paper studies the algorithm of the adaptive grid and fuzzy interacting multiple model (AGFIMM) for maneuvering target tracking, while focusing on the problems of the fixed structure multiple model (FSMM) algorithm's cost-efficiency ratio being not high and the Markov transition probability of the interacting multiple model (IMM) algorithm being difficult to determine exactly. This algorithm realizes the adaptive model set by adaptive grid adjustment, and obtains each model matching degree in the model set by fuzzy logic inference. The simulation results show that the AGFIMM algorithm can effectively improve the accuracy and cost-efficiency ratio of the multiple model algorithm, and as a result is suitable for enineering apolications.