The standard implementation of the hybrid GMRES algorithm for solving large nonsymmetric linear systems involves a Gram-Schmidt process which is a potential source of significant numerical error. An alternative implem...The standard implementation of the hybrid GMRES algorithm for solving large nonsymmetric linear systems involves a Gram-Schmidt process which is a potential source of significant numerical error. An alternative implementation is outlined here in which orthogonalization by Householder transformations replaces the Gram-Schmidt process. Numerical experiments show that the new implementation is more stable.展开更多
In order to study cavitation characteristics of a 2-D hydrofoil, the method that combines nonlinear cavitation model and mixed-iteration is used to predict and analyze the cavitation performance of hydrofoils. The cav...In order to study cavitation characteristics of a 2-D hydrofoil, the method that combines nonlinear cavitation model and mixed-iteration is used to predict and analyze the cavitation performance of hydrofoils. The cavitation elements are nonlinearly disposed based on the Green formula and perturbation potential panel method. At the same time, the method that combines cavity shape for fixed cavity length （CSCL） iteration and cavity shape for fixed cavitation number （CSCN） iteration is used to work out the thickness and length of hydrofoil cavitations. Through analysis of calculation results, it can be concluded that the jump of pressure and velocity potentially exist between cavitation end area and non-cavitations area on suction surface when cavitation occurs on hydrofoil. In certain angles of attack, the cavitation number has a negative impact on the length of cavitations. And under the same angle of attack and cavitation number, the bigger the thickness of the hydrofoil, the shorter the cavitations length.展开更多
In this paper, new solutions for the problem of pose estimation from correspondences between 3D model lines and 2D image lines are proposed. Traditional line-based pose estimation methods rely on the assumption that t...In this paper, new solutions for the problem of pose estimation from correspondences between 3D model lines and 2D image lines are proposed. Traditional line-based pose estimation methods rely on the assumption that the noises(perpendicular to the line) for the two endpoints are statistically independent. However, these two noises are in fact negatively correlated when the image line segment is fitted using the least-squares technique. Therefore, we design a new error function expressed by the average integral of the distance between line segments. Three least-squares techniques that optimize both the rotation and translation simultaneously are proposed in which the new error function is exploited. In addition, Lie group formalism is utilized to describe the pose parameters, and then, the optimization problem can be solved by means of a simple iterative least squares method. To enhance the robustness to outliers existing in the match data, an M-estimation method is developed to convert the pose optimization problem into an iterative reweighted least squares problem. The proposed methods are validated through experiments using both synthetic and real-world data. The experimental results show that the proposed methods yield a clearly higher precision than the traditional methods.展开更多
文摘The standard implementation of the hybrid GMRES algorithm for solving large nonsymmetric linear systems involves a Gram-Schmidt process which is a potential source of significant numerical error. An alternative implementation is outlined here in which orthogonalization by Householder transformations replaces the Gram-Schmidt process. Numerical experiments show that the new implementation is more stable.
基金Supported by the National Natural Science Foundation of China （Grant No. 41176074） China Postdoctoral Science Foundation （Grant No.2012M512133） Specialized Research Fund for the Doctoral Program of Higher Education （Grant No.20102304120026）
文摘In order to study cavitation characteristics of a 2-D hydrofoil, the method that combines nonlinear cavitation model and mixed-iteration is used to predict and analyze the cavitation performance of hydrofoils. The cavitation elements are nonlinearly disposed based on the Green formula and perturbation potential panel method. At the same time, the method that combines cavity shape for fixed cavity length （CSCL） iteration and cavity shape for fixed cavitation number （CSCN） iteration is used to work out the thickness and length of hydrofoil cavitations. Through analysis of calculation results, it can be concluded that the jump of pressure and velocity potentially exist between cavitation end area and non-cavitations area on suction surface when cavitation occurs on hydrofoil. In certain angles of attack, the cavitation number has a negative impact on the length of cavitations. And under the same angle of attack and cavitation number, the bigger the thickness of the hydrofoil, the shorter the cavitations length.
基金supported by the National Basic Research Program of China(“973”Project)(Grant No.2013CB733100)National Natural Science Foundation of China(Grant No.11332012)
文摘In this paper, new solutions for the problem of pose estimation from correspondences between 3D model lines and 2D image lines are proposed. Traditional line-based pose estimation methods rely on the assumption that the noises(perpendicular to the line) for the two endpoints are statistically independent. However, these two noises are in fact negatively correlated when the image line segment is fitted using the least-squares technique. Therefore, we design a new error function expressed by the average integral of the distance between line segments. Three least-squares techniques that optimize both the rotation and translation simultaneously are proposed in which the new error function is exploited. In addition, Lie group formalism is utilized to describe the pose parameters, and then, the optimization problem can be solved by means of a simple iterative least squares method. To enhance the robustness to outliers existing in the match data, an M-estimation method is developed to convert the pose optimization problem into an iterative reweighted least squares problem. The proposed methods are validated through experiments using both synthetic and real-world data. The experimental results show that the proposed methods yield a clearly higher precision than the traditional methods.
