The simplified linear model of Grad-Shafranov （GS） reconstruction can be reformulated into an inverse boundary value problem of Laplace＇s equation. Therefore, in this paper we focus on the method of solving the inv...The simplified linear model of Grad-Shafranov （GS） reconstruction can be reformulated into an inverse boundary value problem of Laplace＇s equation. Therefore, in this paper we focus on the method of solving the inverse boundary value problem of Laplace＇s equation. In the first place, the variational regularization method is used to deal with the ill- posedness of the Cauchy problem for Laplace＇s equation. Then, the ＇L-Curve＇ principle is suggested to be adopted in choosing the optimal regularization parameter. Finally, a numerical experiment is implemented with a section of Neumann and Dirichlet boundary conditions with observation errors. The results well converge to the exact solution of the problem, which proves the efficiency and robustness of the proposed method. When the order of observation error δ is 10-1, the order of the approximate result error can reach 10-3.展开更多
To achieve real-time control of tokamak plasmas, the equilibrium reconstruction has to be completed sufficiently quickly. For the case of an EAST tokamak experiment, real-time equilibrium reconstruction is generally r...To achieve real-time control of tokamak plasmas, the equilibrium reconstruction has to be completed sufficiently quickly. For the case of an EAST tokamak experiment, real-time equilibrium reconstruction is generally required to provide results within 1ms. A graphic processing unit（GPU） parallel Grad–Shafranov（G-S） solver is developed in P-EFIT code,which is built with the CUDA？ architecture to take advantage of massively parallel GPU cores and significantly accelerate the computation. Optimization and implementation of numerical algorithms for a block tri-diagonal linear system are presented. The solver can complete a calculation within 16 μs with 65×65 grid size and 27 μs with 129×129 grid size, and this solver supports that P-EFIT can fulfill the time feasibility for real-time plasma control with both grid sizes.展开更多
基于Zoeppritz方程对介质密度偏导数所建立的偏导方程的精确解,构造了多角度反演地层介质密度的反演方程,在偏导数求解过程中考虑了介质密度对波速度的影响因素,并由此实现了利用反射系数梯度精确解计算地层密度的多角度联合反演.通过...基于Zoeppritz方程对介质密度偏导数所建立的偏导方程的精确解,构造了多角度反演地层介质密度的反演方程,在偏导数求解过程中考虑了介质密度对波速度的影响因素,并由此实现了利用反射系数梯度精确解计算地层密度的多角度联合反演.通过数值算例考察了计算方法,结果显示:反演方法对层状地层模型不论反射波是否存在相干现象均获得了较好的反演结果,反演迭代10次后计算结果的最大相对误差能够收敛到1%之内;随着反演角度的增加地层介质密度反演的精度逐步提高,反演具有自动校正能力,有快的计算速度.本方法克服了传统AVO(Amplitude Versus Offset)基于Zoeppritz方程近似所遇到的困难,不受反演角度大小及反射界面对波反射强弱的限制,为地层介质密度的多角度包括大角度反演提供了一种新的快速有效的计算方法.展开更多
2009年2月21日THEMIS-C卫星在磁尾X=-15.7RE(RE为地球半径,1RE=6371km)观测到典型的磁通量绳事件.采用Grad-Shafranov重构技术研究该磁通量绳的特性、内部磁场和电流结构.研究表明,磁通量绳不变轴位于GSM(geocentric solar magnetospher...2009年2月21日THEMIS-C卫星在磁尾X=-15.7RE(RE为地球半径,1RE=6371km)观测到典型的磁通量绳事件.采用Grad-Shafranov重构技术研究该磁通量绳的特性、内部磁场和电流结构.研究表明,磁通量绳不变轴位于GSM(geocentric solar magnetospheric coordinates)坐标为(-0.3975,0.8905,0.2213)的方向,基本位于晨昏方向;通量绳的横截面尺度约为2RE,内部轴向磁通量为1.3×106Wb.与经验模型相比,在对磁通量绳几何形状不做约束的情况下,重构出磁尾X=-15.7RE处磁通量绳横截面上的磁场、电流强度分布图像.通量绳核心部位具有无力场位形结构,而随着径向距离的增加,磁场在偏离轴对称分布的区域逐渐表现为非无力位形.展开更多
It is difficult to obtain the asymmetrical factor along the observation direction parallel to the plasma mid-plane when the detected radiation is also in the mid-plane. This paper considers the magnetic surfaces and G...It is difficult to obtain the asymmetrical factor along the observation direction parallel to the plasma mid-plane when the detected radiation is also in the mid-plane. This paper considers the magnetic surfaces and Grad-Shafranov shift, and develops a new method for inverse asymmetric electron density information, during magnetic equilibrium configuration in a tokamak.展开更多
Through solving the Zoeppritz's partial derivative equations, we have obtained accurate partial derivatives of reflected coefficients of seismic wave with respect to Pand S-wave velocities.With those partial deriv...Through solving the Zoeppritz's partial derivative equations, we have obtained accurate partial derivatives of reflected coefficients of seismic wave with respect to Pand S-wave velocities.With those partial derivatives, a multi-angle inversion is developed for seismic wave velocities.Numerical examples of different formation models show that if the number of iterations goes over 10, the relative error of inversion results is less than 1%, whether or not there is interference among the reflection waves.When we only have the reflected seismograms of P-wave, and only invert for velocities of P-wave, the multi-angle inversion is able to obtain a high computation precision.When we have the reflected seismograms of both P-wave and VS-wave, and simultaneously invert for the velocities of P-wave and VS-wave, the computation precisions of VS-wave velocities improves gradually with the increase of the number of angles, but the computation precision of P-wave velocities becomes worse.No matter whether the reflected seismic waves from the different reflection interface are coherent or non-coherent, this method is able to achieve a higher computation precision.Because it is based on the accurate solution of the gradient of SWRCs without any additional restriction, the multi-angle inversion method can be applied to seismic inversion of total angles.By removing the difficulties caused by simplified Zoeppritz formulas that the conventional AVO technology struggles with, the multiangle inversion method extended the application range of AVO technology and improved the computation precision and speed of inversion of seismic wave velocities.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.41175025)
文摘The simplified linear model of Grad-Shafranov （GS） reconstruction can be reformulated into an inverse boundary value problem of Laplace＇s equation. Therefore, in this paper we focus on the method of solving the inverse boundary value problem of Laplace＇s equation. In the first place, the variational regularization method is used to deal with the ill- posedness of the Cauchy problem for Laplace＇s equation. Then, the ＇L-Curve＇ principle is suggested to be adopted in choosing the optimal regularization parameter. Finally, a numerical experiment is implemented with a section of Neumann and Dirichlet boundary conditions with observation errors. The results well converge to the exact solution of the problem, which proves the efficiency and robustness of the proposed method. When the order of observation error δ is 10-1, the order of the approximate result error can reach 10-3.
基金supported by the National Magnetic Confinement Fusion Research Program of China(Grant No.2014GB103000)the National Natural Science Foundation of China(Grant No.11575245)the National Natural Science Foundation of China for Youth(Grant No.11205191)
文摘To achieve real-time control of tokamak plasmas, the equilibrium reconstruction has to be completed sufficiently quickly. For the case of an EAST tokamak experiment, real-time equilibrium reconstruction is generally required to provide results within 1ms. A graphic processing unit（GPU） parallel Grad–Shafranov（G-S） solver is developed in P-EFIT code,which is built with the CUDA？ architecture to take advantage of massively parallel GPU cores and significantly accelerate the computation. Optimization and implementation of numerical algorithms for a block tri-diagonal linear system are presented. The solver can complete a calculation within 16 μs with 65×65 grid size and 27 μs with 129×129 grid size, and this solver supports that P-EFIT can fulfill the time feasibility for real-time plasma control with both grid sizes.
文摘基于Zoeppritz方程对介质密度偏导数所建立的偏导方程的精确解,构造了多角度反演地层介质密度的反演方程,在偏导数求解过程中考虑了介质密度对波速度的影响因素,并由此实现了利用反射系数梯度精确解计算地层密度的多角度联合反演.通过数值算例考察了计算方法,结果显示:反演方法对层状地层模型不论反射波是否存在相干现象均获得了较好的反演结果,反演迭代10次后计算结果的最大相对误差能够收敛到1%之内;随着反演角度的增加地层介质密度反演的精度逐步提高,反演具有自动校正能力,有快的计算速度.本方法克服了传统AVO(Amplitude Versus Offset)基于Zoeppritz方程近似所遇到的困难,不受反演角度大小及反射界面对波反射强弱的限制,为地层介质密度的多角度包括大角度反演提供了一种新的快速有效的计算方法.
文摘2009年2月21日THEMIS-C卫星在磁尾X=-15.7RE(RE为地球半径,1RE=6371km)观测到典型的磁通量绳事件.采用Grad-Shafranov重构技术研究该磁通量绳的特性、内部磁场和电流结构.研究表明,磁通量绳不变轴位于GSM(geocentric solar magnetospheric coordinates)坐标为(-0.3975,0.8905,0.2213)的方向,基本位于晨昏方向;通量绳的横截面尺度约为2RE,内部轴向磁通量为1.3×106Wb.与经验模型相比,在对磁通量绳几何形状不做约束的情况下,重构出磁尾X=-15.7RE处磁通量绳横截面上的磁场、电流强度分布图像.通量绳核心部位具有无力场位形结构,而随着径向距离的增加,磁场在偏离轴对称分布的区域逐渐表现为非无力位形.
文摘It is difficult to obtain the asymmetrical factor along the observation direction parallel to the plasma mid-plane when the detected radiation is also in the mid-plane. This paper considers the magnetic surfaces and Grad-Shafranov shift, and develops a new method for inverse asymmetric electron density information, during magnetic equilibrium configuration in a tokamak.
基金supported by Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality(PHR(IHLB))(Grant No.PHR201107145)
文摘Through solving the Zoeppritz's partial derivative equations, we have obtained accurate partial derivatives of reflected coefficients of seismic wave with respect to Pand S-wave velocities.With those partial derivatives, a multi-angle inversion is developed for seismic wave velocities.Numerical examples of different formation models show that if the number of iterations goes over 10, the relative error of inversion results is less than 1%, whether or not there is interference among the reflection waves.When we only have the reflected seismograms of P-wave, and only invert for velocities of P-wave, the multi-angle inversion is able to obtain a high computation precision.When we have the reflected seismograms of both P-wave and VS-wave, and simultaneously invert for the velocities of P-wave and VS-wave, the computation precisions of VS-wave velocities improves gradually with the increase of the number of angles, but the computation precision of P-wave velocities becomes worse.No matter whether the reflected seismic waves from the different reflection interface are coherent or non-coherent, this method is able to achieve a higher computation precision.Because it is based on the accurate solution of the gradient of SWRCs without any additional restriction, the multi-angle inversion method can be applied to seismic inversion of total angles.By removing the difficulties caused by simplified Zoeppritz formulas that the conventional AVO technology struggles with, the multiangle inversion method extended the application range of AVO technology and improved the computation precision and speed of inversion of seismic wave velocities.
