The tokamak start-up is a very important phase during the process to obtain a suitable equalizing plasma, and its governing model can be described as a set of nonlinear ordinary differential equations（ODEs）. In this...The tokamak start-up is a very important phase during the process to obtain a suitable equalizing plasma, and its governing model can be described as a set of nonlinear ordinary differential equations（ODEs）. In this paper, we first estimate the parameters in the original model and set up an accurate model to express how the variables change during the start-up phase, especially how the plasma current changes with respect to time and the loop voltage. Then, we apply the control parameterization method to obtain an approximate optimal parameters selection problem for the loop voltage design to achieve a desired plasma current target. Computational optimal control techniques such as the variational method and the costate method are employed to solve the problem, respectively. Finally, numerical simulations are performed and the results obtained via different methods are compared. Our numerical parameterization method and optimization procedure turn out to be effective.展开更多
In this paper we present a new type of Restarted Krylov methods for calculating peripheral eigenvalues of symmetric matrices. The new framework avoids the Lanczos tridiagonalization process, and the use of polynomial ...In this paper we present a new type of Restarted Krylov methods for calculating peripheral eigenvalues of symmetric matrices. The new framework avoids the Lanczos tridiagonalization process, and the use of polynomial filtering. This simplifies the restarting mechanism and allows the introduction of several modifications. Convergence is assured by a monotonicity property that pushes the eigenvalues toward their limits. The Krylov matrices that we use lead to fast rate of convergence. Numerical experiments illustrate the usefulness of the proposed approach.展开更多
The start depth in gravity anomaly inversion is discussed in this paper, and a newmethod called "test comparing method" is presented to determine the start depth when both boring dataand seismic data are not...The start depth in gravity anomaly inversion is discussed in this paper, and a newmethod called "test comparing method" is presented to determine the start depth when both boring dataand seismic data are not available. Anticline and synline density interface models are designed to test themethed; the calculated resall agreed well with the designed value, which Proved tha the new method canbe used to determine the start depth in the guity anomal inversion when boring data and seisndc dataare not available.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.61104048 and 61473253)the National High Technology Research and Development Program of China(Grant No.2012AA041701)
文摘The tokamak start-up is a very important phase during the process to obtain a suitable equalizing plasma, and its governing model can be described as a set of nonlinear ordinary differential equations（ODEs）. In this paper, we first estimate the parameters in the original model and set up an accurate model to express how the variables change during the start-up phase, especially how the plasma current changes with respect to time and the loop voltage. Then, we apply the control parameterization method to obtain an approximate optimal parameters selection problem for the loop voltage design to achieve a desired plasma current target. Computational optimal control techniques such as the variational method and the costate method are employed to solve the problem, respectively. Finally, numerical simulations are performed and the results obtained via different methods are compared. Our numerical parameterization method and optimization procedure turn out to be effective.
文摘In this paper we present a new type of Restarted Krylov methods for calculating peripheral eigenvalues of symmetric matrices. The new framework avoids the Lanczos tridiagonalization process, and the use of polynomial filtering. This simplifies the restarting mechanism and allows the introduction of several modifications. Convergence is assured by a monotonicity property that pushes the eigenvalues toward their limits. The Krylov matrices that we use lead to fast rate of convergence. Numerical experiments illustrate the usefulness of the proposed approach.
文摘The start depth in gravity anomaly inversion is discussed in this paper, and a newmethod called "test comparing method" is presented to determine the start depth when both boring dataand seismic data are not available. Anticline and synline density interface models are designed to test themethed; the calculated resall agreed well with the designed value, which Proved tha the new method canbe used to determine the start depth in the guity anomal inversion when boring data and seisndc dataare not available.
