In this paper we develop two conforming finite element methods for a fourth order bi-wave equation arising as a simplified Ginzburg-Landau-type model for d-wave superconductors in absence of applied magnetic field. Un...In this paper we develop two conforming finite element methods for a fourth order bi-wave equation arising as a simplified Ginzburg-Landau-type model for d-wave superconductors in absence of applied magnetic field. Unlike the biharmonic operator A2, the bi-wave operator □^2 is not an elliptic operator, so the energy space for the bi-wave equation is much larger than the energy space for the biharmonic equation. This then makes it possible to construct low order conforming finite elements for the bi-wave equation. However, the existence and construction of such finite elements strongly depends on the mesh. In the paper, we first characterize mesh conditions which allow and not allow construction of low order conforming finite elements for approximating the bi-wave equation. We then construct a cubic and a quartic conforming finite element. It is proved that both elements have the desired approximation properties, and give optimal order error estimates in the energy norm, suboptimal （and optimal in some cases） order error estimates in the H1 and L^2 norm. Finally, numerical experiments are presented to guage the efficiency of the proposed finite element methods and to validate the theoretical error bounds.展开更多
In this paper,a two-grid mixed finite element method(MFEM)of implicit Backward Euler(BE)formula is presented for the fourth order time-dependent singularly perturbed Bi-wave problem for d-wave superconductors by the n...In this paper,a two-grid mixed finite element method(MFEM)of implicit Backward Euler(BE)formula is presented for the fourth order time-dependent singularly perturbed Bi-wave problem for d-wave superconductors by the nonconforming EQ_(1)^(rot) element.In this approach,the original nonlinear system is solved on the coarse mesh through the Newton iteration method,and then the linear system is computed on the fine mesh with Taylor’s expansion.Based on the high accuracy results of the chosen element,the uniform superclose and superconvergent estimates in the broken H^(1)-norm are derived,which are independent of the negative powers of the perturbation parameter appeared in the considered problem.Numerical results illustrate that the computing cost of the proposed two-grid method is much less than that of the conventional Galerkin MFEM without loss of accuracy.展开更多
在遥感海浪数据质量控制研究中,由于数据的复杂与不规则性,传统质量控制方法对海浪数据单点异常值的检测具有一定局限性。深度学习具有强大的特征学习能力,在解决非线性复杂问题方面具有一定优势,将其应用在数据质量控制领域可以提高异...在遥感海浪数据质量控制研究中,由于数据的复杂与不规则性,传统质量控制方法对海浪数据单点异常值的检测具有一定局限性。深度学习具有强大的特征学习能力,在解决非线性复杂问题方面具有一定优势,将其应用在数据质量控制领域可以提高异常值检测能力。本研究采用遥感海浪有效波高数据,构建双向长短期记忆网络(bi-directional long short term memory,Bi-LSTM)模型对有效波高进行预测,结合阈值方法进行异常检测,与3σ准则法、孤立森林模型法、 LSTM模型法以及VAE-LSTM模型法进行异常检测精度比较,探究基于Bi-LSTM的质量控制模型在遥感海浪数据异常值检测方面的能力。试验结果表明,Bi-LSTM质量控制模型具有良好的异常值检测效果,其精准率、召回率、 F1分数和运行时间分别为91%、 93%、 92和3.35 s,综合评价效果最佳,可有效对遥感海浪数据进行质量控制。展开更多
基金partially supported by the NSF grant DMS-0710831
文摘In this paper we develop two conforming finite element methods for a fourth order bi-wave equation arising as a simplified Ginzburg-Landau-type model for d-wave superconductors in absence of applied magnetic field. Unlike the biharmonic operator A2, the bi-wave operator □^2 is not an elliptic operator, so the energy space for the bi-wave equation is much larger than the energy space for the biharmonic equation. This then makes it possible to construct low order conforming finite elements for the bi-wave equation. However, the existence and construction of such finite elements strongly depends on the mesh. In the paper, we first characterize mesh conditions which allow and not allow construction of low order conforming finite elements for approximating the bi-wave equation. We then construct a cubic and a quartic conforming finite element. It is proved that both elements have the desired approximation properties, and give optimal order error estimates in the energy norm, suboptimal （and optimal in some cases） order error estimates in the H1 and L^2 norm. Finally, numerical experiments are presented to guage the efficiency of the proposed finite element methods and to validate the theoretical error bounds.
基金supported by the National Natural Science Foundation of China(Grant Nos.12201640,12071443).
文摘In this paper,a two-grid mixed finite element method(MFEM)of implicit Backward Euler(BE)formula is presented for the fourth order time-dependent singularly perturbed Bi-wave problem for d-wave superconductors by the nonconforming EQ_(1)^(rot) element.In this approach,the original nonlinear system is solved on the coarse mesh through the Newton iteration method,and then the linear system is computed on the fine mesh with Taylor’s expansion.Based on the high accuracy results of the chosen element,the uniform superclose and superconvergent estimates in the broken H^(1)-norm are derived,which are independent of the negative powers of the perturbation parameter appeared in the considered problem.Numerical results illustrate that the computing cost of the proposed two-grid method is much less than that of the conventional Galerkin MFEM without loss of accuracy.
文摘在遥感海浪数据质量控制研究中,由于数据的复杂与不规则性,传统质量控制方法对海浪数据单点异常值的检测具有一定局限性。深度学习具有强大的特征学习能力,在解决非线性复杂问题方面具有一定优势,将其应用在数据质量控制领域可以提高异常值检测能力。本研究采用遥感海浪有效波高数据,构建双向长短期记忆网络(bi-directional long short term memory,Bi-LSTM)模型对有效波高进行预测,结合阈值方法进行异常检测,与3σ准则法、孤立森林模型法、 LSTM模型法以及VAE-LSTM模型法进行异常检测精度比较,探究基于Bi-LSTM的质量控制模型在遥感海浪数据异常值检测方面的能力。试验结果表明,Bi-LSTM质量控制模型具有良好的异常值检测效果,其精准率、召回率、 F1分数和运行时间分别为91%、 93%、 92和3.35 s,综合评价效果最佳,可有效对遥感海浪数据进行质量控制。
