The artificial boundary method is one of the most popular and effective numerical methods tor solving partial differential equations on unbounded domains, with more than thirty years development. The artificiM boundar...The artificial boundary method is one of the most popular and effective numerical methods tor solving partial differential equations on unbounded domains, with more than thirty years development. The artificiM boundary method has reached maturity in recent years. It has been applied to various problems in scientific and engineering computations, and the theoretical issues such as the convergence and error estimates of the artificial boundary method have been solved gradually. This paper reviews the development and discusses different forms of the artificial boundary method.展开更多
Consider a semiparametric regression model with linear time series errors Y_k= x′ _kβ + g(t_k) + ε_k, 1 ≤ k ≤ n, where Y_k's are responses, x_k =(x_(k1),x_(k2),···,x_(kp))′ and t_k ∈ T is con...Consider a semiparametric regression model with linear time series errors Y_k= x′ _kβ + g(t_k) + ε_k, 1 ≤ k ≤ n, where Y_k's are responses, x_k =(x_(k1),x_(k2),···,x_(kp))′ and t_k ∈ T is contained in R are fixed design points, β =(β_1,β_2,···,β_p)′ is an unknown parameter vector, g(·) is an unknown bounded real-valuedfunction defined on a compact subset T of the real line R, and ε_k is a linear process given byε_k = ∑ from j=0 to ∞ of ψ_je_(k-j), ψ_0=1, where ∑ from j=0 to ∞ of |ψ_j| < ∞, and e_j,j=0, +-1, +-2,···, ard i.i.d. random variables. In this paper we establish the asymptoticnormality of the least squares estimator of β, a smooth estimator of g(·), and estimators of theautocovariance and autocorrelation functions of the linear process ε_k.展开更多
Consider the regression model Y i=x τ iβ+g(t i)+ε i for i=1,…, n. Here (x i, t i) are known and nonrandom design points and ε i are i.i.d. random errors.The family of nonparametric estimates n(·) of g(·...Consider the regression model Y i=x τ iβ+g(t i)+ε i for i=1,…, n. Here (x i, t i) are known and nonrandom design points and ε i are i.i.d. random errors.The family of nonparametric estimates n(·) of g(·) including some known estimates is proposed. Based on the model Y i=x τ i+ n(t i)+ε i, the Berry-Esseen bounds of the distribution of the least-squares estimator of β are investigated.展开更多
Applications for piezoelectric effect have grown rapidly, and piezoelectric materials play important roles in countless areas of modem life. By means of twoscale method and coupled boundary layer, some new kinds of tw...Applications for piezoelectric effect have grown rapidly, and piezoelectric materials play important roles in countless areas of modem life. By means of twoscale method and coupled boundary layer, some new kinds of twoscale asymptotic expansions for solutions to the electrical potential and the displacement in quasi-periodic structure under coupled piezoelectric effect are derived, and the homogenization constants of piezoelectric materials are presented. The coupled twoscale relation between the electrical potential and the displacement is set up, and some improved asymptotic error estimates are analyzed.展开更多
In this paper, we introduce a domain decomposition method with non-matching grids for solving Dirichlet exterior boundary problems by coupling of finite element method （FEM） and natural boundary element method（BEM...In this paper, we introduce a domain decomposition method with non-matching grids for solving Dirichlet exterior boundary problems by coupling of finite element method （FEM） and natural boundary element method（BEM）. We first derive the optimal energy error estimate of the nonconforming approximation generated by this method. Then we apply a Dirichlet-Neumann（D-N） alternating algorithm to solve the coupled discrete system. It will be shown that such iterative method possesses the optimal convergence. The numerical experiments testify our theoretical results.展开更多
基金supported by National National Science Foundation of China(Grant No.10971116)FRG of Hong Kong Baptist University(Grant No.FRG1/11-12/051)
文摘The artificial boundary method is one of the most popular and effective numerical methods tor solving partial differential equations on unbounded domains, with more than thirty years development. The artificiM boundary method has reached maturity in recent years. It has been applied to various problems in scientific and engineering computations, and the theoretical issues such as the convergence and error estimates of the artificial boundary method have been solved gradually. This paper reviews the development and discusses different forms of the artificial boundary method.
基金CHEN Min's work is supported by Grant No. 70221001 and No. 70331001 from NNSFC and Grant No. KZCX2-SW-118 from CAS.
文摘Consider a semiparametric regression model with linear time series errors Y_k= x′ _kβ + g(t_k) + ε_k, 1 ≤ k ≤ n, where Y_k's are responses, x_k =(x_(k1),x_(k2),···,x_(kp))′ and t_k ∈ T is contained in R are fixed design points, β =(β_1,β_2,···,β_p)′ is an unknown parameter vector, g(·) is an unknown bounded real-valuedfunction defined on a compact subset T of the real line R, and ε_k is a linear process given byε_k = ∑ from j=0 to ∞ of ψ_je_(k-j), ψ_0=1, where ∑ from j=0 to ∞ of |ψ_j| < ∞, and e_j,j=0, +-1, +-2,···, ard i.i.d. random variables. In this paper we establish the asymptoticnormality of the least squares estimator of β, a smooth estimator of g(·), and estimators of theautocovariance and autocorrelation functions of the linear process ε_k.
文摘Consider the regression model Y i=x τ iβ+g(t i)+ε i for i=1,…, n. Here (x i, t i) are known and nonrandom design points and ε i are i.i.d. random errors.The family of nonparametric estimates n(·) of g(·) including some known estimates is proposed. Based on the model Y i=x τ i+ n(t i)+ε i, the Berry-Esseen bounds of the distribution of the least-squares estimator of β are investigated.
基金supported by the National Natural Science Foundation of China(Grant Nos.10801042,11126132,and 11171257)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20104410120001)San Diego supported by China Scholarship Council from July 2012 to July 2013
文摘Applications for piezoelectric effect have grown rapidly, and piezoelectric materials play important roles in countless areas of modem life. By means of twoscale method and coupled boundary layer, some new kinds of twoscale asymptotic expansions for solutions to the electrical potential and the displacement in quasi-periodic structure under coupled piezoelectric effect are derived, and the homogenization constants of piezoelectric materials are presented. The coupled twoscale relation between the electrical potential and the displacement is set up, and some improved asymptotic error estimates are analyzed.
基金The work of this author was supported by Natural Science Foundation of China(G10371129) The work of this author was supported by the National Basic Research Program of China under the grant G19990328,2005CB321701 the National Natural Science Foundation of China.
文摘In this paper, we introduce a domain decomposition method with non-matching grids for solving Dirichlet exterior boundary problems by coupling of finite element method （FEM） and natural boundary element method（BEM）. We first derive the optimal energy error estimate of the nonconforming approximation generated by this method. Then we apply a Dirichlet-Neumann（D-N） alternating algorithm to solve the coupled discrete system. It will be shown that such iterative method possesses the optimal convergence. The numerical experiments testify our theoretical results.
