A new wavelet-based finite element method is proposed for solving the Poisson equation. The wavelet bases of Hermite cubic splines on the interval are employed as the multi-scale interpolation basis in the finite elem...A new wavelet-based finite element method is proposed for solving the Poisson equation. The wavelet bases of Hermite cubic splines on the interval are employed as the multi-scale interpolation basis in the finite element analysis. The lifting scheme of the wavelet-based finite element method is discussed in detail. For the orthogonal characteristics of the wavelet bases with respect to the given inner product, the corresponding multi-scale finite element equation can be decoupled across scales, totally or partially, and suited for nesting approximation. Numerical examples indicate that the proposed method has the higher efficiency and precision in solving the Poisson equation.展开更多
We formulate and analyze the Crank-Nicolson Hermite cubic orthogonal spline collocation method for the solution of the heat equation in one space variable with nonlocal boundary conditions involving integrals of the u...We formulate and analyze the Crank-Nicolson Hermite cubic orthogonal spline collocation method for the solution of the heat equation in one space variable with nonlocal boundary conditions involving integrals of the unknown solution over the spatial interval.Using an extension of the analysis of Douglas and Dupont[23]for Dirichlet boundary conditions,we derive optimal order error estimates in the discrete maximum norm in time and the continuous maximum norm in space.We discuss the solution of the linear system arising at each time level via the capacitance matrix technique and the package COLROWfor solving almost block diagonal linear systems.We present numerical examples that confirm the theoretical global error estimates and exhibit superconvergence phenomena.展开更多
A storage-efficient reconstruction framework for cartographic planar contours is developed.With a smaller number of control points,we aim to calculate the area and perimeter as well as to reconstruct a smooth curve.Th...A storage-efficient reconstruction framework for cartographic planar contours is developed.With a smaller number of control points,we aim to calculate the area and perimeter as well as to reconstruct a smooth curve.The input data forms an oriented contour,each control point of which consists of three values:the Cartesian coordinates(x,y)and tangent angleθ.Two types of interpolation methods are developed,one of which is based on an arc spline while the other one is on a cubic Hermite spline.The arc spline-based method reconstructs a G1 continuous curve,with which the exact area and perimeter can be calculated.The benefit of using the Hermite spline-based method is that it can achieve G2 continuity on most control points and can obtain the exact area,whereas the resulting perimeter is approximate.In a numerical experiment for analytically defined curves,more accurate computation of the area and perimeter was achieved with a smaller number of control points.In another experiment using a digital elevation model data,the reconstructed contours were smoother than those by a conventional method.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 50805028 and 50875195)the Open Foundation of the State Key Laboratory of Structural Analysis for In-dustrial Equipment (No. GZ0815)
文摘A new wavelet-based finite element method is proposed for solving the Poisson equation. The wavelet bases of Hermite cubic splines on the interval are employed as the multi-scale interpolation basis in the finite element analysis. The lifting scheme of the wavelet-based finite element method is discussed in detail. For the orthogonal characteristics of the wavelet bases with respect to the given inner product, the corresponding multi-scale finite element equation can be decoupled across scales, totally or partially, and suited for nesting approximation. Numerical examples indicate that the proposed method has the higher efficiency and precision in solving the Poisson equation.
基金The research of J.C.Lopez-Marcos is supported in part by Ministerio de Ciencia e Innovacion,MTM2011-25238.
文摘We formulate and analyze the Crank-Nicolson Hermite cubic orthogonal spline collocation method for the solution of the heat equation in one space variable with nonlocal boundary conditions involving integrals of the unknown solution over the spatial interval.Using an extension of the analysis of Douglas and Dupont[23]for Dirichlet boundary conditions,we derive optimal order error estimates in the discrete maximum norm in time and the continuous maximum norm in space.We discuss the solution of the linear system arising at each time level via the capacitance matrix technique and the package COLROWfor solving almost block diagonal linear systems.We present numerical examples that confirm the theoretical global error estimates and exhibit superconvergence phenomena.
文摘A storage-efficient reconstruction framework for cartographic planar contours is developed.With a smaller number of control points,we aim to calculate the area and perimeter as well as to reconstruct a smooth curve.The input data forms an oriented contour,each control point of which consists of three values:the Cartesian coordinates(x,y)and tangent angleθ.Two types of interpolation methods are developed,one of which is based on an arc spline while the other one is on a cubic Hermite spline.The arc spline-based method reconstructs a G1 continuous curve,with which the exact area and perimeter can be calculated.The benefit of using the Hermite spline-based method is that it can achieve G2 continuity on most control points and can obtain the exact area,whereas the resulting perimeter is approximate.In a numerical experiment for analytically defined curves,more accurate computation of the area and perimeter was achieved with a smaller number of control points.In another experiment using a digital elevation model data,the reconstructed contours were smoother than those by a conventional method.
