2008年9月24-26日，受奥地利Wolfgang Pauli Institute的邀请，笔者参加了由维也纳大学Wolfgang Pauli Institute组织举办的“The Gross-Pitaevskii Equation and Its Application for BEC in Optical Lattices”国际研讨会。
1999年10月25至29日,我应邀参加了在日本千叶大学举办的第12届区域分解国际会议。会上著名的美国数学家Roland Glowinski和法国数学家Jacques-Louis Lions分别作了题为"Embedding Methods for Flow with Moving Rigid Boundaries,A...1999年10月25至29日,我应邀参加了在日本千叶大学举办的第12届区域分解国际会议。会上著名的美国数学家Roland Glowinski和法国数学家Jacques-Louis Lions分别作了题为"Embedding Methods for Flow with Moving Rigid Boundaries,Application to theDirect Numerical Simulation of Sedimentation and Fluidization Phenomena"和"VirtualControl and Applications"的特邀报告。展开更多
A Wavelet-Galerkin method is proposed to solve the singular perturbation problem with boundary layers numerically. Because there are boundary layers in the solution of the singular perturbation problem, the approximat...A Wavelet-Galerkin method is proposed to solve the singular perturbation problem with boundary layers numerically. Because there are boundary layers in the solution of the singular perturbation problem, the approximation spaces with different scale wavelets and boundary bases are chosen. In addition, the computation of the inner integrals is transformed to an eigenvalue problem. Therefore, a high accuracy method with reasonable computation is obtained. On the other hand, there is an explicit diagonal preconditioning which makes the condition number of the stiff matrix become bounded by a constant. The error estimate of the Wavelet-Galerkin method and the analysis of the computation complexity are given. The numerical examples show that the method is feasible and effective for solving the singular perturbation problem with boundary layers numerically.展开更多
文摘2008年9月24-26日，受奥地利Wolfgang Pauli Institute的邀请，笔者参加了由维也纳大学Wolfgang Pauli Institute组织举办的“The Gross-Pitaevskii Equation and Its Application for BEC in Optical Lattices”国际研讨会。
文摘1999年10月25至29日,我应邀参加了在日本千叶大学举办的第12届区域分解国际会议。会上著名的美国数学家Roland Glowinski和法国数学家Jacques-Louis Lions分别作了题为"Embedding Methods for Flow with Moving Rigid Boundaries,Application to theDirect Numerical Simulation of Sedimentation and Fluidization Phenomena"和"VirtualControl and Applications"的特邀报告。
基金Doctoral Program Foundation ofHigher Education of China
文摘A Wavelet-Galerkin method is proposed to solve the singular perturbation problem with boundary layers numerically. Because there are boundary layers in the solution of the singular perturbation problem, the approximation spaces with different scale wavelets and boundary bases are chosen. In addition, the computation of the inner integrals is transformed to an eigenvalue problem. Therefore, a high accuracy method with reasonable computation is obtained. On the other hand, there is an explicit diagonal preconditioning which makes the condition number of the stiff matrix become bounded by a constant. The error estimate of the Wavelet-Galerkin method and the analysis of the computation complexity are given. The numerical examples show that the method is feasible and effective for solving the singular perturbation problem with boundary layers numerically.
