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An Adaptive Physics-Informed Neural Network with Two-Stage Learning Strategy to Solve Partial Differential Equations
《Numerical Mathematics(Theory,Methods and Applications)》2023年第2期298-322,共25页Shuyan Shi Ding Liu Ruirui Ji Yuchao Han 
Fund for Research on National Ma-jor Research Instruments of the National Science Foundation of China(NSFC)(Grant No.62127809).
Physics-Informed Neural Network(PINN)represents a new approach to solve Partial Differential Equations(PDEs).PINNs aim to solve PDEs by integrating governing equations and the initial/boundary conditions(I/BCs)into a ...
关键词：Physics informed neural networks partial differential equations two-stage learning scientific computing 
An Efficient Cartesian Grid-Based Method for Scattering Problems with Inhomogeneous Media
《Numerical Mathematics(Theory,Methods and Applications)》2023年第2期541-564,共24页Haixia Dong Wenjun Ying Jiwei Zhang 
supported by the NSFC(Grant No.12001193),by the Scientific Research Fund of Hunan Provincial Education Department(Grant No.20B376);by the Key Projects of Hunan Provincial Department of Education(Grant No.22A033);by the Changsha Municipal Natural Science Foundation(Grant Nos.kq2014073,kq2208158).W.Ying is supported by the NSFC(Grant No.DMS-11771290);by the Science Challenge Project of China(Grant No.TZ2016002);by the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDA25000400).J.Zhang was partially supported by the National Natural Science Foundation of China(Grant No.12171376);by the Fundamental Research Funds for the Central Universities(Grant No.2042021kf0050);by the Natural Science Foundation of Hubei Province(Grant No.2019CFA007).
Boundary integral equations provide a powerful tool for the solution of scattering problems.However,often a singular kernel arises,in which case the standard quadratures will give rise to unavoidable deteriorations in...
关键词：Transmission problem inhomogeneous media Cartesian grid-based method modified fourth-order compact difference scheme fast Fourier transform preconditioned conjugate gradient solver. 
A Primal-Dual Hybrid Gradient Algorithm to Solve the LLT Model for Image Denoising被引量：1
《Numerical Mathematics(Theory,Methods and Applications)》2012年第2期260-277,共18页Chunxiao Liu Dexing Kong Shengfeng Zhu 
We propose an efficient gradient-type algorithm to solve the fourth-order LLT denoising model for both gray-scale and vector-valued images.Based on the primal-dual formulation of the original nondifferentiable model,t...
关键词：LLT model image denoising PRIMAL-DUAL 
Convergence Estimates for Some Regularization Methods to Solve a Cauchy Problem of the Laplace Equation
《Numerical Mathematics(Theory,Methods and Applications)》2011年第4期459-477,共19页T.Wei H.H.Qin H.W.Zhang 
supported by the NSF of China(10971089);the Fundamental Research Funds for the Central Universities(lzujbky-2010-k10).
In this paper,we give a general proof on convergence estimates for some regularization methods to solve a Cauchy problem for the Laplace equation in a rectangular domain.The regularization methods we considered are:a ...
关键词：Cauchy problem Laplace equation regularization methods convergence estimates 
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