The main purpose of this paper is to give stability analysis and error estimates of the ultra-weak local discontinuous Galerkin(UWLDG)method coupled with a spectral deferred correction(SDC)temporal discretization meth...The main purpose of this paper is to give stability analysis and error estimates of the ultra-weak local discontinuous Galerkin(UWLDG)method coupled with a spectral deferred correction(SDC)temporal discretization method up to fourth order,for solving the fourth-order equation.The UWLDG method introduces fewer auxiliary variables than the local discontinuous Galerkin method and no internal penalty terms are required for stability,which is efficient for high order partial differential equations(PDEs).The SDC method we adopt in this paper is based on second-order time integration methods and the order of accuracy is increased by two for each additional iteration.With the energy techniques,we rigorously prove the fully discrete schemes are unconditionally stable.By the aid of special projections and initial conditions,the optimal error estimates of the fully discrete schemes are obtained.Furthermore,we generalize the analysis to PDEs with higher even-order derivatives.Numerical experiments are displayed to verify the theoretical results.展开更多
针对数字图像无线通信系统中低信噪比下图像质量的"门限效应",提出了一种基于tent map混沌系统的高阶量纠错编码方法。仿真实验中与LDPC(low-density parity-check)码、镜像Baker码对比发现,压缩图像经LDPC码处理后出现"...针对数字图像无线通信系统中低信噪比下图像质量的"门限效应",提出了一种基于tent map混沌系统的高阶量纠错编码方法。仿真实验中与LDPC(low-density parity-check)码、镜像Baker码对比发现,压缩图像经LDPC码处理后出现"门限效应",且信噪比低于2.2dB时,图像的峰值信噪比(peak signal to noise ratio,PSNR)急剧下降,而高阶量纠错码图像的PSNR随信噪比(signal to noise ratio,SNR)呈线性变化;与镜像Baker码相比,高阶量纠错码图像的PSNR有5dB的增益,并提高了编译码效率和带宽利用率,具有较强的纠错能力和较低的编译码复杂度。展开更多
基金supported by the NSFC(Grant No.12001171)supported by the NSFC(Grant No.12271492).
文摘The main purpose of this paper is to give stability analysis and error estimates of the ultra-weak local discontinuous Galerkin(UWLDG)method coupled with a spectral deferred correction(SDC)temporal discretization method up to fourth order,for solving the fourth-order equation.The UWLDG method introduces fewer auxiliary variables than the local discontinuous Galerkin method and no internal penalty terms are required for stability,which is efficient for high order partial differential equations(PDEs).The SDC method we adopt in this paper is based on second-order time integration methods and the order of accuracy is increased by two for each additional iteration.With the energy techniques,we rigorously prove the fully discrete schemes are unconditionally stable.By the aid of special projections and initial conditions,the optimal error estimates of the fully discrete schemes are obtained.Furthermore,we generalize the analysis to PDEs with higher even-order derivatives.Numerical experiments are displayed to verify the theoretical results.
文摘针对数字图像无线通信系统中低信噪比下图像质量的"门限效应",提出了一种基于tent map混沌系统的高阶量纠错编码方法。仿真实验中与LDPC(low-density parity-check)码、镜像Baker码对比发现,压缩图像经LDPC码处理后出现"门限效应",且信噪比低于2.2dB时,图像的峰值信噪比(peak signal to noise ratio,PSNR)急剧下降,而高阶量纠错码图像的PSNR随信噪比(signal to noise ratio,SNR)呈线性变化;与镜像Baker码相比,高阶量纠错码图像的PSNR有5dB的增益,并提高了编译码效率和带宽利用率,具有较强的纠错能力和较低的编译码复杂度。
