波动方程正反演的小波多重网络方法

By combining wavelet method with multi-grid ethod,.wavelet-Galerkin-multigrid method is constructed for wave equation simulation,.therefore the computational efficiency is greatly improved. A dynamically adaptive.wavelet collocation algorithm is designed for two-dimensional wave equation, it can.dynamically trace oscillation or oddness. For the inverse problem of wo-dimensional wave equation, the well log is introduced, thus a widely convergent Generalized.Pulse-Spectrum-Technique is constructed. The inversion process is stable, widely.convergent and costs less computational effort. The convergence analysis is given for the Landweber iteative method when the nonlinear operator and its right hand are all non-exact. The method is applied to the inverse problem of one-dimensional wave equation. Some preliminary results are given on the Pride theory for sound-electricityeffect.

本项目将开展一、二维波动方程正反演的小波多重网格方法研究。主要内容包括：波动方程正演的完全自适应小波方法的设计；小波.—多重网格方法的构造；波动方程反演的小波—多重网格—大范围收敛广义脉冲谱方法研究；上述方法均将完成相应的应用软件及数值实验，反演方法将完成收敛性分析。此项研究将填补空白，具有理论与应用的双重重要意义。