多尺度辛格式求解复杂介质波传问题

在哈密顿体系中引入小波分析，利用辛格式和紧支正交小波对波动方程的时、空间变量进行联合离散近似，构造了多尺度辛格式——MSS（Multiresolution Symplectic Scheme）．将地震波传播问题放在小波域哈密顿体系下的多尺度辛几何空间中进行分析，利用小波基与辛格式的特性，有效改善了计算效率，可解决波动力学长时模拟追踪的稳定性与逼真性．

Multiresolution Symplectic Scheme for Wave Propagation in Complex Media

A fast adaptive symplectic algorithm named multiresolution symplectic scheme (MSS) was first presented to solve the problem of the wave propagation in complex media, using the symplectic scheme and Daubechies' compactly supported orthogonal wavelet transform to respectively discretise the time and space dimension of wave equation. The problem was solved in multiresolution symplectic geometry space under the conservative Hamiltonian system rather than the traditional Lagrange system. Due to the fascinating properties of the wavelets and symplectic scheme, MSS is a promising method because of little computational burden, robustness and reality of long_time simulation.