高频波传播的冻结高斯近似
Frozen Gaussian approximation for high frequency wave propagation
AI总结：
提出冻结高斯近似方法，通过积分表示和相平面渐近分析高效计算高频波传播，解决焦散和波束扩散问题，提高渐近精度。
摘要：
我们提出了用于计算高频波传播的冻结高斯近似。该方法通过积分表示来近似波动方程的解。它基于相平面上的渐近分析，提供了一种高效的计算工具。与几何光学相比，它在焦散附近提供了有效的解。与高斯束方法相比，它不仅克服了波束扩散的缺点，还提高了渐近精度。我们给出了几个数值例子，验证了冻结高斯近似在存在焦散和高斯束扩散时表现良好。
英文摘要：
We propose the frozen Gaussian approximation for computation of high frequency wave propagation. This method approximates the solution to the wave equation by an integral representation. It provides a highly efficient computational tool based on the asymptotic analysis on the phase plane. Compared to geometric optics, it provides a valid solution around caustics. Compared to the Gaussian beam method, it not only overcomes the drawback of beam spreading but also improves the asymptotic accuracy. We give several numerical examples to verify that the frozen Gaussian approximation performs well in the presence of caustics and when the Gaussian beam spreads.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
