Efficient Computational Methods for Accurate Simulation of Wave Propagation

本研究项目旨在发展精确而有效的计算方法，以进行涉及有界和无界区域的波传播的大规模模拟。由此产生的方法将使声学、无损评估、地震工程、医学成像、无线通信、石油勘探和地雷探测等领域遇到的无数工程问题的解决方案得到改进。该项目的几个方面具有重要意义：在有界域中模拟波传播的情况下，一种新的色散减少技术有望在不牺牲任何精度的情况下将频域模拟的计算成本降低几个数量级。对于暂态（时域）分析，将色散减少技术与一些改进的时间步进算法相结合可以显著降低分析成本。拟议的调查还将包括误差估计研究，以使这些算法能够自适应使用，以进一步降低计算成本。由于有限元法等标准数值方法仅限于有界域问题，因此需要特殊的方法来模拟无界域中的波传播。提出了两种新的方法，一种是基于时空离散化的方法，另一种是基于连分数近似的方法。时空技术在获得高度精确的方法方面显示出希望，这种方法比现有的同等精度的方法要有效得多。基于连分数近似的初步工作表明，有可能获得高度经济而又精确的局部吸收边界条件。本研究的其他方面包括设计有效且稳定的方案来耦合无界域方法和有界域方法。预计所提出的方法的计算成本降低将能够准确和详细地模拟涉及波传播的几个重要物理过程。

: The research project is aimed at developing accurate as well as efficient computational methods for large-scale simulations involving wave propagation in bounded and unbounded domains. The resulting methods will enable improved solution of countless engineering problems encountered in the fields of acoustics, nondestructive evaluation, earthquake engineering, medical imaging, wireless communications, oil exploration and landmine detection. Several aspects of the project are significant: In the case of modeling wave propagation in bounded domains, a new dispersion reducing technique is expected to bring down the computational cost of frequency-domain simulations by several orders of magnitude without sacrificing any accuracy. For transient (time-domain) analysis, a combination of the dispersion reducing technique and some modified time-stepping algorithms could significantly reduce the cost of analysis. The proposed investigation will also include error estimation studies to enable adaptive use of these algorithms for further reduction in computational cost. Since standard numerical methods such as finite element methods are limited to bounded domain problems, special methods are necessary to model wave propagation in unbounded domains. Proposed are two new methods - one based on space-time discretizations and the other based on continued fraction approximations. Space-time techniques are showing promise in obtaining highly accurate methods that are significantly more efficient than the existing methods of comparable accuracy. Preliminary work based on continued fraction approximations indicates the possibility of obtaining highly economical, yet accurate local absorbing boundary conditions. Other aspects of this research include devising efficient and stable schemes to couple unbounded domain methods with bounded domain methods. It is expected that the computational cost reduction from the proposed methods will enable accurate and detailed simulation of several important physical processes involving wave propagation.