Efficient Computational Methods for Accurate Simulation of Wave Propagation

该研究项目旨在为涉及有界和无界域中的波传播的大规模模拟开发准确和高效的计算方法。 由此产生的方法将使无数的工程问题，在声学，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领域遇到的更好的解决方案。该项目的几个方面是重要的：在有界域中建模波传播的情况下，一种新的色散减少技术有望将频域模拟的计算成本降低几个数量级，而不会牺牲任何精度。 对于瞬态（时域）分析，色散减少技术和一些修改的时间步进算法的组合可以显着降低分析的成本。 拟议的调查还将包括误差估计研究，使这些算法的自适应使用，进一步降低计算成本。由于标准的数值方法，如有限元法是有限的有界域的问题，特殊的方法是必要的模型波传播在无界域。 提出了两种新的方法-一个基于时空离散和其他基于连分式近似。 空时技术在获得高精度方法方面显示出希望，这些方法比现有的可比精度方法效率高得多。 基于连续分数近似的初步工作表明，获得高度经济，但准确的局部吸收边界条件的可能性。 本研究的其他方面包括设计有效和稳定的计划耦合无界域方法与有界域方法。预计所提出的方法的计算成本降低，将能够准确和详细的模拟涉及波传播的几个重要的物理过程。

: 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.