Mathematical Sciences: Numerical Solution of Differential Equations in Mechanics

研究人员将开发和实施算法， 水波的计算机模拟，包括 波 算法将基于边界积分 公式与时间推进算法一起推进 自由的边界。 一些新的数值技术， 在应用于水波问题之前，将使用。 在 特别是，一种新的快速多电平技术将被应用于 求解积分方程，这是积分方程的主要部分。 解决方案过程 调查人员将撰写一份强有力的， 高效的计算机程序，这将被记录和放置 在公共领域不受限制地使用，例如，通过 海洋学家、工程师、流体动力学家和数值计算专家 分析机构的 调查人员将彻底验证代码 通过数值测试和数值分析， 将其结果与实验室实验进行比较。 这项工作将提高可靠性和效率， 在流体力学的计算机模拟，如出现在 离岸结构的建模，船只通过 水和潮汐能发电。 计算机的最新进展 算法将被调整和应用的第一次， 这些领域，使调查人员能够非常迅速地利用 计算机硬件 通过发展一个公开的 可用的计算机代码这项工作将有助于转移 从理论数学研究到技术 应用.

The investigators will develop and implement algorithms for the computer modelling of water waves, including the breaking of waves. The algorithms will be based on a boundary integral formulation together with a time-marching algorithm to advance the free boundary. A number of new numerical techniques, never before applied to water wave problems, will be used. In particular, a new fast multilevel technique will be applied to solve the integral equations, which is the dominant part of the solution process. The investigators will write a robust and efficient computer program, which will be documented and placed in the public domain for unrestricted use, e.g., by oceanographers, engineers, fluid dynamicists, and numerical analysts. The investigators will validate the code thoroughly both through numerical testing and numerical analysis, and will compare its results with laboratory experiments. This work will improve the reliability and efficiency of computer simulations in hydrodynamics, such as arise in the modelling of off-shore structures, movement of boats through water, and tidal energy generation. Recent advances in computer algorithms will be adapted and applied for the first time in these areas, enabling the investigators to exploit very fast computer hardware. Through the development of a publicly available computer code this work will contribute to the transfer of ideas from theoretical mathematical research to technological applications.