High-Order Embedded Interface Methods for Wave-Problems

波动问题的高阶嵌入式接口方法

• 批准号: 0074257
• 负责人: Jan Hesthaven
• 金额: $ 7万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-08-01 至 2004-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0074257&HistoricalAwards=false
• 关键词: Order; Embedded; Interface; Methods; Wave

We propose to develop a new family of stable high-order finitedifference methods suitable for the solution of wave problemsinvolving many interfaces and significant geometric complexity.These complications are addressed by embedding the computationalproblem into a Cartesian grid and formulating methods such thatthe position of the material interfaces as well as the physicalproperties of the solution across the interface is accounted forproperly to the order of the scheme. Staggered grid as well asnon-staggered grid methods will be explored with the emphasis onthe development of a rigorous mathematical foundation for theseschemes to ensure robustness and uniform stability for all grid sizes and embedded geometries. Appealing properties of embeddingmethods such as the ability to model moving interfaces and theintroduction of virtual interfaces to enhance parallel performancewill be exploited to model a variety of wave problems inelectromagnetics, acoustics, seismology, and elasticity.The increasing interest in the accurate and efficient solutionof wave-dominated problems, e.g. problems in acoustic and electromagnetics, over very long periods of time has spawned an interest in the formulation of high-order accurate computationalmethods for such problems. In this effort we propose to developa new class of computational techniques, specifically aimed atthe reliable and robust modeling of problems of a realisticsize and complexity, e.g., the modeling of the propagation ofelectromagnetic and acoustic noise and its environmental impact, andthe modeling of underground waves of interest to the oil industry.The proposed methods are unique in maintaining a very simple computational structure without sacrificing the accuracy, henceovercoming a number of well known difficulties associated withexisting methods which require some kind of automated generation ofthe computational grid on which the solution is computed.These proposed developments will enable the modeling ofvery complex and realistic scenarios and will, in combination with high-performance computing facilities for which themethods are well suited, allow for the modeling and analysisof complex wave dominated problems in a variety of areas of interestto engineers and scientists.

我们建议开发一类新的稳定高阶有限差分方法，适用于解决涉及许多界面和显着几何复杂性的波动问题。通过将计算问题嵌入笛卡尔网格并制定方法来解决这些复杂问题，以便材料界面的位置以及跨界面的解决方案的物理属性都根据方案的顺序正确考虑。将探索交错网格和非交错网格方法，重点是为这些方案开发严格的数学基础，以确保所有网格尺寸和嵌入几何形状的鲁棒性和均匀稳定性。嵌入方法的吸引人的特性，例如对移动界面进行建模的能力以及引入虚拟接口以增强并行性能，将被用来对电磁学、声学、地震学和弹性中的各种波动问题进行建模。人们对准确有效地解决波动问题越来越感兴趣。主导问题，例如声学和电磁学问题在很长一段时间内引起了人们对制定此类问题的高阶精确计算方法的兴趣。在这项工作中，我们建议开发一类新型计算技术，专门针对现实规模和复杂性问题的可靠和鲁棒建模，例如，电磁和声学噪声的传播及其环境影响的建模，以及地下波的建模所提出的方法在保持非常简单的计算结构而不牺牲准确性方面是独特的，因此克服了与现有方法相关的许多众所周知的困难，现有方法需要某种自动生成解决方案的计算网格这些拟议的发展将能够对非常复杂和现实的场景进行建模，并将与这些方法非常适合的高性能计算设施相结合，允许对工程师感兴趣的各种领域中复杂的波浪主导问题进行建模和分析和科学家。