Adaptive Wavelet Methods for Boundary Integral Equations

边界积分方程的自适应小波方法

• 批准号: 9973427
• 负责人: Yuesheng Xu
• 金额: $ 12.07万
• 依托单位: North Dakota State University Fargo
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-07-15 至 2001-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9973427&HistoricalAwards=false
• 关键词: Adaptive; Wavelet; Methods; Boundary; Integral

9973427This proposed research aims at developing adaptive fast algorithms using wavelet bases in the Galerkin, Petrov-Galerkin, collocation, product integration and quadrature methods for both linear and nonlinear boundary integral equations whose solutions may have singularities. We will also consider efficient evaluation of potentials which relates the solution of a boundary integral equation with the solution of the original boundary value problem.The primary purpose of the proposed research is to understand how wavelet bases can be employed to improve the computational efficiency of the commonly used conventional numerical methods for boundary integral equations while preserving the attractive features of the conventional methods such as high convergence order and stability. The ultimate goal of this project is to provide computationally efficient algorithms for high-performance computing in science and engineering.

9973427本研究的目的是利用小波基在Galerkin、Petrov-Galerkin、配置、积积分和正交方法中对解可能有奇异性的线性和非线性边界积分方程开发自适应快速算法。我们还将考虑将边界积分方程的解与原边值问题的解联系起来的势的有效求值。本研究的主要目的是了解如何利用小波基来提高边界积分方程常用的传统数值方法的计算效率，同时保持传统方法的高收敛阶和稳定性等吸引人的特点。该项目的最终目标是为科学和工程中的高性能计算提供计算效率高的算法。