Adaptive Wavelet Methods for Boundary Integral Equations

9973427这项研究的目的是开发自适应快速算法，使用小波基的Galerkin，Petrov-Galerkin，配置，积积分和求积方法的线性和非线性边界积分方程的解决方案可能有奇异性。 我们亦会考虑如何有效地计算将边界积分方程的解与原边值问题的解联系起来的势函数。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，同时保留传统方法的吸引人的特点，如高精度、高精度、高精度等。收敛阶和稳定性。 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。

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.