Adaptive Wavelet Methods for Boundary Integral Equations

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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.