B-Spline approximation and fast wavelet transform for an efficient evaluation of particular solutions for Poisson's equation
Based on the idea of the Dual Reciprocity Method, a numerical method has been devised to interpolate the source term of the Poisson's equation by using B-spline approximation and then use them to approximate particular solutions. The advantage of such a construction is the possibility of using the Fast Wavelet Transform to minimize the number of coefficients in the wavelet expansion. Practical concerns in the implementation of the method are discussed. Three numerical examples are presented to validate the approach.
b-spline wavelets particular solutions poisson's equation dual reciprocity method newton potential