The Dual Reciprocal B-Spline Wavelet Boundary Element Method for Non-homogeneous Potential Problems

This paper aims to propose a dual reciprocity wavelet boundary element method (DR WBEM) to study non-homogeneous potential problems. For non-homogeneous potential problems, the scaling functions of the B-spline wavelet on the interval (BSWI) are applied to replace traditional polynomial interpolation. The boundary variables represented by wavelet expansion coefficients are transformed from wavelet space to physical space through non-singular transformation matrices. To ensure good boundary compatibility, the second-order scaling functions are used to approximate geometric boundaries. The dual reciprocity method is applied to handle the domain integral terms arising from the use of homogeneous potential problems fundamental solutions, maintaining the advantage of requiring only discretized boundaries for the boundary element method. Numerical examples show that the double reciprocity B-spline wavelet boundary element method achieves superior performance compared to the traditional boundary element method in dealing with non-homogeneous potential problems.