A two-dimensional (2D) boundary element method (BEM) is proposed by replacing traditional polynomial interpolation with one-dimensional (1D) scaling functions of B-spine wavelet on the interval (BSWI). Potential problem and elasticity problem are investigated by BSWI BEM. For these two problems, the boundary variables represented by coefficients of wavelets expansions are transformed from wavelet space to physical space through the nonsingular transformation matrices. To make the curve boundary able to be compatible well, the second-order scaling functions are applied to approximate geometric boundary. In addition, singular integral problems appearing in BSWI BEM are solved. Numerical examples verify that BSWI BEM has a desirable performance by comparing with conventional 2D BEM.

提出了一种二维（2D）边界元法（BEM），将传统的多项式插值替换为区间上的B-spine小波（BSWI）的一维（1D）标度函数。BSWI BEM研究了潜在问题和弹性问题。对于这两个问题，由小波展开系数表示的边界变量通过非奇异变换矩阵从小波空间变换到物理空间。为了使曲线边界能够很好地兼容，将二阶缩放函数应用于近似几何边界。此外，解决了BSWI BEM中出现的奇异积分问题。通过与传统二维边界元法的比较，数值示例验证了 BSWI 边界元法具有理想的性能。