This paper gives a refinement of a general method for the construction of multivariate numerical integration formulas that use merely boundary points as evaluation points. Boundary quadrature formulas are constructed by using the optimal dimensionality-reducing expansion and quadrature formulas for the integrals of periodic functions with wavelet weights. Boundary quadrature formulas are also used to solve boundary value problems of partial differential equations.
"Construction of boundary quadrature formulas using wavelets", Proc. SPIE 2569, Wavelet Applications in Signal and Image Processing III, (1 September 1995); doi: 10.1117/12.217636; https://doi.org/10.1117/12.217636