Complexity and accuracy of the grid-based direct-volume integration BEM for quasilinear problems

In order for the boundary element method to be competitive when compared with other methods for solving nonlinear problems, the volume integral must be evaluated accurately and efficiently. The recently proposed cell-based volume integration method evaluates the volume integral on uniform Cartesian cells and therefore avoids volume discretization of the problem domain. However, this method requires the solutions of an additional integral equation; hence its efficiency must be examined. Moreover, the accuracy of the method for the boundary integral analysis of nonlinear problems needs to be studied. In this paper, we present the complexity and accuracy analysis of the BEM coupled with the cell-based volume integration method (herein termed as the grid-based direct-volume integration BEM), for solving quasilinear problems. Various numerical examples are employed to verify the theoretical findings.