A truly boundary-only meshfree method for inhomogeneous problems based on recursive composite multiple reciprocity technique

This study presents a novel technique called the recursive composite multiple reciprocity method (RC-MRM), to develop a truly boundary-only meshfree boundary particle method (BPM) for general inhomogeneous problems. It does not require any inner nodes to evaluate the particular solution, and thus it is a truly boundary-only numerical method. “Composite” in the RC-MRM implies that the RC-MRM employs a high-order composite differential operator rather than a high-order Laplacian operator in the standard MRM to annihilate inhomogeneous term of various types and enables the present BPM to handle a much wider variety of inhomogeneous problems, while the “recursive” algorithm in the RC-MRM significantly reduces CPU time and storage requirements of the original MRM. In addition, we also find high-order harmonic solutions of the Laplacian operator. Numerical illustrations reveals that the present BPM has rapid convergence, high accuracy and efficiency, and mathematical simplicity, through various two- and three-dimensional benchmark problems.