In applied mathematics, the boundary particle method (BPM) is a boundary-only meshless (meshfree) collocation technique, in the sense that none of inner nodes are required in the numerical solution of nonhomogeneous partial differential equations.
For instance, the so-called DR-BEM and MR-BEM are popular BEM techniques in the numerical solution of nonhomogeneous problems.
[citation needed] Compared with the DRM, the MRM is computationally more expensive in the construction of the interpolation matrices and has limited applicability to general nonhomogeneous problems due to its conventional use of high-order Laplacian operators in the annihilation process.
The recursive composite multiple reciprocity method (RC-MRM),[3][4] was proposed to overcome the above-mentioned problems.
[8] The method has been applied to inverse Cauchy problem associated with Poisson[9] and nonhomogeneous Helmholtz equations.