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In [[applied mathematics]], the '''boundary particle method (BPM)''' is a truly boundary-only [[meshfree method|meshless (meshfree)]] [[collocation method|collocation technique]], in the sense that none of inner nodes are required at all in the numerical solution of nonhomogeneous [[partial differential equations]]. Numerical experiments also show that the BPM has spectral [[convergence]]. Its interpolation matrix can be symmetric and the method is easy-to-implement and free of integration and mesh. Thanks to its boundary-only merit, the BPM has clear edge over the other numerical schemes in the solution of [[optimization]] and [[inverse problems]], where only a part of boundary data is usually accessible.
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