A mesh-based partition of unity method for discontinuity modeling

This study explores a numerical analysis scheme, the manifold method, within the framework of the partition of unity method. The manifold method is rooted in the discrete element method and has been used in solving discrete-continuum interaction problems. At its core, two meshes are employed in an analysis: the mathematical mesh provides the nodes for building a finite covering of the solution domain and the partition of unity functions; while the physical mesh provides the domain of integration. After providing a geometric interpretation and giving a construct overview, the working of the method is illustrated with a number of examples.

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