In this approach, the cut runs through elements. Those elements, which are divided by the cut, are duplicated on each neighbouring partition and are marked as shared elements. The elements belonging solely to a particular partition will be referred to as local ones. The geometry of a duplicated element is described using node(s) assigned to the same partition and by node(s) owned by a different partition, which local copies are called remote-copy nodes (see Fig. 2). The remote-copy nodes on a particular partition are assigned with local DOFs. In order to guarantee the correctness of the solution, a modification of the single processor algorithm in terms of exchange of remote-copy node internal forces values has to be made. The nodal internal forces are computed only for local partition nodes. The nodal internal forces for remote-copy nodes are received from the partitions owning the counterparts of remote-copy local node. Thus, each partition has to set all remote-copy node internal forces according to the values received from remote partitions, where corresponding remote node counterparts are local nodes. Similarly, each partition has to send its local node values to other partitions, where corresponding remote copies exist. The correct masses for remote-copy nodes must be established by an operation analogous to internal force contribution exchange before the time-stepping algorithm starts. The solution algorithm, extended by mass and internal forces exchange for remote-copy nodes, is summarized in Table 2.
The process of mutual exchange of internal nodal force values must be repeated for each time step to guarantee the correctness of the solution. In order to efficiently handle this exchange, each partition assembles its send and receive communication maps for all partitions. The send map contains the local node numbers, for which the exchange, in terms of sending the local nodal values to a particular remote partition, is required. The receive map contains the remote-copy node numbers, for which the exchange, in terms of receiving the nodal values from a particular remote partition, is required.