In this approach, the cut runs through element sides and corresponding nodes. The nodes lying on partition boundaries are marked as shared nodes. These nodes are shared by all adjacent partitions. On each partition, the shared nodes have assigned unique local code numbers. The elements are uniquely assigned to particular partitions (see Fig. 1). In order to guarantee the correctness of the solution of the partitioned problem, a modification of the single processor algorithm is necessary. The equilibrium equations at local partition nodes are solved without any change. However, at shared nodes, one is confronted with the necessity to assemble contributions from two or more adjacent partitions. The correctness has been enforced by exchange of contributions of shared node internal forces between partitions. Each partition has to add the contributions received from neighbouring partitions to the locally assembled shared node internal force and to send its shared node contributions to neighbouring partitions. Since the partitioned domains contain only the local elements, the correct mass matrix has to be established by an analogous data exchange operation before the time-stepping algorithm starts. The solution algorithm, extended by the internal force and mass contributions exchanges for shared nodes, is presented in Table 1.
The process of mutual exchange of internal nodal force contributions 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. While the send map contains the shared node numbers, for which the exchange, in terms of sending the local contributions to a particular remote partition, is required, the receive map contains the shared node numbers, for which the exchange, in terms of receiving the contributions from a particular remote partition, is required.