Adaptive reduced order modelling in a domain decomposition framework

This paper proposes to merge domain decomposition methods with model order reduction methods. On one side, domain decompositon methods are a well-known way to divide a large mechanical problem into several smaller pieces easier to solve. It is very suitable to parallel computing since those subproblems can be solved independently using a coarse global problem to link the solutions together. On the other side, model order reduction methods are used to reduce the size of a problem using usually projections of the space of unknows onto spaces of much smaller dimensions. This enables to solve problems faster while keeping some accuracy. In this paper, we propose to use the balancing domain decomposition method coupled with the proper orthogonal decompostion method. To save time for assembling the stiffness matrix, the hyper-reduction method will be used.