can be used for a transient simulation by any standard time stepping algorithm. Note that the primal assembly technique is analogue to assembly of super-elements in finite element methods. Dual assembly In the dual assembly formulation the global set of DoFs is retained and an assembly is made by a priori satisfying the equilibrium condition . Again, the Lagrange multipliers represent the interface forces connecting the DoFs at the interface. As these are unknowns, they are moved to the left-hand side of the equation. In order to satisfy compatibility, a second equation is added to the system, now operating on the displacements: The dually assembled system can be written in matrix form as: This dually assembled system can also be used in a transient simulation by means of a standard time stepping algorithm. Substructuring in the frequency domain In order to write out the equations for frequency based substructuring (FBS), the dynamic equilibrium first has to be put in the frequency domain. Starting with the dynamic equilibrium in the physical domain: Taking the Fourier transform of this equation gives the dynamic equilibrium in the frequency domain: Matrix is referred to as the dynamic stiffness matrix. This matrix consists of the complex-valued frequency-dependent functions that describe the force required to generate a unit harmonic displacement at a certain DoF. The inverse of the matrix is defined as and yields the more intuitive admittance notation: The receptance matrix contains the frequency response functions (FRFs) of the structure which describe the displacement response to a unit input force. Other variants of the receptance matrix are the mobility and accelerance matrix, which respectively describe the velocity and acceleration response. The elements of the dynamic stiffness (or impedance in general) and receptance (or admittance in general) matrix are defined as follows: Coupling in the frequency domain In order to couple two substructures in the frequency domain, use is made of the admittance and impedance matrices of both substructures. Using the definition of substructures A and B as introduced previously, the following impedance and admittance matrices are defined (note that the frequency dependency is omitted from the terms to improve readability): The two admittance and impedance matrices can be put in block diagonal form in order to align with the global set of DoFs : The off-diagonal zero terms show that at this point no coupling is present between the two substructures. In order to create