Generating better subspaces for solving structural dynamics problems

where n is the forcing function. In our problems, the mass and stiffness matrices are symmetric with the former semidefinite and the latter being positive definite. (We have ignored the damping term for now but it will be relevant in future.) The forcing function n is a product of a vector f that specifies the spatial distribution of the force and a scalar function g(t) that governs the temporal variation, i.e., n(t) = f × g(t). The dimension n of the matrices M and K is typically large, hence we seek to reduce the size of the problem to make it computationally less intensive. We can do so by using a full rank transformation matrix T ∈ Rn×`, with orthonormal columns and with ` n, such that the projected matrices T MT and T KT retain interesting properties of the original problem. The transformation reduces the problem to an ODE in ` variables as follows: Mrv̈ +Krv = T f × g, (2)