Computational improvement of gravitational mode calculation of basins discretised by orthogonal curvilinear grids

The present note illustrates a criterion to improve the computational capability of the approaches proposed by Beltrami et al. [Beltrami, G.M., Bargagli, A., Briganti, R., 2003. Gravitational mode calculation of basins discretised by orthogonal curvilinear grids. Ocean Engineering 30, 833-853] for the direct numerical solution of the eigenvalue problem associated to the linear shallow-water equations when adiabatic boundary conditions apply. It is shown that-given the nature of its spatial differential operator-the problem can be solved by the singular value decomposition (SVD) of the real bidiagonal matrix resulting from a previous ad hoc Householder reduction of the operator matrix image. This procedure actually requires 1/8 of the random-access memory (RAM) needed by a standard library routine to compute all the eigenvalues and eigenvectors of the matrix image of the above-mentioned differential operator. Given the intrinsic limitation of a computing-machine RAM, this procedure dramatically improves the computational capability of both the proposed approaches.