A new spectral domain technique for the calculation of eigenvalues in curvilinear coordinates

We describe a new algorithm, used to decompose the system matrices of Finite Differences and Finite Integration into their high and low spectral parts. This is done by representing the matrix in terms of a new set of basis vectors in a sub space of the solution space excluding a priori large eigenvalues. The resulting mapping is symmetric and so contains orthogonal eigenvectors. The use of this method for the calculation of resonant frequencies yields a strong reduction of the algebraic condition and the solution time