## J. Modal Analysis of a Closed Fluid Domain (MOD 4)

In this analysis, only the pressure field is concerned. Moreover, as zero pressure and/or zero flux conditions are applied on everyboundary, the components of Y appearing in the equation are all zeros. Thus:

([H] - w2[M1]) P = 0

The code computes the eigenvalues and eigenvectors of thelinear system that are the eigenfrequencies and modes of the fluid domain. Theuser must remember that the zero flux condition is the natural condition of thefinite-element formulation and that it applies automatically to all boundaries,if no other condition is prescribed. This modal analysis can for example beused to determine the frequencies associated with singularities occurring inthe use of an external Helmholtz integral formulation (irregular frequencies). The computation is done using real values with no internal losses. This typeof analysis can be done only in double precision.