Orthogonal modes of a fully anisotropic and heterogeneous elastic medium

The aim of this short note is to give a synthetic presentation of the mathematical elements that are used to solve the elastic wave system of equations in a bounded anisotropic elastic body, in a general framework. In particular, the proof of existence of a basis of orthogonal modes is given. We explain how these modes can by used to efficiently approach dynamic problems in time or harmonic regimes.