On the spectrum of the multigroup diffusion equations

Solution of 3D multigroup, linearly anisotropic scattering, criticality problems by the AN boundary-element response-matrix method

“…If the scattering is isotropic, it has been proved (Ciolini et al, 2002) that the parameters κ h are all distinct and positive. More complicate problems (anisotropic scattering and multigroup problems, other than, of course, the problems referring to multiplying systems) may involve complex eigenvalues, a circumstance that is considered in Cossa et al (2010) and Saracco et al (2012); the Q matrix of the first paper corresponds essentially to minus the Q matrix now introduced and the κ 2 eigenvalue is now replacing −B 2 . The following conclusions are drawn: (i) if κ 2 h > 0, then one must simply take for κ h the positive root of…”

“…The reference geometry of this example is that of a well known 3D benchmark problem (Smith et al, 2005). As shown in Fig.…”