In the FOSLS formulation of (3.1), the Boltzmann operator is rewritten with the absorption cross-section
the space-angle FOSLS formulation is to minimize the scaled least-squares functional
For the multi-group, anisotropic scattering case, the FOSLS formulation is generalized by using the scaling operator
Two of the advantages of a FOSLS formulation are that it leads to symmetric positive-definite linear systems, and that it is endowed with a computable a posteriori error measure ().
Further notations and definitions are needed for the FOSLS functional.
For self-containment, we review some of the existing theory for the FOSLS formulation of (1.1)-(1.2).
Theory for the FOSLS formulation of (1.1)-(1.2) has been developed only for the monoenergetic, isotropic scattering form of the Boltzmann equation.
Since a FOSLS [P.sub.n] formulation of (3.1) leads to a "displacement" formulation of (4.14), [a.sub.0](u; v) = ([nabla]u,[nabla]v) and Bu = [([c.sub.1]u, [c.sub.2][nabla] * u).sup.t].
The above [P.sub.n] - h finite element discretization of the FOSLS formulation was implemented.
In this paper, we presented two system multigrid algorithms for solving the anisotropic scattering Boltzmann equation formulated as a FOSLS minimization problem.
FOSLS chair Julie Devall said: "We would welcome any ideas put forward, and would also like to hear from young people who have ideas on how Slaithwaite Station can be improved."
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