1,622 research outputs found
A multigroup diffusion solver using pseudo transient continuation for a radiation-hydrodynamic code with patch-based AMR
We present a scheme to solve the nonlinear multigroup radiation diffusion
(MGD) equations. The method is incorporated into a massively parallel,
multidimensional, Eulerian radiation-hydrodynamic code with adaptive mesh
refinement (AMR). The patch-based AMR algorithm refines in both space and time
creating a hierarchy of levels, coarsest to finest. The physics modules are
time-advanced using operator splitting. On each level, separate level-solve
packages advance the modules. Our multigroup level-solve adapts an implicit
procedure which leads to a two-step iterative scheme that alternates between
elliptic solves for each group with intra-cell group coupling. For robustness,
we introduce pseudo transient continuation (PTC). We analyze the magnitude of
the PTC parameter to ensure positivity of the resulting linear system, diagonal
dominance and convergence of the two-step scheme. For AMR, a level defines a
subdomain for refinement. For diffusive processes such as MGD, the refined
level uses Dirichet boundary data at the coarse-fine interface and the data is
derived from the coarse level solution. After advancing on the fine level, an
additional procedure, the sync-solve (SS), is required in order to enforce
conservation. The MGD SS reduces to an elliptic solve on a combined grid for a
system of G equations, where G is the number of groups. We adapt the partial
temperature scheme for the SS; hence, we reuse the infrastructure developed for
scalar equations. Results are presented. (Abridged)Comment: 46 pages, 14 figures, accepted to JC
Automorphic equivalence of the representations of Lie algebras
We prove that if a field k is infinite, char(k)=0 and k has not nontrivial
automorphisms then automorphic equivalence of representations of Lie algebras
coincide with geometric equivalence. We achieve our result by consideration of
1-sorted objects. We suppose that our method can be perspective in the further
researches.Comment: 28 page
Free Malcev algebra of rank three
We find a basis of the free Malcev algebra on three free generators over a
field of characteristic zero. The specialty and semiprimity of this algebra are
proved. In addition, we prove the decomposability of this algebra into
subdirect sum of the free Lie algebra rank three and the free algebra of rank
three of variety of Malcev algebras generated by a simple seven-dimensional
Malcev algebra
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