论文信息 - Exploiting Symmetry in Solving Linear Equations

Exploiting Symmetry in Solving Linear Equations

Recent efforts have shown the efficacy of applying group theoretical methods to the numerical treatment of certain partial differential equations via finite differences and finite elements, see [2, 3, 4, 5, 7, 8, 9, 12]. The articles, e.g., [4, 7], have demonstrated that the use of discretizations of partial differential equations which are suitably adapted to respect symmetry properties yield highly useful decompositions which can reduce computational effort, improve the numerical conditioning of problems, and significantly facilitate the study of bifurcation behavior at singularities. The results in the present paper extend those in [1, 4] via a systematic introduction of group representation theory.

K. Georg | R. Miranda

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