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The Local and Parallel Finite Element Scheme for Electric Structure Eigenvalue Problems

机译：The Local and Parallel Finite Element Scheme for Electric Structure Eigenvalue Problems

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摘要

In this paper, an efficient multiscale finite element method via local defect-correction technique is developed. This method is used to solve the Schrodinger eigenvalue problem with three-dimensional domain. First, this paper considers a three-dimensional bounded spherical region, which is the truncation of a three-dimensional unbounded region. Using polar coordinate transformation, we successfully transform the three-dimensional problem into a series of one-dimensional eigenvalue problems. These one-dimensional eigenvalue problems also bring singularity. Second, using local refinement technique, we establish a new multiscale finite element discretization method. The scheme can correct the defects repeatedly on the local refinement grid, which can solve the singularity problem efficiently. Finally, the error estimates of eigenvalues and eigenfunctions are also proved. Numerical examples show that our numerical method can significantly improve the accuracy of eigenvalues.

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    Lin Fubiao; Cao Junying; Liu Zhixin;

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    Guizhou Minzu Univ, Sch Data Sci & Informat Engn, Guiyang 550025, Peoples R China;

    Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550025, Peoples R China|Guizhou Univ Finance & Econ, Guizhou Key Lab Big Data Stat Anal, Guiyang 550025, Guizhou, Peoples R China;

    Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550025, Peoples R China;

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