1. A modified multilevel algorithm for large-scale scientific and engineering computing.
- Author
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Li, Junpu, Chen, Wen, Qin, Qing-Hua, and Fu, Zhuojia
- Subjects
- *
THRESHOLDING algorithms , *ALGORITHMS , *SCIENTIFIC computing - Abstract
Abstract A modified multilevel algorithm for solving the excessive storage requirements and ill-conditioning encountered in the boundary-type discretization method is proposed. The modified multilevel algorithm is an extension of the modified dual-level algorithm from dual levels to multiple levels. The method is a kernel-independent method. The core idea is the layer-by-layer calculation and then layer-by-layer correction. Making use of a multilevel structure, the original sparse matrix of the modified dual-level algorithm breaks down into a series of smaller sparse matrices corresponding to different fine meshes. The final matrix to be solved is hereby transformed to a series of smaller sparse matrices instead of a fully-populated matrix. The preconditioning effect originating from the recursive computations among the coarse mesh and fine meshes constitutes its core competitive attribute. The method evaluates far-field contributions only by the coarse mesh and uses a gradual approach to evaluate the near-field contributions. The storage requirements and computing complexity are hereby further reduced significantly. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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