Journal
APPLIED MATHEMATICAL MODELLING
Volume 81, Issue -, Pages 457-472Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2020.01.010
Keywords
Dual interpolation boundary face method; Moving-least-squares approximation; Hermite-type approximation; Thin-wall structure; Small feature sizes
Funding
- National Natural Science Foundation of China [11772125, 11472102]
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This paper presents the dual interpolation boundary face method combined with a Hermite-type moving-least-squares approximation for solving complex two-dimensional potential problems. Compared to the standard algorithms, this combined method is better suited for structures with small feature sizes such as short edges and small chamfers. The interpolation functions, if constructed in cyclic coordinates, making it difficult to apply this new method to deal with complex structures with small feature sizes in which only one source point is assigned. The Hermite-type approximation formulated in Cartesian coordinates is able to completely overcome this obstacle by searching for source points on adjacent edges. Additionally, an improved and incomplete quadratic polynomial basis is presented to obtain an accurate algorithm for the Hermite-type approximation. We use several numerical examples to demonstrate the high accuracy and efficiency of the proposed method for solving various engineering structures with small feature sizes. (C) 2020 Elsevier Inc. All rights reserved.
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