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- W4313894606 abstract "Abstract The covariant derivative is a generalization of differentiating vectors. The Euclidean derivative is a special case of the covariant derivative in Euclidean space. The covariant derivative gathers broad attention, particularly when computing vector derivatives on curved surfaces and volumes in various applications. Covariant derivatives have been computed using the metric tensor from the analytically known curved axes. However, deriving the global axis for the domain has been mathematically and computationally challenging for an arbitrary two-dimensional (2D) surface. Consequently, computing the covariant derivative has been difficult or even impossible. A novel high-order numerical scheme is proposed for computing the covariant derivative on any 2D curved surface. A set of orthonormal vectors, known as moving frames, expand vectors to compute accurately covariant derivatives on 2D curved surfaces. The proposed scheme does not require the construction of curved axes for the metric tensor or the Christoffel symbols. The connectivity given by the Christoffel symbols is equivalently provided by the attitude matrix of orthonormal moving frames. Consequently, the proposed scheme can be extended to the general 2D curved surface. As an application, the Helmholtz‐Hodge decomposition is considered for a realistic atrium and a bunny." @default.
- W4313894606 created "2023-01-10" @default.
- W4313894606 creator A5036201402 @default.
- W4313894606 date "2023-01-09" @default.
- W4313894606 modified "2023-09-25" @default.
- W4313894606 title "High-Order Method with Moving Frames to Compute the Covariant Derivatives of Vectors on General 2D Curved Surfaces" @default.
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- W4313894606 doi "https://doi.org/10.1007/s42967-022-00225-x" @default.
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