Numerical methods for energy flux of temperature diffusion equation on unstructured meshes

Lv, Guixia; Shen, Longjun; Shen, Zhijun

doi:10.1002/cnm.1171

Cited by 11 publications

(7 citation statements)

References 18 publications

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“…The resulting scheme provides convergence rates that is higher than one, but does not satisfy the linearity preserving criterion. The fifth type of explicit weights is given in [32] through a finite point method and is linearity preserving, however, it is still discontinuity dependent and mesh topology dependent. As shown in Fig.…”

Section: The Former Weights For the Vertex Unknownsmentioning

confidence: 99%

“…To our knowledge, there exists in the literature some ways to find the weights for the nine-point scheme, such as by Taylor expansion [22,43], by a straightforward bilinear interpolation [22,43] or its modification [5], by finite point method [32] or by some others [47]. All these methods are either discontinuity dependent or mesh topology dependent.…”

Section: Introductionmentioning

confidence: 99%

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A nine-point scheme with explicit weights for diffusion equations on distorted meshes

Gao

2011

Applied Numerical Mathematics

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Section: The Former Weights For the Vertex Unknownsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A nine-point scheme with explicit weights for diffusion equations on distorted meshes

Gao

2011

Applied Numerical Mathematics

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“…Meshing is a crucial component in geometric and mechanical analysis [58,[87][88][89][90][91][92][93][94]. In this work, we employ triangle meshes for the geometric representation of macromolecules.…”

Section: Curvature Estimates On Triangle Meshesmentioning

confidence: 99%

Geometric modeling of subcellular structures, organelles, and multiprotein complexes

Feng

Xia

Tong

et al. 2012

Numer Methods Biomed Eng

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SUMMARY Recently, the structure, function, stability, and dynamics of subcellular structures, organelles, and multi-protein complexes have emerged as a leading interest in structural biology. Geometric modeling not only provides visualizations of shapes for large biomolecular complexes but also fills the gap between structural information and theoretical modeling, and enables the understanding of function, stability, and dynamics. This paper introduces a suite of computational tools for volumetric data processing, information extraction, surface mesh rendering, geometric measurement, and curvature estimation of biomolecular complexes. Particular emphasis is given to the modeling of cryo-electron microscopy data. Lagrangian-triangle meshes are employed for the surface presentation. On the basis of this representation, algorithms are developed for surface area and surface-enclosed volume calculation, and curvature estimation. Methods for volumetric meshing have also been presented. Because the technological development in computer science and mathematics has led to multiple choices at each stage of the geometric modeling, we discuss the rationales in the design and selection of various algorithms. Analytical models are designed to test the computational accuracy and convergence of proposed algorithms. Finally, we select a set of six cryo-electron microscopy data representing typical subcellular complexes to demonstrate the efficacy of the proposed algorithms in handling biomolecular surfaces and explore their capability of geometric characterization of binding targets. This paper offers a comprehensive protocol for the geometric modeling of subcellular structures, organelles, and multiprotein complexes.

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“…is a suitably defined mean diffusion tensor on B 1 B 2 , the expression for the discrete flux (10) leads to that in [13]. In addition, (10) is equivalent to formula (8) in [23] by some tedious calculus, but [23] is contributed to a cell-vertex scheme in which the vertex unknowns are involved, whereas in this paper a cell-centered scheme will be given by eliminating the vertex unknowns in (10). The vertex unknown in the discrete flux (12) will be eliminated by expressing it as a linear combination of the neighboring cell-centered unknowns, which will be discussed in the subsequent subsections.…”

Section: Remark 21mentioning

confidence: 99%

“…The coefficients in the linear combinations are known as the weights. To our knowledge, there exists in the literature some ways to find the weights for the vertex unknowns, such as by Taylor expansion [13,24], by a straightforward bilinear interpolation [25] or its modification [4], by finite point method [17] or by some others [28]. Most of these methods are obtained in the isotropic case, and all these methods are either discontinuity dependent or mesh topology dependent.…”

mentioning

confidence: 99%

A linearity‐preserving cell‐centered scheme for the heterogeneous and anisotropic diffusion equations on general meshes

Gao

2010

Numerical Methods in Fluids

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Abstract. In this paper a finite volume scheme for the heterogeneous and anisotropic diffusion equations is proposed on general, possibly nonconforming meshes. This scheme has both cell-centered unknowns and vertex unknowns. The vertex unknowns are treated as intermediate ones and are expressed as a linear weighted combination of the surrounding cell-centered unknowns, which reduces the scheme to a completely cell-centered one. We propose two types of new explicit weights which allow arbitrary diffusion tensors, and are neither discontinuity dependent nor mesh topology dependent. Both the derivation of the scheme and that of new weights satisfy the linearity preserving criterion which requires that a discretization scheme should be exact on linear solutions. The resulting new scheme is called as the linearity preserving cell-centered scheme and the numerical results show that it maintain optimal convergence rates for the solution and flux on general polygonal distorted meshes in case that the diffusion tensor is taken to be anisotropic, at times heterogeneous, and/or discontinuous.

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Numerical methods for energy flux of temperature diffusion equation on unstructured meshes

Cited by 11 publications

References 18 publications

A nine-point scheme with explicit weights for diffusion equations on distorted meshes

A nine-point scheme with explicit weights for diffusion equations on distorted meshes

Geometric modeling of subcellular structures, organelles, and multiprotein complexes

A linearity‐preserving cell‐centered scheme for the heterogeneous and anisotropic diffusion equations on general meshes

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