Molecular Surface Mesh Smoothing with Subdivision

Khan, Dawar; Gui, Sheng; Cheng, Zhanglin

doi:10.1007/978-3-031-50072-5_19

Cited by 1 publication

(2 citation statements)

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“…However, efficiently generating high-quality biomolecular meshes via the entire toolchain involves a laborious process with a significant level of manual intervention. 33,36,37 Thus, we aim to find a new strategy that does not rely on highquality molecular surface meshing while ensuring the accuracy of the numerical results. From the analysis of the PBE (see, for example, ref 1), the electrostatic potential ϕ can be split into two components: ϕ = G + ϕ r .…”

Section: Introductionmentioning

confidence: 99%

“…More details can be found in the literature. , With this toolchain, we have successfully generated meshes for many protein systems and performed finite element simulations on them. However, efficiently generating high-quality biomolecular meshes via the entire toolchain involves a laborious process with a significant level of manual intervention. ,, …”

Section: Introductionmentioning

confidence: 99%

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An Unfitted Finite Element Poisson–Boltzmann Solver with Automatic Resolving of Curved Molecular Surface

Liu,

Gui,

et al. 2024

J. Phys. Chem. B

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So far, the existing Poisson−Boltzmann (PB) solvers that accurately take into account the interface jump conditions need a pregenerated body-fitted mesh (molecular surface mesh). However, qualified biomolecular surface meshing and its implementation into numerical methods remains a challenging and laborious issue, which practically hinders the progress of further developments and applications of a bunch of numerical methods in this field. In addition, even with a molecular surface mesh, it is only a low-order approximation of the original curved surface. In this article, an interface-penalty finite element method (IPFEM), which is a typical unfitted finite element method, is proposed to solve the Poisson−Boltzmann equation (PBE) without requiring the user to generate a molecular surface mesh. The Gaussian molecular surface is used to represent the molecular surface and can be automatically resolved with a high-order approximation within our method. Theoretical convergence rates of the IPFEM for the linear PB equation have been provided and are well validated on a benchmark problem with an analytical solution (we also noticed from numerical examples that the IPFEM has similar convergence rates for the nonlinear PBE). Numerical results on a set of different-sized biomolecules demonstrate that the IPFEM is numerically stable and accurate in the calculation of biomolecular electrostatic solvation energy.

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Section: Introductionmentioning

confidence: 99%