Optimal preconditioners on solving the Poisson equation with Neumann boundary conditions

Lee, Byungjoon; Min, Chohong

doi:10.1016/j.jcp.2021.110189

Cited by 3 publications

(2 citation statements)

References 18 publications

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“…Tests using the universal but simple-minded Jacobi preconditioning yielded no improvements. While preconditioning is generally advised to improve the convergence of CG, it is still a subject of active research in the context of the Poisson equation with Neumann BCs, 29 let alone mixed boundary conditions.…”

Section: Theory and Methodsmentioning

confidence: 99%

Fast and Accurate Multidimensional Free Energy Integration

Hénin

2021

J. Chem. Theory Comput.

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Enhanced sampling and free energy calculation algorithms of the thermodynamic integration family (such as the adaptive biasing force (ABF) method) are not based on the direct computation of a free energy surface but rather of its gradient. Integrating the free energy surface is nontrivial in dimensions higher than one. Here, the author introduces a flexible, portable implementation of a Poisson equation formalism to integrate free energy surfaces from estimated gradients in dimensions 2 and 3 using any combination of periodic and nonperiodic (Neumann) boundary conditions. The algorithm is implemented in portable C ++ and provided as a standalone tool that can be used to integrate multidimensional gradient fields estimated on a grid using any algorithm, such as umbrella integration as a post-treatment of umbrella sampling simulations. It is also included in the implementation of ABF (and its extended-system variant eABF) in the Collective Variables Module, enabling the seamless computation of multidimensional free energy surfaces within ABF and eABF simulations. A Python-based analysis toolchain is provided to easily plot and analyze multidimensional ABF simulation results, including metrics to assess their convergence. The Poisson integration algorithm can also be used to perform Helmholtz decomposition of noisy gradient estimates on the fly, resulting in an efficient implementation of the projected ABF (pABF) method proposed by Lelievre and co-workers. In numerical tests, pABF is found to lead to faster convergence with respect to ABF in simple cases of low intrinsic dimension but seems detrimental to convergence in a more realistic case involving degenerate coordinates and hidden barriers due to slower exploration. This suggests that variance reduction schemes do not always yield convergence improvements when applied to enhanced sampling methods.

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Section: Theory and Methodsmentioning

confidence: 99%

Fast and Accurate Multidimensional Free Energy Integration

Hénin

2021

J. Chem. Theory Comput.

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“…A Step 4 Poisson equation solving. After obtaining the vector field shown, the solution of Poisson's equation is solved using iterations of the Laplace matrix [31]. Then:…”

Section: Poisson Surface Reconstruction Converts the Work Of Surface ...mentioning

confidence: 99%

A Study on the Development of Professional Training in Physical Education in Colleges and Universities under Information Technology

Zhang,

2023

Applied Mathematics and Nonlinear Sciences

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The deep integration of technology and college sports professional training can effectively stimulate the enthusiasm of students for sports training and, to a certain extent, reduce the danger of professional training. This paper first introduces the virtual reality technology under information technology to build a virtual sports training framework, and through virtual sports training, can effectively realize the immersive training of participants. Secondly, we use LiDAR to obtain point cloud data for the virtual scene of college sports professional training and reconstruct the virtual scene using the Poisson surface 3D reconstruction algorithm. Based on the OpenPose human posture estimation algorithm, the training movements of students in the virtual scene are identified, which helps coaches to better formulate standardized training movements. Finally, to verify the effectiveness of the method given in this paper in college physical education training, a series of quantitative analyses was carried out. The results show that the training loss of the Poisson surface 3D reconstruction algorithm is about 0.087 after 180 rounds of iteration, the verification accuracy is about 87.62%, and the training loss of the OpenPose algorithm is about 0.04% when the number of iterations reaches about 130 times. After using VR technology to carry out professional training in sports, the score of students in the experimental group in terms of active learning interest is 4.487±0.324 points, which is about 1 point higher than that of the control group. Virtual reality technology can effectively promote the innovation and reform of sports professional training in colleges and universities, enhance the student’s interest in learning sports training, and provide a guarantee for improving students’ physical quality.

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Poisson Solver for Upscaling the Physical Properties of Porous Materials

Khachkova

Lisitsa

2021

Computational Science and Its Applications – ICCSA 2021

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Optimal preconditioners on solving the Poisson equation with Neumann boundary conditions

Cited by 3 publications

References 18 publications

Fast and Accurate Multidimensional Free Energy Integration

Fast and Accurate Multidimensional Free Energy Integration

A Study on the Development of Professional Training in Physical Education in Colleges and Universities under Information Technology

Poisson Solver for Upscaling the Physical Properties of Porous Materials

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