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Projection Improved SPAI Preconditioner for FGMRES

Numerical Mathematics(Theory,Methods and Applications) 2023年第4期16卷 1035-1052页

作者： Mingguang Geng Shuli Sun LTCS Department of Mechanics and Engineering ScienceCollege of EngineeringPeking UniversityBeijing 100871China

Krylov subspace methods are widely used for solving sparse linear algebraic equations,but they rely heavily on preconditioners,and it is difficult to find an effective preconditioner that is efficient and stable for all *** this paper,a novel projection strategy including the orthogonal and the oblique projection is proposed to improve the preconditioner,which can enhance the efficiency and stability of *** proposed strategy can be considered as a minimization process,where the orthogonal projection minimizes the energy norm of error and the oblique projection minimizes the 2-norm of the residual,meanwhile they can be regarded as approaches to correct the approximation by solving low-rank inverse of the *** strategy is a wide-ranging approach and provides a way to transform the constant preconditioner into a variable *** paper discusses in detail the projection strategy for sparse approximate inverse(SPAI)preconditioner applied to flexible GMRES and conducts the numerical test for problems from different *** results show that the proposed projection strategy can significantly improve the solving process,especially for some non-converging and slowly convergence systems.

关键词： Generalized minimal residual preconditioner sparse approximate inverse oblique projection orthogonal projection

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Clustering solver for displacement-based numerical homogenization

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Theoretical & Applied Mechanics Letters 2022年第3期12卷 207-212页

作者： Shaoqiang Tang Xi Zhu HEDPS CAPT and LTCSCollege of EngineeringPeking UniversityBeijing 100871China

Based on strain-clustering via k-means,we decompose computational domain into clusters of possibly disjoint *** cells in each cluster take the same strain,we reconstruct displacement *** further propose a new way to condensate the governing equations of displacement-based finite element method to reduce the complexity while maintain the *** examples are presented to illustrate the efficiency of the clustering *** convergence studies are performed for the *** complexities which is common in existing clustering analysis methods,the proposed clustering solver is easy to implement,particularly for numerical homogenization using commercial softwares.

关键词： Clustering Finite element method Numerical homogenization

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Effect of geometric parameters and grazing incidence on magnetic polaritons excited in 1D multi-groove gratings

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Science China(Technological Sciences) 2021年第8期64卷 1589-1598页

作者： Su ChengShuai Fu CeJi LTCS and Department of Mechanics and Engineering Science College of EngineeringPeking UniversityBeijing100871China

In this paper,effect of geometric parameters and grazing incidence on excitation of magnetic polaritons(MPs)in a 1D multigroove grating with different groove depths made of silver was *** results reveal that when the distance between grooves is sufficiently small,the resonance wavelengths of MPs excited in the grooves of unequal depths exhibit red shift with decrease of the distance,contrary to the case with equal groove *** shift of the MP resonance wavelengths was explained with the LC circuit ***,it was found that the resonance wavelengths of MPs depend linearly on the groove depths except when the difference between the groove depths is *** the grooves have equal depths,a large drop of the absorptance can occur due to the interaction and cancellation of the electric field vectors in the region between the ***,the results show that when a TM wave is at grazing incidence,MPs can be excited simultaneously in the grooves at a blue-shifted wavelength due to reduction of the effective capacitance,resulting in a dramatic enhancement of the ***,the results in this work may provide useful guidance in the design of wavelength-selective absorbers based on MPs.

关键词： multi-groove grating magnetic polaritons absorptance LC circuit model

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Displacement reconstruction and strain refinement of clustering-based homogenization

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Theoretical & Applied Mechanics Letters 2021年第6期11卷 343-349页

作者： Lei Zhang Shaoqiang Tang HEDPS and LTCS College of EngineeringPeking UniversityBeijing 100871China

Recently proposed clustering-based methods provide an efficient way for homogenizing heterogeneous materials,yet without concerning the detailed distribution of the mechanical *** coarse fields of the clustering-based methods as an initial guess,we develop an iteration strategy to fastly and accurately resolve the displacement,strain and stress based on the Lippmann-Schwinger equation,thereby benefiting the local mechanical analysis such as the detection of the stress *** a simple elastic case,we explore the convergence of the method and give an instruction for the selection of the reference *** tests show the efficiency and fast convergence of the reconstruction method in both elastic and hyper-elastic materials.

关键词： Homogenization Self-consistent clustering analysis Lippmann-Schwinger equation Green’s function

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Experimental study of Young’s modulus and internal friction of low-melting-point gallium using modified piezoelectric ultrasonic composite oscillator technique

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Theoretical & Applied Mechanics Letters 2025年第2期15卷 163-167页

作者： Chuanyang Jiang Wenshuo Bai Mingyu Xie Xiangpeng Li Jiao Yu Hao Huang Lu Cao Faxin Li LTCS and College of Engineering Peking UniversityBeijing 100871China Center for Applied Physics and Technology Peking UniversityBeijing 100871China College of Mechanical and Electrical Engineering Soochow UniversitySuzhou 215000China Liaoning Provincial Key Laboratory of Novel Micro-Nano Functional Materials Liaoning Petrochemical UniversityFushun 113001China National Innovation Institute of Defence Technology Academy of Military ScienceBeijing 100071China

As an emerging multifunctional metal with the lowest melting point except for mercury,gallium combines a wide range of metallic and non-metallic elements to form advanced semiconductors critically important in cutting-edge ***,due to its low melting point and poor machinability,it is quite difficult to simultaneously characterize gallium’s elastic properties and damping characteristics using conventional methods,which is es-sential in designing and evaluating gallium-based ***,developing effective methods to achieve accurate and efficient measurements of Young’s modulus and corresponding internal friction of gallium is of great *** letter studies simultaneous measurements of the variations in Young’s modulus and internal friction of gallium at varying temperatures by employing the modified piezoelectric ultrasonic composite oscil-lator *** the explicit theoretical formulas with the measured resonance and anti-resonance frequencies,it has been discovered that Young’s modulus undergoes an approximately linear decrease as the temperature rises,declining from 83.84 GPa at -70℃ to 79.37 GPa at 20℃.Moreover,like aluminum in the same Group ⅢA of the Periodic Table of Elements and exhibits a grain-boundary internal friction peak,gallium displays a longitudinal internal friction peak at approximately-12°C,with the peak value reaching 1.77×10^(-3).This basic research on gallium’s elastic properties and damping characteristics under low-temperature condi-tions will inspire further explorations of the mechanical properties of a diverse spectrum of low-melting-point functional materials and facilitate applications of gallium-based structures under complex conditions.

关键词： Gallium Piezoelectric transducer Electromechanical impedance Young’s modulus Internal friction

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A Moving Boundary Smoothing Method and Extension in Meshless Dynamic Boundary Problems

SSRN

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SSRN 2024年

作者： Xu, Haobin LTCS Department of Mechanics and Engineering Sciences College of Engineering Peking University Beijing100871 China

The dynamic boundary problem in meshless methods is extensively investigated, focusing on rapidly and effectively moving particles along with the boundary motion. Recognizing the limitations of sine function interpolation and background mesh mapping, as well as the complexities of reconstruction methods, we hence propose a moving boundary smoothing method to address these challenges. This method leverages mesh deformation and smoothing methods commonly occurred in dynamic boundary and mesh optimization problems used in mesh based methods. By integrating concepts akin to mesh deformation and smoothing, it facilitates particle movement with boundary motion or deformation and optimizes particle distribution post-movement. Additionally, by relaxing the outer boundary constraint and introducing a pulling operation, this method can be extended to a relaxed boundary reconstruction approach for a further boundary movement. Through comprehensive comparisons with other methods, both the proposed method and its extension demonstrate significant capability in handling boundary movement and resulting in relatively regular particle distributions. Simulations using the NACA0012 airfoil further validate the effectiveness of the proposed approach. © 2024, The Authors. All rights reserved.

关键词： Mesh generation

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Why neural networks apply to scientific computing?

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Theoretical & Applied Mechanics Letters 2021年第3期11卷 125-129页

作者： Shaoqiang Tang Yang Yang HEDPS and LTCS College of EngineeringPeking UniversityBeijing 100871China

In recent years,neural networks have become an increasingly powerful tool in scientific *** universal approximation theorem asserts that a neural network may be constructed to approximate any given continuous function at desired *** backpropagation algorithm further allows efficient optimization of the parameters in training a neural *** by GPU’s,effective computations for scientific and engineering problems are thereby *** addition,we show that finite element shape functions may also be approximated by neural networks.

关键词： Neural networks Universal approximation theorem Backpropagation algorithm

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Energy-Based Boundary Conditions for Non-ordinary Peridynamics in Two Space Dimensions

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Multiscale Science and engineering 2023年第1期5卷 23-34页

作者： Zhu, Siqi Wang, Bonan Tang, Shaoqiang China Nuclear Power Engineering Co. Ltd. Beijing China HDPS and LTCS College of Engineering Peking University Beijing China

Energy-based boundary conditions (EBCs) are developed for 2D non-ordinary peridynamics (NOPD). Similar to the design of one-dimensional boundary conditions, we introduce Lyapunov functions and propose a set of boundary conditions which can guarantee the energy decay. By matching the dispersion relation at the long-wave limit, some of the coefficients are tuned to gain better results. Then we propose two-way boundary conditions for two-dimensional peridynamics based on EBCs. Finally, the effectiveness and stability of the proposed EBCs are demonstrated by numerical tests and energy evolution.

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Active tuning of anisotropic phonon polaritons in natural van der Waals crystals with negative permittivity substrates and its application in energy transport

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Opto-Electronic Science 2024年第6期3卷 1-19页

作者： Shuo Chen Xiaohu Wu Ceji Fu LTCS and Department of Mechanics and Engineering Science College of EngineeringPeking UniversityBeijing 100871China Shandong Institute of Advanced Technology Jinan 250100China

Phonon polaritons(PhPs)exhibit directional in-plane propagation and ultralow losses in van der Waals(vdW)crystals,offering new possibilities for controlling the flow of light at the ***,these PhPs,including their directional propagation,are inherently determined by the anisotropic crystal structure of the host *** in-plane anisotropic PhPs can be manipulated by twisting engineering,such as twisting individual vdW slabs,dynamically adjusting their propagation presents a significant *** limited application of the twisted bilayer structure in bare films further restricts its *** this study,we present a technique in which anisotropic PhPs supported by bare biaxial vdW slabs can be actively tuned by modifying their local dielectric ***,we predict that the iso-frequency contour of PhPs can be reoriented to enable propagation along forbidden directions when the crystal is placed on a substrate with a moderate negative ***,we systematically investigate the impact of polaritonic coupling on near-field radiative heat transfer(NFRHT)between heterostructures integrated with different substrates that have negative *** main findings reveal that through the analysis of dispersion contour and photon transmission coefficient,the excitation and reorientation of the fundamental mode facilitate increased photon tunneling,thereby enhancing heat transfer between ***,the annihilation of the fundamental mode hinders heat ***,we find the enhancement or suppression of radiative energy transport depends on the relative magnitude of the slab thickness and the vacuum gap ***,the effect of negative permittivity substrates on NFRHT along the[001]crystalline direction ofα-MoO3 is *** spectral band where the excited fundamental mode resulting from the negative permittivity substrates is shifted to the first Reststrahlen Band(RB 1)ofα-MoO_(3) and

关键词： anisotropic phonon polaritons forbidden direction substrate with a negative permittivity near-field energy transport

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A Uniform Accurate Boundary Treatment for the One-Dimensional Non-Local Models

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Journal of Peridynamics and Nonlocal Modeling 2023年第2期5卷 155-182页

作者： Pang, Gang Ji, Songsong Zhang, Jiwei Qian, Dong School of Mathematical Science Beihang University Beijing 100083 China HEDPS CAPT and LTCS College of Engineering Peking University Beijing 100871 China School of Mathematics and Statistics and Hubei Key Laboratory of Computational Science Wuhan University Wuhan 430072 China Department of Mechanical Engineering University of Texas at Dallas Richardson 75080-3021 TX United States

A uniform boundary treatment is proposed to construct the exact artificial boundary conditions for the one-dimensional non-local models. To this end, we first convert the governing equation of the non-local model into a semi-discretized version, and then an accurate numerical method is proposed for computing the Green’s function for the semi-discretized non-local model. These Green’s functions are then used to build the exact boundary conditions corresponding to the semi-discretized model. The numerical method is applied for three non-local models. The numerical results illustrate the efficiency of the boundary conditions. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

关键词： Boundary treatment Green’s functions Recursive relationship Semi-discretized non-local models

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