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CONVERGENCE ANALYSIS OF SOME FINITE ELEMENT PARALLEL ALGORITHMS FOR THE STATIONARY INCOMPRESSIBLE MHD EQUATIONS

Journal of computational mathematics 2024年第1期42卷 49-70页

作者： Xiaojing Dong Yinnian He Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China Institute of Applied Physics and Computational Mathematics Beijing 100088China School of Mathematics and Statistics Xi'an Jiaotong UniversityXi'an 710049China

By combination of iteration methods with the partition of unity method(PUM),some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics(MHD)with different physical parameters are presented and *** algorithms are highly *** first,a global solution is obtained on a coarse grid for all approaches by one of the iteration *** parallelized residual schemes,local corrected solutions are calculated on finer meshes with overlapping *** subdomains can be achieved flexibly by a class of *** proposed algorithm is proved to be uniformly stable and ***,one numerical example is presented to confirm the theoretical findings.

关键词： Partition of unity method Local and parallel algorithm Finite element method Iteration methods Magnetohydrodynamics

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An Algebraic Multigrid-Based Physical Factorization Preconditioner for the Multi-Group Radiation Diffusion Equations in Three Dimensions

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Numerical mathematics(Theory,Methods and Applications) 2023年第2期16卷 410-432页

作者： Xiaoqiang Yue Zekai Zhang Xiaowen Xu Shuying Zhai Shi Shu National Center for Applied Mathematics in Hunan Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationHunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtan 411105China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100094China School of Mathematical Sciences Huaqiao UniversityQuanzhou 362021China.

The paper investigates the robustness and parallel scaling properties of a novel physical factorization preconditioner with algebraic multigrid subsolves in the iterative solution of a cell-centered finite volume discretization of the threedimensional multi-group radiation diffusion *** key idea is to take advantage of a particular kind of block factorization of the resulting system matrix and approximate the left-hand block matrix selectively spurred by parallel processing *** spectral property of the preconditioned matrix is then *** practical strategy is considered sequentially and in ***,numerical results illustrate the numerical robustness,computational efficiency and parallel strong and weak scalabilities over the real-world structured and unstructured coupled problems,showing its competitiveness with many existing block preconditioners.

关键词： Radiation diffusion equations physical factorization preconditioning algebraic multigrid parallel and distributed computing

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αSetup-PCTL:An Adaptive Setup-Based Two-Level Preconditioner for Sequence of Linear Systems of Three-Temperature Energy Equations

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Communications in computational Physics 2022年第10期32卷 1287-1309页

作者： Silu Huang Xiaoqiang Yue Xiaowen Xu Laboratory of Computational Physics Institute of Applied Physics and ComputationalMathematicsBeijing 100088China National Center for Applied Mathematics in Hunan Key Laboratory of Intelligent Computing and Information Processing of Ministry of EducationHunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtan 411105China

The iterative solution of the sequence of linear systems arising from threetemperature(3-T)energy equations is an essential component in the numerical simulation of radiative hydrodynamic(RHD)***,due to the complicated application features of the RHD problems,solving 3-T linear systems with classical preconditioned iterative techniques is *** address this difficulty,a physicalvariable based coarsening two-level(PCTL)preconditioner has been proposed by dividing the fully coupled system into four individual easier-to-solve *** its nearly optimal complexity and robustness,the PCTL algorithm suffers from poor efficiency because of the overhead associatedwith the construction of setup phase and the solution of ***,the PCTL algorithm employs a fixed strategy for solving the sequence of 3-T linear systems,which completely ignores the dynamically and slowly changing features of these linear *** address these problems and to efficiently solve the sequence of 3-T linear systems,we propose an adaptive two-level preconditioner based on the PCTL algorithm,referred to as α*** adaptive strategies of the αSetup-PCTL algorithm are inspired by those of αSetup-AMG algorithm,which is an adaptive-setup-based AMG solver for sequence of sparse linear *** proposed αSetup-PCTL algorithm could adaptively employ the appropriate strategies for each linear system,and thus increase the overall *** results demonstrate that,for 36 linear systems,the αSetup-PCTL algorithm achieves an average speedup of 2.2,and a maximum speedup of 4.2 when compared to the PCTL algorithm.

关键词： Sequence of linear systems sparse linear solver preconditioning methods radiation hydrodynamics simulation

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A phase-field model for non-small cell lung cancer under the effects of immunotherapy

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Mathematical Biosciences and engineering 2023年第10期20卷 1860-18694页

作者： Wagner, Andreas Schlicke, Pirmin Fritz, Marvin Kuttler, Christina Oden, J. Tinsley Schumann, Christian Wohlmuth, Barbara School of Computation Information and Technology Technical University of Munich Bavaria Munich Germany Computational Methods for PDEs Johann Radon Institute for Computational and Applied Mathematics Upper Austria Linz Austria Oden Institute for Computational Engineering and Sciences The University of Texas at Austin AustinTX United States Clinic of Pneumology Thoracic Oncology Sleep and Respiratory Critical Care Klinikverbund Allgäu Bavaria Kempten Germany

Formulating mathematical models that estimate tumor growth under therapy is vital for improving patient-specific treatment plans. In this context, we present our recent work on simulating non-small-scale cell lung cancer (NSCLC) in a simple, deterministic setting for two different patients receiving an immunotherapeutic treatment. At its core, our model consists of a Cahn-Hilliard-based phase-field model describing the evolution of proliferative and necrotic tumor cells. These are coupled to a simplified nutrient model that drives the growth of the proliferative cells and their decay into necrotic cells. The applied immunotherapy decreases the proliferative cell concentration. Here, we model the immunotherapeutic agent concentration in the entire lung over time by an ordinary differential equation (ODE). Finally, reaction terms provide a coupling between all these equations. By assuming spherical, symmetric tumor growth and constant nutrient inflow, we simplify this full 3D cancer simulation model to a reduced 1D model. We can then resort to patient data gathered from computed tomography (CT) scans over several years to calibrate our model. Our model covers the case in which the immunotherapy is successful and limits the tumor size, as well as the case predicting a sudden relapse, leading to exponential tumor growth. Finally, we move from the reduced model back to the full 3D cancer simulation in the lung tissue. Thereby, we demonstrate the predictive benefits that a more detailed patient-specific simulation including spatial information as a possible generalization within our framework could yield in the future. © 2023 the Author(s), licensee AIMS Press.

关键词： Nutrients

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Input-to-state stabilization for a 2 × 2 hyperbolic system cascaded with an ODE 37

Input-to-state stabilization for a 2 × 2 hyperbolic system ...

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37th Youth Academic Annual Conference of Chinese Association of Automation, YAC 2022

作者： Zhang, Han-Wen Wang, Jun-Min Wang, Jing Shanxi University School of Automation and Software Engineering Shanxi Taiyuan030006 China Theory and Computation in Information Security Beijing Institute of Technology School of Mathematics and Statistics Key Laboratory of Mathematical Beijing100081 China Delft Institute of Applied Mathematics Delft University of Technology Mekelweg 4 Delft2628 CD Netherlands

ISBN: (纸本)9781665465366

The paper deals with the input-to-state stabilization for the 2×2 system of first-order hyperbolic equations, which convect in opposite directions cascaded with an unstable ODE equation. First, an inverse backstepping transformation is introduced to obtain a target system. Then, by active disturbance rejection control (ADRC) method, the disturbance is estimated via a disturbance estimator with time-varying gain. When the unmatched disturbances are absent, the disturbance estimator is exponentially convergent to the matched disturbance. Furthermore, in order to reject the matched disturbance and obtain the input-to-state stability of the system, the controller is proposed by using the disturbance estimator. Finally, numerical simulations are presented to validate theoretical results. © 2022 IEEE.

关键词： Backstepping

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Two Physics-Based Schwarz Preconditioners for Three-Temperature Radiation Diffusion Equations in High Dimensions

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Communications in computational Physics 2022年第8期32卷 829-849页

作者： Xiaoqiang Yue Jianmeng He Xiaowen Xu Shi Shu Libo Wang National Center for Applied Mathematics in Hunan Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationHunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtan 411105P.R.China Laboratory of Computational Physics Institute of Applied Physics and ComputationalMathematicsBeijing 100094P.R.China College of Information Science and Technology JinanUniversityGuangzhou 510632P.R.China

We concentrate on the parallel,fully coupled and fully implicit solution of the sequence of 3-by-3 block-structured linear systems arising from the symmetrypreserving finite volume element discretization of the unsteady three-temperature radiation diffusion equations in high *** this article,motivated by[***,***,***,SIAM *** ***.33(2012)653–680]and[***,***,***,***.442(2021)110513],we aim to develop the additive and multiplicative Schwarz preconditioners subdividing the physical quantities rather than the underlying domain,and consider their sequential and parallel implementations using a simplified explicit decoupling factor approximation and algebraic multigrid subsolves to address such linear ***,computational efficiencies and parallel scalabilities of the proposed approaches are numerically tested in a number of representative real-world capsule implosion benchmarks.

关键词： Radiation diffusion equations Schwarz methods algebraic multigrid parallel and distributed computing

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CellMirror: Deciphering Cell Populations from Spatial Transcriptomics Data by Interpretable Contrastive Learning 1

CellMirror: Deciphering Cell Populations from Spatial Transc...

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1st IEEE International Conference on Medical Artificial Intelligence, MedAI 2023

作者： Xia, Junjie Cui, Jiangnan Huang, Zhenyu Zhang, Shuangquan Yao, Fang Zhang, Yijian Zuo, Chunman Institute of Artificial Intelligence Donghua University Department of Applied Mathematics Shanghai China College of Computer Science and Technology Jilin University Changchun China School of Cyber Science and Engineering Nanjing University of Science and Technology Nanjing China Institute of Maternal and Child Medicine Southern Medical University Affiliated Shenzhen Maternity and Child Healthcare Hospital Shenzhen China Xinhua Hospital Affiliated Shanghai Jiao Tong University of Medicine Department of General Surgery Shanghai China Institute of Artificial Institute Donghua University Shanghai China Jilin University Key Laboratory of Symbolic Computation and Knowledge Engineering Ministry of Education Changchun China

ISBN: (纸本)9798350358780

Spatial transcriptomics (ST) has enabled us elucidating tumor microenvironments, however, the technological limitations without single-cell resolution severely hinder its application. Here, we propose CellMirror, an interpretable contrastive learning model to decipher heterogeneous cell populations in ST data by single-cell RNA-sequencing (scRNA-seq) data. Specifically, CellMirror learns the disentangled shared (representing biological variations in both data) and salient features (specific to ST data) by two contrastive variational encoders, while constructing the relations between genes and features by a shared linear decoder. In various cancer samples, CellMirror outperforms other tools in learning common features for label transfer, and interpretation of features. Particularly, in breast cancer studies, CellMirror detects finer domains in ST data missed by other methods, and is robust to dissect cell populations in ST data using independent scRNA-seq data. These results demonstrate applications of CellMirror in interpreting the complex tumor structure in ST data by integrating scRNA-seq data. © 2023 IEEE.

关键词： Data integration

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Lattice Boltzmann simulation reveals supercritical bifurcation in flow mode transitions of power-law fluids in the four-roll mill

arXiv

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arXiv 2025年

作者： Yu, Yuan Jiang, Xiao Gu, Qingqing Lin, Chuandong Zhu, Qingyong Yuan, Hai-Zhuan School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China National Center for Applied Mathematics in Hunan Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China School of Energy and Power Engineering University of Shanghai for Science and Technology Shanghai200093 China Sino-French Institute of Nuclear Engineering and Technology Sun Yat-sen University Zhuhai519082 China School of Aeronautics and Astronautics Sun Yat-sen University Shenzhen518107 China

The four-roll mill has been traditionally viewed as a device generating simple extensional flow with a central stagnation point. Our systematic investigation using a two-relaxation-time regularized lattice Boltzmann (TRT-RLB) model reveals unexpected richness in the flow physics, identifying two previously unreported supercritical bifurcation modes: a quadrifoliate vortex mode featuring four symmetrical counter-rotating vortices, and a dumbbell-shaped quad-vortex mode where vortices detach from but remain symmetric about the stagnation point. The numerical framework, representing the first successful extension of TRT-RLB method to power-law fluid dynamics, enables comprehensive mapping of flow characteristics across Reynolds numbers (1 ≤ Re ≤ 50), power-law indices (0.7 ≤ n ≤ 1.3), and geometric configurations. The transition from quadrifoliate vortex mode exhibits distinct pathways depending on the power-law index: at relatively small n, the flow undergoes a direct supercritical bifurcation to simple extensional flow, while at relatively large n, it evolves through an intermediate dumbbell-shaped state. Among geometric parameters, the roller radius r emerges as the dominant factor controlling bifurcation points and vortex dimensions, whereas the roller-container gap δ exerts minimal influence on flow regimes. The transitions between flow modes can be precisely characterized through the evolution of vortex dimensions and velocity gradients at the stagnation point, providing quantitative criteria for flow regime identification. These findings enrich our fundamental understanding of bifurcation phenomena in extensional devices and provide quantitative guidelines for achieving desired flow patterns in four-roll mill applications. Copyright © 2025, The Authors. All rights reserved.

关键词： Vortex flow

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Input-to-state stabilization for a 2 × 2 hyperbolic system cascaded with an ODE

Input-to-state stabilization for a 2 × 2 hyperbolic system ...

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Youth Academic Annual Conference of Chinese Association of Automation (YAC)

作者： Han-Wen Zhang Jun-Min Wang Jing Wang School of Automation and Software Engineering Shanxi University Taiyuan Shanxi China School of Mathematics and Statistics & Key Laboratory of Mathematical Theory and Computation in Information Security Beijing Institute of Technology Beijing China Delft Institute of Applied Mathematics Delft University of Technology Mekelweg 4 Delft Netherlands

ISBN: (纸本)9781665465373

关键词： Robust control Backstepping Automation Numerical simulation Control systems Mathematical models Stability analysis

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Quantum Circuits for the Heat Equation with Physical Boundary Conditions Via Schrödingerisation

SSRN

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SSRN 2024年

作者： Jin, Shi Liu, Nana Yu, Yue School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Shanghai Jiao Tong University Shanghai200240 China University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan Xiangtan University Hunan Xiangtan411105 China

This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. These equations and/or their discretized forms usually do not evolve via unitary dynamics, thus are not suitable for quantum simulation. Boundary conditions (either time-dependent or independent) make the problem more difficult. To tackle this challenge, the Schrödingerisation method can be employed, which converts linear partial and ordinary differential equations with non-unitary dynamics into systems of Schrödinger-type equations, via the so-called warped phase transformation that maps the equation into one higher dimension. Despite advancements in Schrödingerisation techniques, the explicit implementation of quantum circuits for solving general PDEs, especially with physical boundary conditions, remains underdeveloped. We present two methods for handling the inhomogeneous terms arising from time-dependent physical boundary conditions. One approach utilizes Duhamel's principle to express the solution in integral form and employs linear combination of unitaries (LCU) for coherent state preparation. Another method applies an augmentation to transform the inhomogeneous problem into a homogeneous one. We then apply the quantum simulation technique from [CJL23] to transform the resulting non-autonomous system to an autonomous system in one higher dimension. We provide detailed implementations of these two methods and conduct a comprehensive complexity analysis in terms of queries to the time evolution input oracle. © 2024, The Authors. All rights reserved.

关键词： Boundary conditions

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