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An Efficient Staggered Scheme for Solving the Poromechanics Problem of Quasi-Static Cardiac Perfusion

International Journal for Numerical Methods in Biomedical Engineering 2025年第4期41卷 e70030页

作者： Wang, Xuan Cai, Li Ma, Pengfei Gao, Hao Xi'an Key Laboratory of Scientific Computation and Applied Statistics Xi'an China NPU-UoG International Cooperative Lab for Computation and Application in Cardiology Xi'an China School of Mathematics and Statistics Northwestern Polytechnical University Xi'an China School of Mathematics and Statistics University of Glasgow Glasgow United Kingdom

The ventricles can be considered a type of poroelastic material, where the mass and pressure of the interstitial fluid, along with the displacement of the skeleton, are the three primary physical quantities of interest. Based on the free energy function of the poroelastic material, we propose a simplified model that requires only two fields to be directly solved, with another quantity obtained through post-processing. To solve this model, we first discretize the equations with the backward Euler scheme and finite element method, leading to a nonlinear system of equations, which can be solved using the Newton method in a monolithic way. For computational efficiency, we proposed a staggered scheme, where the large nonlinear system is divided into two smaller independent systems, and each only solves for one field using the Newton method. The numerical results showed the staggered scheme is more efficient than the monolithic scheme and that the two schemes achieve the same results, and are also in good agreement with those reported in the literature. Finally, we applied the staggered scheme to ventricular myocardial perfusion models and obtained the blood perfusion patterns in the myocardium during the cardiac systole. © 2025 John Wiley & Sons Ltd.

关键词： cardiac perfusion finite element method poroelastic material staggered scheme

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Fully GPU-Accelerated Immersed Boundary Method for Fluid-Structure Interaction in Complex Cardiac Models

arXiv

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arXiv 2025年

作者： Ma, Pengfei Cai, Li Wang, Xuan Luo, Xiaoyu Gao, Hao Xi’an Key Laboratory of Scientific Computation and Applied Statistics China School of Mathematics and Statistics Northwestern Polytechnical University China School of Mathematics and Statistics University of Glasgow United Kingdom

Fluid-structure interaction (FSI) plays a crucial role in cardiac mechanics, where the strong coupling between fluid flow and deformable structures presents significant computational challenges. The immersed boundary (IB) method efficiently handles large deformations and contact without requiring mesh regeneration. However, solving complex FSI problems demands high computational efficiency, making GPU acceleration essential to leverage massive parallelism, high throughput, and memory bandwidth. We present a fully GPU-accelerated algorithm for the IB method to solve FSI problems in complex cardiac models. The Navier-Stokes equations are discretized using the finite difference method, while the finite element method is employed for structural mechanics. Traditionally, IB methods are not GPU-friendly due to irregular memory access and limited parallelism. The novelty of this work lies in eliminating sparse matrix storage and operations entirely, significantly improving memory access efficiency and fully utilizing GPU computational capability. Additionally, the structural materials can be modeled using general hyperelastic constitutive laws, including fiber-reinforced anisotropic biological tissues such as the Holzapfel-Ogden (HO) model. Furthermore, a combined geometric multigrid solver is used to accelerate the convergence. The full FSI system, consisting of millions of degrees of freedom, achieves a per-timestep computation time of just 0.1 seconds. We conduct FSI simulations of the left ventricle, mitral valve, and aortic valve, achieving results with high consistency. Compared to single-core CPU computations, our fully GPU-accelerated approach delivers speedups exceeding 100 times. Copyright © 2025, The Authors. All rights reserved.

关键词： Fluid structure interaction

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Cooperative networked systems: Multiple graphs, coalitional games, new probabilistic models

Cooperative networked systems: Multiple graphs, coalitional ...

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Mediterranean Conference on Control and Automation

作者： Baras, John S. Applied Mathematics Statistics and Scientific Computation Program Institute for Systems Research University of Maryland College Park United States

ISBN: (纸本)9781457701252

Networked systems are ubiquitous. A taxonomy of networked systems includes infrastructure and communication networks, social and economic networks, biological networks and biological swarms, robotic swarms, and several other categories. Most networked systems include physical components and cyber components implemented in various ways. Thus many networked systems come from the domain of cyberphysical systems (CPS). Cooperative networked systems represent from a certain abstract point of view a distributed and (at least partially) asynchronous implementation of the well known cycle "sense-decide-actuate" of control systems. Yet the interaction of dynamics, sensing, control and decision making, with network structures has created the need for a new scientific basis for the modeling, analysis, design and performance evaluation of such networked systems. For example, efforts to develop a new "Network Science" have emerged. Similarly, efforts to develop new theories of computation that emphasize multiple agents interacting over networks, beyond the conventional concepts and principles of computation and computability, have been also undertaken very recently. In another direction, several efforts have been undertaken very recently to develop models for such systems that integrate continuous and event-triggered dynamics within a framework that permits validation and testing of correctness. Thus the consideration of cooperative networked systems have raised fundamental new questions and challenges. © 2011 IEEE.

关键词： Decision making

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Realistic-science, technology, engineering, and mathematics assisted by google classroom as a learning innovation in the new normal era to improve statistical thinking skill 7

Realistic-science, technology, engineering, and mathematics ...

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7th International Conference on mathematics, Science, and Education 2020, ICMSE 2020

作者： Ardiansyah, A.S. Novita, N.A. Zhintya, H. Kurnianto, D. Mathematics Education Study Program Universitas Negeri Semarang Indonesia Applied Statistics and Computation Study Program Universitas Negeri Semarang Indonesia

Based on government policies regarding the implementation of learning from home, it is necessary the learning innovation to continue learning in the new normal era by utilizing existing technological advances. In this digital era, statistics thinking is important because it is needed to be able to interpret and understand and make good decisions from the statistical data obtained. From these problems, one of the innovations that can be done is by implementing Realistic mathematics Education integrated Science, Technology, Engineering, and mathematics assisted by Google Classroom (R-STEM-GC). This paper aims to determine the effect of R-STEM-GC learning on students' statistical thinking skills. This paper uses literature review method research that identifies, assesses, and interprets all findings on a research topic to answer existing research questions. It can concluded that realistic learning was more effective in terms of students' mathematical reasoning and communication than conventional learning;learning with the application of STEM can improve students' problem solving abilities compared to conventional learning;and the use of google classrooms that can improve communication skills. From the results of this analysis, the application of R-STEM-GC learning can be an innovative solution in improving students' statistical thinking skills in new normal era. © Published under licence by IOP Publishing Ltd.

关键词： Students

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A high order conservative upwind algorithm for the incompressible Navier Stokes equations

A high order conservative upwind algorithm for the incompres...

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作者： Ghosh, Debojyoti Baeder, James D. University of Maryland College Park MD 20742 United States Applied Mathematics and Statistics and Scientific Computation Australia Department of Aerospace Engineering Australia

ISBN: (纸本)9781617389221

The incompressible Navier Stokes equations are solved numerically using the Fractional Step algorithm. A Cartesian staggered-grid solver based on a high order upwind reconstruction of the convective flux is developed for high Reynolds number and inviscid flows. The Weighted Essentially Non-Oscillatory Schemes are used in conjunction with Runge-Kutta time-stepping. Upwinding based on velocity components is necessary for non-oscillatory and stable solutions at high Reynolds numbers. The conservative and non-conservative flux formulations are compared since differences are expected due to the numerical error in satisfying the continuity equation. The algorithm is validated against benchmark flow problems. The accuracy and convergence properties are analyzed on an isolated vortex convection problem. Finally, the performance of the algorithm on inviscid problems with strong gradients is demonstrated by simulating the evolution of a shear layer and leapfrogging of vortex rings. © 2010 by the American Institute of Aeronautics and Astronautics, Inc.

关键词： Reynolds number

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A lumped parameter model for evaluating coronary artery blood supply capacity

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Mathematical Biosciences and Engineering 2024年第4期21卷 5838-5862页

作者： Cai, Li Zhong, Qian Xu, Juan Huang, Yuan Gao, Hao School of Mathematics and Statistics Northwestern Polytechnical University Xi’an710129 China NPU-UoG International Cooperative Lab for Computation and Application in Cardiology Xi’an710129 China Xi’an Key Laboratory of Scientific Computation and Applied Statistics Xi’an710129 China Department of Mathematics University of Cambridge CambridgeCB2 1TN United Kingdom School of Mathematics and Statistics University of Glasgow GlasgowG12 8QQ United Kingdom

The coronary artery constitutes a vital vascular system that sustains cardiac function, with its primary role being the conveyance of indispensable nutrients to the myocardial tissue. When coronary artery disease occurs, it will affect the blood supply of the heart and induce myocardial ischemia. Therefore, it is of great significance to numerically simulate the coronary artery and evaluate its blood supply capacity. In this article, the coronary artery lumped parameter model was derived based on the relationship between circuit system parameters and cardiovascular system parameters, and the blood supply capacity of the coronary artery in healthy and stenosis states was studied. The aortic root pressure calculated by the aortic valve fluid-structure interaction (AV FSI) simulator was employed as the inlet boundary condition. To emulate the physiological phenomenon of sudden pressure drops resulting from an abrupt reduction in blood vessel radius, a head loss model was connected at the coronary artery’s entrance. For each coronary artery outlet, the symmetric structured tree model was appended to simulate the terminal impedance of the missing downstream coronary arteries. The particle swarm optimization (PSO) algorithm was used to optimize the blood flow viscous resistance, blood flow inertia, and vascular compliance of the coronary artery model. In the stenosis states, the relative flow and fractional flow reserve (FFR) calculated by numerical simulation corresponded to the published literature data. It was anticipated that the proposed model can be readily adapted for clinical application, serving as a valuable reference for diagnosing and treating patients. © 2024 the Author(s), licensee AIMS Press.

关键词： Blood vessels

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Active Passive Control and Discharge Concentration analysis of Inter Particle Spacing Radius of nanofluid: Ratio of Momentum to Thermal Diffusivities

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Case Studies in Thermal Engineering 2025年

作者： Maalee Almheidat F.M. Allehiany M.A. Aljohani Nguyen Minh Tuan Khadijah M. Abualnaja Ali Haider Yufeng Nie Emad E. Mahmoud Department of Mathematics The University of Jordan Amman Jordan Mathematics Department Faculty of Sciences Umm Al-Qura University Makkah Saudi Arabia Department of Mathematics and Statistics College of Science Taibah University Yanbu Saudi Arabia Faculty of Information Technology Posts and Telecommunications Institute of Technology Ho Chi Minh campus11 Nguyen Dinh Chieu Street District 1 Ho Chi Minh City Viet Nam Department of Mathematics and Statistics Collage of Science Taif University P.O. Box 11099 Taif 21944 Saudi Arabia School of Mathematics and Statistics Xi'an Key Laboratory of Scientific Computation and Applied Statistics Northwestern Polytechnical University Xi'an 710072 PR China

Significance This research introduces a novel investigation of the thermal and hydrodynamic behavior of copper nanoparticles with larger radii and increasing interparticle spacing under varying ratios of momentum to thermal diffusivities. Such conditions capture the combined effects of nanoparticle size and spacing because they influence pollutant discharge analysis like wastewater treatment and industrial pollutant mitigation. Motive This study investigates the thermal and mass transport in a cross-fluid model under the influence of Rayleigh-Benard convention. This study emphasizes pollutant discharge effects and diffusivity ratio variations with unique concept of active and passive control mechanism. Furthermore, present analysis incorporates inter-particle spacing and the influence of larger nanoparticle radii concept for heat and mass transfer efficiency. Velocity is controlled through inclined magnetic fields and thermal transport scrutinized through exponential heat radiation effect. Methodology The formulated system of partial differential equations (PDEs) is further transferred into ordinary differential equations (ODEs) using similarity tools. Obtained ODEs are passed under bvp4c scheme to get initial solution and artificial neural network scheme named as Levenberg Marquardt neural network (LMNN) is utilized to predict the solution. Findings With higher flow index behavior, the velocity of nanofluid increasing for shrinking case with smaller particle spacing , it increases for larger particle spacing , while on the other hand, for stretching case , it increases with smaller particle spacing and it decreases for larger particle spacing . For higher local pollutant source parameter and external pollutant source parameter, the concentration of nanofluid decreases for active control and increases for passive control.

关键词： Cross Fluid Model Rayleigh-Benard Convection Active-Passive Controls Pollutant Discharge Effects Inter particle spacing Combination of bvp4c and ANN

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A stochastic dynamic program for the single-day surgery scheduling problem

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IIE Transactions on Healthcare Systems Engineering 2011年第4期1卷 213-225页

作者： Herring, William L. Herrmann, Jeffrey W. Applied Mathematics and Statistics and Scientific Computation Mathematics Building Univerisity of Maryland College Park MD 20742 United States Department of Mechanical Engineering and Institute for Systems Research University of Maryland College Park MD United States

Scheduling elective surgeries involves sequential decision-making on the part of the operating room (OR) manager, who must continually balance the costs of deferring waiting cases and blocking higher-priority cases. While surgery scheduling has received extensive treatment in the literature, this paper presents the first modeling approach to capture this aspect of the process while incorporating block schedules, block release policies, and surgical waiting lists. The result is a stochastic dynamic programming formulation for the evolution of the schedule for a single day in an OR suite over the days leading up to the day of surgery. A general formulation is presented and theoretical results are obtained for a single-room version. These results demonstrate that optimal waiting list decisions for a single OR follow a threshold policy that preserves a desired amount of OR time for the remaining demand from the room's allocated surgical specialty. An algorithm for determining the optimal thresholds is presented, followed by computational results. © 2011 Copyright Taylor and Francis Group, LLC.

关键词： dynamic programming healthcare management operating room optimization scheduling

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Preconditioning techniques for reduced basis methods for parameterized elliptic partial differential equations

Preconditioning techniques for reduced basis methods for par...

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作者： Elman, Howard C. Forstall, Virginia Department of Computer Science Institute for Advanced Computer Studies University of Maryland College ParkMD20742 United States Applied Mathematics and Statistics and Scientific Computation Program University of Maryland College ParkMD20742 United States

The reduced basis methodology is an efficient approach to solve parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space, and an online step utilizes this approximation, the reduced basis, to solve a smaller reduced problem, which provides an accurate estimate of the solution. Traditionally, the reduced problem is solved using direct methods. However, the size of the reduced system needed to produce solutions of a given accuracy depends on the characteristics of the problem, and it may happen that the size is significantly smaller than that of the original discrete problem but large enough to make direct solution costly. In this scenario, it may be more effective to use iterative methods to solve the reduced problem. We construct preconditioners for reduced iterative methods which are derived from preconditioners for the full problem. This approach permits reduced basis methods to be practical for larger bases than direct methods allow. We illustrate the effectiveness of iterative methods for solving reduced problems by considering two examples, the steady-state diffusion and convection-diffusion-reaction equations. © 2015 Society for Industrial and applied mathematics.

关键词： Iterative methods

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A multiobjective optimization approach to smart growth in land development

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Socio-Economic Planning Sciences 2006年第3期40卷 212-248页

作者： Gabriel, Steven A. Faria, José A. Moglen, Glenn E. Department of Civil and Environmental Engineering University of Maryland College Park MD 20742 United States Applied Mathematics and Scientific Computation Program University of Maryland College Park MD 20742 United States

In this paper we apply a multiobjective optimization model of Smart Growth to land development. The term Smart Growth is meant to describe development strategies-that do not promote urban sprawl. However, the term is somewhat open to interpretation. The multiobjective aspects arise when considering the conflicting interests of the various stakeholders involved in land development decisions: the government planner, the environmentalist, the conservationist, and the land developer. We present a formulation-employing linear and convex quadratic objective functions subject to polyhedral and binary constraints for the stakeholders. The resulting optimization problems are convex, quadratic mixed integer programs that are NP-complete. We report numerical results with this model for Montgomery County, Maryland, and present them using a geographic information system (GIS). © 2005 Elsevier Ltd. All rights reserved.

关键词： Geographic Information System Integer programming Land use planning Large Scale Optimization Multiple objective programming Quadratic programming Smart Growth

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