Article
Mathematics, Applied
Hennes Hajduk
Summary: A framework for enforcing discrete maximum principles in discontinuous Galerkin discretizations is presented, applicable to scalar conservation laws and hyperbolic systems. Piecewise Bernstein polynomials are used as shape functions, a new invariant domain preserving DG scheme is designed and extended by subcell flux limiters for high-order bound preserving approximation. Numerical results for various benchmark problems are presented, considering linear and nonlinear scalar problems, Euler equations of gas dynamics, and the shallow water system.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
Nawfel Benatia, Abdellah El Kacimi, Omar Laghrouche, Ahmed Ratnani
Summary: This paper presents a high-order finite element method for solving time-harmonic Maxwell short wave problems. The method incorporates enhanced basis functions and element-level static condensation to improve the conditioning and reduce memory requirements. Benchmark tests demonstrate the accuracy and efficiency of the proposed method.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Engineering, Multidisciplinary
Roberto J. Cier, Sergio Rojas, Victor M. Calo
Summary: The translated text describes a stable finite element formulation for advection-diffusion-reaction problems that allows for robust automatic adaptivity. The method efficiently demonstrates high applicability in various engineering applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Rida Malik, Faheem Khan, Muhammad Basit, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Emad E. Mahmoud, Masnour S. M. Lotayif
Summary: A new numerical technique using operational matrices of Bernstein polynomials is proposed to obtain numerical solutions of third-order ordinary differential equations (ODEs). These operational matrices can be used for solving various problems in integral and differential equations. The method discretizes the system into algebraic equations for direct solution and is verified using examples from Physics and Engineering, demonstrating comparison between approximate and exact solutions through tables and graphs.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Mathematics, Applied
Hossain Chizari, Vishal Singh, Farzad Ismail
Summary: This study presents the developments of linearity preserving (LP) residual distribution (RD) schemes for unsteady hyperbolic and hyperbolic-parabolic equations. By modifying classic RD schemes such as LDA using an explicit time integration and utilizing a classical aerodynamics philosophy on the standard finite-element technique, the new approach achieves true LP even for unsteady advection-diffusion cases and addresses the limitations of previous analytical approaches.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Chemistry, Analytical
Calvin Kielas-Jensen, Venanzio Cichella, Thomas Berry, Isaac Kaminer, Claire Walton, Antonio Pascoal
Summary: This paper presents a method for generating trajectories for autonomous system operations using Bernstein polynomials. The method enables efficient evaluation and enforcement of constraints, guaranteeing feasibility and safety of the trajectories in complex environments.
Article
Mathematics, Applied
Francesco Aldo Costabile, Maria Italia Gualtieri, Anna Napoli
Summary: This study investigates the theoretical and computational treatment of general high odd-order nonlinear differential equations with Lidstone-Euler second-type boundary conditions. The associated interpolation problem is considered, followed by a theorem on the existence and uniqueness of solutions to the boundary value problem. Two different numerical solution approaches are illustrated, with numerical examples demonstrating the validity and applicability of the algorithms proposed.
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
David Lee
Summary: Upwinded mass fluxes are used for advection operators discretised using mixed mimetic spectral elements. This method improves accuracy by adding dissipation biased toward high wave numbers, removes spectral gaps in the dispersion relation, and achieves energy conservation through skew-symmetric formulations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
Julee Shahni, Randhir Singh
Summary: This paper proposes an efficient numerical technique based on the Bernstein polynomials for the numerical solution of the derivative dependent Emden-Fowler boundary value problems. By converting the integral equation into a system of nonlinear equations using the Bernstein collocation method and solving it efficiently with a suitable iterative method, accurate numerical solutions are obtained. The method is analyzed for error and compared with other known techniques.
ENGINEERING WITH COMPUTERS
(2022)
Article
Automation & Control Systems
Mohammad Hossein Heydari, Mohsen Razzaghi, Shabnam Zhagharian
Summary: In this work, a new class of two-dimensional optimal control problems is introduced using distributed-order fractional derivative in the Caputo form. The orthonormal Bernstein polynomials are utilized to solve these problems numerically. The proposed approach approximates the state and control variables using polynomials and converts the problem into a system of algebraic equations using the method of Lagrange multipliers. The accuracy and capability of this method are demonstrated through numerical examples.
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE
(2023)
Article
Mathematics, Applied
M. H. Heydari, Z. Avazzadeh, A. Atangana
Summary: In this paper, a coupled system of nonlinear reaction-advection-diffusion equations is generalized to a variable-order fractional one using the Caputo-Fabrizio fractional derivative. A new formulation of the discrete Legendre polynomials, namely the orthonormal shifted discrete Legendre polynomials, is introduced to establish an appropriate method for the system. The devised method transforms the system into a system of algebraic equations using these polynomials and their operational matrices with the collocation technique, which is proven to be accurate through the analysis of two numerical examples.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics, Applied
Konrad Simon, Joern Behrens
Summary: A new framework of numerical multiscale methods is introduced for advection-dominated problems in climate sciences, addressing difficulties faced by current methods when lower order terms are dominant. The method involves a semi-Lagrangian based reconstruction of subgrid variability into a multiscale basis by solving local inverse problems, resembling a Eulerian method with multiscale stabilized basis globally. Example runs in one and two dimensions are shown, along with comparisons to standard methods to support the ideas presented. Future extensions to other types of Galerkin methods, higher dimensions and nonlinear problems are discussed.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Engineering, Multidisciplinary
V. M. Calo, M. Los, Q. Deng, I. Muga, M. Paszynski
Summary: This paper introduces a method called isoGeometric Residual Minimization (iGRM) for solving stationary advection-dominated diffusion problems. The method stabilizes the solution through residual minimization and uses B-spline basis functions for discretization. It delivers similar quality solutions as the Discontinuous Petrov-Galerkin (DPG) method but is limited to tensor-product meshes.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mathematics, Applied
Dimitar K. Dimitrov, Geno P. Nikolov
Summary: This study investigates the optimal constants of discrete Markov-Bernstein inequalities for specified parameters, and explores their properties. Three conclusions about these constants were proven, demonstrating their behavior under different conditions. Additionally, a similar inequality was proved for sequences, establishing a relationship between the optimal constants and the smallest eigenvalues of Jacobi matrices.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Saurabh Kumar, Vikas Gupta
Summary: In this study, a numerical technique using fractional-order Lagrange polynomials and Newton's iterative method is proposed to solve variable-order time-fractional advection-diffusion equations. The method is simple to use and provides highly accurate approximate solutions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Computer Science, Interdisciplinary Applications
R. Anderson, V. Dobrev, Tz. Kolev, D. Kuzmin, M. Quezada de Luna, R. Rieben, V. Tomov
JOURNAL OF COMPUTATIONAL PHYSICS
(2017)
Article
Computer Science, Interdisciplinary Applications
V. Dobrev, T. Z. Kolev, D. Kuzmin, R. Rieben, V. Tomov
JOURNAL OF COMPUTATIONAL PHYSICS
(2018)
Article
Mathematics, Applied
Robert W. Anderson, Veselin A. Dobrev, Tzanio V. Kolev, Robert N. Rieben, Vladimir Z. Tomov
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2018)
Article
Nuclear Science & Technology
T. S. Haut, P. G. Maginot, V. Z. Tomov, B. S. Southworth, T. A. Brunner, T. S. Bailey
NUCLEAR SCIENCE AND ENGINEERING
(2019)
Article
Mathematics, Applied
Veselin Dobrev, Patrick Knup, Tzanio Kolev, Ketan Mittal, Vladimir Tomov
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2019)
Article
Computer Science, Interdisciplinary Applications
Pedro D. Bello-Maldonado, Tzanio Kolev, Robert N. Rieben, Vladimir Z. Tomov
COMPUTERS & FLUIDS
(2020)
Article
Mathematics, Applied
Robert Anderson, Julian Andrej, Andrew Barker, Jamie Bramwell, Jean-Sylvain Camier, Jakub Cerveny, Veselin Dobrev, Yohann Dudouit, Aaron Fisher, Tzanio Kolev, Will Pazner, Mark Stowell, Vladimir Tomov, Ido Akkerman, Johann Dahm, David Medina, Stefano Zampini
Summary: MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretization approaches and emphasis on usability, portability, and high-performance computing efficiency. Its goal is to provide access to cutting-edge algorithms for high-order finite element meshing, discretizations and linear solvers, while enabling researchers to develop and test new algorithms in general, unstructured, high-order, parallel and GPU-accelerated settings.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
Adrian Sandu, Vladimir Tomov, Lenka Cervena, Tzanio Kolev
Summary: This study introduces novel high-order time integration methods for solving the compressible Euler equations in the Lagrangian frame, which accurately preserve the mass, momentum, and total energy of the system. Numerical results on standard hydrodynamics benchmarks demonstrate high-order convergence on smooth problems and exact numerical preservation of all physically conserved quantities.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Computer Science, Interdisciplinary Applications
Veselin Dobrev, Patrick Knupp, Tzanio Kolev, Ketan Mittal, Vladimir Tomov
Summary: The study introduces an hr-adaptivity framework for optimization of high-order meshes, extending the r-adaptivity method with nonconforming adaptive mesh refinement to better satisfy geometric targets. The methodology is purely algebraic, applicable to various types of meshes and dimensions, and achieves similar accuracy results with significantly fewer mesh nodes.
ENGINEERING WITH COMPUTERS
(2022)
Article
Computer Science, Hardware & Architecture
Tzanio Kolev, Paul Fischer, Misun Min, Jack Dongarra, Jed Brown, Veselin Dobrev, Tim Warburton, Stanimire Tomov, Mark S. Shephard, Ahmad Abdelfattah, Valeria Barra, Natalie Beams, Jean-Sylvain Camier, Noel Chalmers, Yohann Dudouit, Ali Karakus, Ian Karlin, Stefan Kerkemeier, Yu-Hsiang Lan, David Medina, Elia Merzari, Aleksandr Obabko, Will Pazner, Thilina Rathnayake, Cameron W. Smith, Lukas Spies, Kasia Swirydowicz, Jeremy Thompson, Ananias Tomboulides, Vladimir Tomov
Summary: Efficient exploitation of exascale architectures requires new numerical algorithms. CEED, a research partnership focused on developing next-generation discretization software, collaborates with various projects and institutions to optimize performance on large-scale GPU architectures and advance algorithms in fields such as unstructured adaptive mesh refinement and high-order data visualization.
INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING APPLICATIONS
(2021)
Article
Computer Science, Theory & Methods
Ahmad Abdelfattah, Valeria Barra, Natalie Beams, Ryan Bleile, Jed Brown, Jean-Sylvain Camier, Robert Carson, Noel Chalmers, Veselin Dobrev, Yohann Dudouit, Paul Fischer, Ali Karakus, Stefan Kerkemeier, Tzanio Kolev, Yu-Hsiang Lan, Elia Merzari, Misun Min, Malachi Phillips, Thilina Rathnayake, Robert Rieben, Thomas Stitt, Ananias Tomboulides, Stanimire Tomov, Vladimir Tomov, Arturo Vargas, Tim Warburton, Kenneth Weiss
Summary: This paper outlines the research and development activities in the Center for Efficient Exascale Discretization as part of the US Exascale Computing Project, focusing on state-of-the-art high-order finite-element algorithms for high-order applications on GPU-accelerated platforms. The authors discuss GPU developments in various components of the CEED software stack, and report performance and capability improvements in several CEED-enabled applications on both NVIDIA and AMD GPU systems.
PARALLEL COMPUTING
(2021)
Article
Computer Science, Hardware & Architecture
Arturo Vargas, Thomas M. Stitt, Kenneth Weiss, Vladimir Z. Tomov, Jean-Sylvain Camier, Tzanio Kolev, Robert N. Rieben
Summary: The discussion in the article highlights the challenges and solutions for large-scale production codes to rethink numerical algorithms and programming models under advanced heterogeneous computing architectures based on GPU accelerators. The co-design strategy is illustrated with examples from the development of MARBL at Lawrence Livermore National Laboratory, showcasing the significance of innovations and contributions to open-source software libraries.
INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING APPLICATIONS
(2022)
Article
Mathematics, Applied
Terry S. Haut, Ben S. Southworth, Peter G. Maginot, Vladimir Z. Tomov
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2020)
Article
Mathematics, Applied
V Dobrev, T. Kolev, C. S. Lee, V Tomov, P. S. Vassilevski
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2019)
Article
Computer Science, Interdisciplinary Applications
Jin Bao, Zhaoli Guo
Summary: At the equilibrium state of a two-phase fluid system, the chemical potential is constant and the velocity is zero. However, it is challenging to capture this equilibrium state accurately in numerical simulations, resulting in inconsistent thermodynamic interfacial properties and spurious velocities. Therefore, numerical schemes with well-balanced properties are preferred for simulating two-phase flows.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Brian C. Vermeire
Summary: This study presents a framework for implicit large eddy simulation (ILES) of incompressible flows by combining the entropically damped artificial compressibility (EDAC) method with the flux reconstruction (FR) approach. Experimental results demonstrate that the method is accurate and stable for low-order solutions, while higher-order solutions exhibit significantly higher accuracy and lower divergence error compared to reference direct numerical simulation.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Mijian Li, Rui Wang, Xinyu Guo, Xinyu Liu, Lianzhou Wang
Summary: In this study, the flow mechanisms around wall-mounted structures were investigated using Large Eddy Simulation (LES). The impact of inflow turbulence on the flow physics, dynamic response, and hydrodynamic performance was explored. The results revealed strong interference between velocity fluctuations and the wake past the cylinder, as well as significant convection effects in the far wake region.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Donatella Passiatore, Luca Sciacovelli, Paola Cinnella, Giuseppe Pascazio
Summary: A high-order shock-capturing central finite-difference scheme is evaluated for numerical simulations of hyper-sonic high-enthalpy flows out of thermochemical equilibrium. The scheme utilizes a tenth-order accurate central-difference approximation of inviscid fluxes, along with high-order artificial dissipation and shock-capturing terms. The proposed approach demonstrates accuracy and robustness for a variety of thermochemical non-equilibrium configurations.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Philipp Bahavar, Claus Wagner
Summary: Condensation is an important aspect in flow applications, and simulating the gas phase and tracking the deposition rates of condensate droplets can capture the effects of surface droplets on the flow while reducing computational costs.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Andras Szabo, Gyorgy Paal
Summary: This paper introduces an efficient calculation method, the parabolized stability equations (PSE), for solving stability equations. By calculating LU factorization once in each marching step, the time spent on solving linear systems of equations can be significantly reduced. Numerical experiments demonstrate the effectiveness of this method in reducing the solution time for linear equations, and its applicability to similar problems.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
A. Khalifa, M. Breuer
Summary: This study evaluates a recently developed data-driven model for collision-induced agglomerate breakup in high mass loading flows. The model uses artificial neural networks to predict the post-collision behavior of agglomerates, reducing computational costs compared to coupled CFD-DEM simulations.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Chunmei Du, Maojun Li
Summary: This paper considers the bilayer shallow water wave equations in one-dimensional space and presents an invariant domain preserving DG method to avoid Kelvin-Helmholtz instability.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jean-Michel Tucny, Mihir Durve, Andrea Montessori, Sauro Succi
Summary: The prediction of non-equilibrium transport phenomena in disordered media is a challenging problem for conventional numerical methods. Physics-informed neural networks (PINNs) show potential for solving this inverse problem. In this study, PINNs were used to successfully predict the velocity field of rarefied gas flow, and AdamW was found to be the best optimizer.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Min Gao, Pascal Mossier, Claus-Dieter Munz
Summary: In recent decades, the arbitrary Lagrangian-Eulerian (ALE) approach has gained popularity in dealing with fluid flows with moving boundaries. This paper presents a novel algorithm that combines the ALE finite volume (FV) and ALE discontinuous Galerkin (DG) methods into a stable and efficient hybrid approach. The main challenge of this mixed ALE FV and ALE DG method is reducing the inconsistency between the two discretizations. The proposed algorithm is implemented into a loosely-coupled fluid-structure interaction (FSI) framework and is demonstrated through various benchmark test cases and complex scenarios.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Dawid Strzelczyk, Maciej Matyka
Summary: In this study, the numerical convergence of the Meshless Lattice Boltzmann Method (MLBM) is investigated through three benchmark tests. The results are compared to the standard Lattice Boltzmann Method (LBM) and the analytical solution of the Navier-Stokes equation. It is found that MLBM outperforms LBM in terms of error value for the same number of nodes discretizing the domain.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Kanishka Bhattacharya, Tapan Jana, Amit Shaw, L. S. Ramachandra, Vishal Mehra
Summary: In this work, an adaptive algorithm is developed to address the issue of tensile instability in Smoothed Particle Hydrodynamics (SPH) by adjusting the shape of the kernel function to satisfy stability conditions. The effectiveness of the algorithm is demonstrated through dispersion analysis and fluid dynamics simulations.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Luis Laguarda, Stefan Hickel
Summary: We propose several enhancements to improve the accuracy and performance of the digital filter turbulent inflow generation technique, such as introducing a more realistic correlation function and varying target length scales. Additionally, we suggest generating inflow data in parallel at a prescribed time interval to improve computational performance. Based on the results of large-eddy simulations, these enhancements have shown to be beneficial. Suppressing streamwise velocity fluctuations at the inflow leads to the fastest relaxation of pressure fluctuations. However, this approach increases the adaptation length, which can be shortened by artificially increasing the wall-normal Reynolds stresses.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Constantin Zenz, Michele Buttazzoni, Tobias Florian, Katherine Elizabeth Crespo Armijos, Rodrigo Gomez Vazquez, Gerhard Liedl, Andreas Otto
Summary: A new model for compressible multiphase flows involving sharp interfaces and phase change is presented, with a focus on the treatment of compressibility and phase change in the multiphase fluid flow model. The model's accuracy and suitability are demonstrated through comparisons with experimental observations.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Joseph O'Connor, Sylvain Laizet, Andrew Wynn, Wouter Edeling, Peter V. Coveney
Summary: This article aims to apply uncertainty quantification and sensitivity analysis to the direct numerical simulation (DNS) of low Reynolds number wall-bounded turbulent channel flow. By using a highly scalable DNS framework and UQ techniques, the study evaluates the influence of different numerical parameters on the simulation results without explicitly modifying the code. The findings provide guidance for numerical simulations of wall-bounded turbulent flows.
COMPUTERS & FLUIDS
(2024)