Article
Mathematics, Applied
Ruchi Guo, Yulong Xing
Summary: This paper introduces a novel local discontinuous Galerkin method for solving linear elastodynamics problems, achieving energy conservation and optimal convergence rates on Cartesian meshes. Numerical experiments demonstrate several advantages of the proposed method, including exact energy conservation and slow-growing errors in long time simulations.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Alex Kaltenbach, Michael Ruzicka
Summary: In this paper, a local discontinuous Galerkin approximation is proposed for fully nonhomogeneous systems of p-Navier--Stokes type. By using the primal formulation, the well-posedness, stability (a priori estimates), and weak convergence of the method are proved. A new discontinuous Galerkin discretization of the convective term is proposed, and an abstract nonconforming theory of pseudomonotonicity, which is applied to the problem, is developed. The approach is also used to treat the p-Stokes problem.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2023)
Article
Materials Science, Multidisciplinary
M. Grigoriu
Summary: Numerical models are necessary in most applications to characterize the spatial fluctuation of material properties and estimate extremes and other functionals of material responses. These models are deterministic functions of the spatial coordinate and finite sets of random variables. The distributions of extremes and other functionals of material responses can be estimated from samples of material responses to finite dimensional (FD) material models under certain conditions.
MECHANICS OF MATERIALS
(2022)
Article
Automation & Control Systems
Saber Jafarpour, Pedro Cisneros-Velarde, Francesco Bullo
Summary: In this paper, we develop two generalizations of contraction theory, namely, semi-contraction and weak-contraction theory. We propose a geometric framework for semi-contraction theory using the notion of seminorm and introduce matrix semimeasures to characterize their properties. For weakly contracting systems, we prove a dichotomy for the asymptotic behavior of their trajectories and novel sufficient conditions for convergence to an equilibrium. Moreover, we show that every trajectory of a doubly contracting system, i.e., a system that is both weakly and semi-contracting, converges to an equilibrium point. Lastly, our results are applied to various important network systems and provide a sharper sufficient condition for synchronization in diffusively coupled systems.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2022)
Article
Engineering, Aerospace
Shenglian Tan, Yilang Liu, Jiaqing Kou, Weiwei Zhang
Summary: An improved mode multigrid method is proposed to accelerate the convergence of turbulent flows, demonstrating greater efficiency and robustness compared to the original method. The retention of zero-frequency shift modes helps enhance the convergence speed of turbulent flows, reducing the number of iteration steps significantly while maintaining computational accuracy. This improved method can be widely applied to complex engineering problems, providing an efficient solution for turbulent flow simulations.
Article
Mathematics, Applied
Maria Lukacova-Medvid'ova, Philipp Oeffner
Summary: This paper presents the convergence analysis of high-order finite element methods, with a focus on the discontinuous Galerkin scheme. By preserving structure properties and utilizing dissipative weak solutions, the convergence of the multidimensional high-order DG scheme is proven. Numerical simulations validate the theoretical results.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Applied
Xu Yang, Weidong Zhao, Wenju Zhao
Summary: This paper investigates the strong convergence of a fully discrete numerical method for stochastic partial differential equations driven by multiplicative noise. By introducing new weak variational approximation techniques, an analysis framework is presented and error estimates and convergence rates are obtained for the proposed method.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Geosciences, Multidisciplinary
Guanyu Zhou, Liqun Lyu, Mengzhen Xu, Chao Ma, Yunqi Wang, Yujie Wang, Zhaoyin Wang, Markus Stoffel
Summary: Check dams and afforestation are common measures for debris-flow mitigation, but there is a lack of quantitative evaluation methods for their effects. In Laogan Gully, check dams and silver wattle trees were used to reduce debris flow volume and stabilize a large landslide. The study analyzed sedimentation and tree rings to reconstruct debris flow motion and deposition. Based on the results, a model was constructed to evaluate the effects of check dams and afforestation on debris flow mitigation.
Article
Mathematics, Applied
Quoc-Hung Nguyen
Summary: This paper focuses on flows associated with non-smooth vector fields and demonstrates the well-posedness of certain regular Lagrangian flows associated with vector fields. Additionally, it is shown that under certain conditions, non-unique regular Lagrangian flows can exist.
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
(2021)
Article
Mathematics
Wei Zhang, Hui Min
Summary: This paper primarily investigates the weak convergence analysis of the error terms determined by the discretization for solving FBSDEs, based on Ito Taylor expansion, numerical SDE theory, and numerical FBSDEs theory. Through the weak convergence analysis of FBSDEs, better error estimates for recent numerical schemes in solving FBSDEs are further established.
Article
Mathematics, Applied
AllahBakhsh Yazdani Charati, Hamid Momeni, Mohammed S. Cheichan
Summary: In this study, the weak Galerkin finite element method is applied to solve second-order elliptic problems by choosing the lowest degree of polynomial space, and a new stabilizer term is introduced to improve the convergence performance. The scheme achieves O(h) and O(h^2) convergence in the H-1 and L-2 norms, respectively, demonstrating its strength, flexibility, and efficiency through numerical results.
COMPUTATIONAL & APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Ryan G. McClarren, James A. Rossmanith, Minwoo Shin
Summary: The thermal radiative transfer equations describe the propagation and collision of photons, and solving this integro-differential system accurately and efficiently poses several challenges. In this work, a novel hybrid discrete approximation is introduced to reduce the dimensionality of the phase space, and an asymptotic-preserving numerical method with a nodal discontinuous Galerkin discretization in space and a semi-implicit discretization in time is developed to overcome the stiffness challenge. Numerical experiments verify the accuracy, efficiency, and robustness of the proposed method.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Francisco Mengual, Laszlo Szekelyhidi
Summary: We construct infinitely many admissible weak solutions to the 2D incompressible Euler equations for vortex sheet initial data. Our solutions, obtained through convex integration, are smooth outside a turbulence zone which grows linearly in time around the vortex sheet. Furthermore, we show that the growth of the turbulence zone is controlled by the local energy inequality and measures the maximal initial dissipation rate in terms of the vortex sheet strength.
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Qianqian Xie, Yana Guo, Bo-Qing Dong
Summary: This paper focuses on the large-time behavior of 3D shear thickening non-Newtonian fluid equation, and through some new observations and mathematical methods, it establishes the bounds of the error of the solution in the L2 norm for t > 1 large.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Natasha Sharma
Summary: This study introduces a robust a posteriori error estimator for solving stationary convection-diffusion equations in the convection-dominated regime, providing global upper and lower bounds for the error. By relying on adaptively refined meshes based on a posteriori residual-type estimator, optimal convergence order can be achieved in all regimes, not just in the strongly convection-dominated regime.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Engineering, Multidisciplinary
Raimund Burger, Julio Careaga, Stefan Diehl, Romel Pineda
Summary: Reactive settling refers to the process of solid particles settling in a fluid while simultaneously undergoing reactions with the liquid phase. It plays a crucial role in sequencing batch reactors in wastewater treatment plants. A mathematical model is used to describe the operational cycles of the reactor and a finite difference scheme is employed to simulate the denitrification process.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Engineering, Multidisciplinary
Ricardo Ruiz-Baier, Matteo Taffetani, Hans D. Westermeyer, Ivan Yotov
Summary: In this study, a new mixed-primal finite element scheme was proposed to solve the multiphysics model involving fluid flow and consolidation equations without the need for Lagrange multipliers. The research focused on numerical simulations related to geophysical flows and eye poromechanics, exploring different interfacial flow regimes that could help understand early morphologic changes associated with glaucoma in canine species.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Chemical
Raimund Burger, Juan M. Menendez-Aguado, Marlon R. Fulla, Ismael E. Rivera
Summary: A population balance model is used to predict and analyze the wear and steel consumption of balls in a steel ball mill. The experimental data and theoretical predictions show excellent agreement, validating the accuracy of the model.
PARTICULATE SCIENCE AND TECHNOLOGY
(2022)
Article
Geochemistry & Geophysics
Zhuen Ruan, Aixiang Wu, Raimund Buerger, Fernando Betancourt, Rafael Ordonez, Jiandong Wang, Shaoyong Wang, Yong Wang
Summary: The shear-induced polymer-bridging flocculation is widely used in the solid-liquid separation process, and a flocculation kinetics model based on Population Balance Model (PBM) is proposed to model the process. The model includes an aggregation kernel and a breakage kernel, with six fitting parameters determined through global optimization. The proposed PBM effectively quantifies the dynamic evolution of floc size during flocculation.
Article
Infectious Diseases
Amna Tariq, Tsira Chakhaia, Sushma Dahal, Alexander Ewing, Xinyi Hua, Sylvia K. Ofori, Olaseni Prince, Argita D. Salindri, Ayotomiwa Ezekiel Adeniyi, Juan M. Banda, Pavel Skums, Ruiyan Luo, Leidy Y. Lara-Diaz, Raimund Burger, Isaac Chun-Hai Fung, Eunha Shim, Alexander Kirpich, Anuj Srivastava, Gerardo Chowell
Summary: This study utilizes mathematical models to investigate the transmission dynamics and short-term forecasting of the COVID-19 pandemic in Colombia. The findings show a decline in disease transmission at the national and regional level, but variations in incidence rate patterns across different departments. Additionally, the study examines the relationship between mobility and social media trends and the occurrence of case resurgences, along with the geographic heterogeneity of COVID-19 in Colombia.
PLOS NEGLECTED TROPICAL DISEASES
(2022)
Article
Geochemistry & Geophysics
Jiandong Wang, Aixiang Wu, Zhuen Ruan, Raimund Burger, Yiming Wang, Shaoyong Wang, Pingfa Zhang, Zhaoquan Gao
Summary: Cemented paste backfill (CPB) blended with coarse aggregates (CA-CPB) is a widely used technology for environmental protection and underground goaf treatment. This study investigates the influences of solid concentration, coarse aggregates dosage, and cement dosage on the rheological properties and compressive strength of CA-CPB through experimental methods. The results show that solid concentration and cement dosage have the most significant effects on the rheological properties and compressive strength, respectively. Multiple response optimization is performed using an overall desirability function approach to obtain the optimal parameters for high fluidity and strength, providing valuable information for the CA-CPB process in the Chifeng Baiyinnuoer Lead and Zinc Mine.
Article
Mathematics, Applied
Gabriel N. Gatica, Bryan Gomez-Vargas, Ricardo Ruiz-Baier
Summary: In this paper, the a posteriori error analysis for mixed-primal and fully-mixed finite element methods approximating the stress-assisted diffusion of solutes in elastic materials is developed. Two efficient and reliable residual-based a posteriori error estimators are derived and their performance is confirmed through numerical tests, illustrating the effectiveness of adaptive mesh refinement.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Physiology
Wesley de Jesus Lourenco, Ruy Freitas Reis, Ricardo Ruiz-Baier, Bernardo Martins Rocha, Rodrigo Weber dos Santos, Marcelo Lobosco
Summary: This paper investigates the formation of myocardial edema in acute infectious myocarditis and modifies a model to describe the associated dynamics. Computational methods can provide insights into the relationship between pathogens and the immune system, shedding light on the variations in myocarditis inflammation among different patients.
FRONTIERS IN PHYSIOLOGY
(2022)
Article
Engineering, Chemical
Raimund Burger, Julio Careaga, Stefan Diehl, Romel Pineda
Summary: A model of reactive settling is developed for the activated sludge process in wastewater treatment, which accounts for the spatial variability of reaction rates caused by biomass concentration variation. The model includes nonlinear partial differential equations and a numerical scheme for simulating hindered settling, compression, particle dispersion, and fluid dispersion. Experimental data from a pilot plant are used to fit the model, resulting in good predictability of the reactive sedimentation process.
CHEMICAL ENGINEERING SCIENCE
(2023)
Article
Computer Science, Interdisciplinary Applications
Wietse M. Boon, Martin Hornkjol, Miroslav Kuchta, Kent-Andre Mardal, Ricardo Ruiz-Baier
Summary: This paper advances the analysis of discretizations for a fluid-structure interaction model, proposing a five-field mixed-primal finite element scheme and deriving adequate inf-sup conditions. The stability of the formulation is established robustly in all material parameters and its performance is corroborated by several test cases.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Paulo Amorim, Raimund Burger, Rafael Ordonez, Luis Miguel Villada
Summary: This study investigates the spatio-temporal evolution of three biological species in a food chain model consisting of two competitive preys and one predator with intra-specific competition. The model considers the diffusion of the predator species towards higher concentrations of a chemical substance produced by the prey, as well as the movement of the prey away from high concentrations of a substance secreted by the predators. The study proves the local existence of nonnegative solutions and provides numerical simulations to discuss the system.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2023)
Article
Mathematics, Applied
Raimund Buerger, Sonia Valbuena, Carlos A. Vega
Summary: A reduced model of blood flow in arteries is proposed as a hyperbolic system of balance laws in one dimension with the unknowns as cross-sectional area and average flow velocity. An entropy stable finite difference scheme is constructed based on the entropy pair property, employing fourth-order entropy conservative flux and sign-preserving reconstruction, as well as a second-order strong stability preserving Runge-Kutta method. The scheme is computationally inexpensive, well-balanced, and numerically validated.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Geochemistry & Geophysics
Fernando Betancourt, Raimund Burger, Stefan Diehl, Leopoldo Gutierrez, M. Carmen Marti, Yolanda Vasquez
Summary: This article investigates the operation model of a froth flotation column. The model is described by a nonlinear convection-diffusion partial differential equation, incorporating solids-flux and drift-flux theories as well as a model of foam drainage. The model predicts the variations of bubble and (gangue) particle volume fractions with height and time. Through comparison with experimental results, operating charts for a modified version of the model are derived for steady-state operations with a stationary froth layer.
Article
Engineering, Chemical
Gezhong Chen, Cuiping Li, Zhuen Ruan, Raimund Burger, Yuan Gao, Hezi Hou
Summary: This study analyzed the bed drainage channel structure and the effect of coarse particles on the bed porosity and pore connectivity in cemented paste backfill technology. The results showed that the pressure and shear significantly influenced the spherical pore diameter, throat channel radius, and throat channel length. The volume and number of coarse particles had a negative impact on the bed porosity and pore connectivity. This research provides guidance for improving mining efficiency and reducing the number of tailings ponds.
MINERALS ENGINEERING
(2023)
Article
Mathematics, Interdisciplinary Applications
Raimund Burger, Stefan Diehl, M. Carmen Marti, Yolanda Vasquez
Summary: This article formulates a triangular system of conservation laws with discontinuous flux to model the one-dimensional flow of two disperse phases through a continuous one. The triangularity is due to the distinction between a primary and a secondary disperse phase, where the movement of the primary disperse phase is independent of the local volume fraction of the secondary phase. The article presents a monotone numerical scheme supported by theoretical arguments, and provides numerical examples and estimations of numerical error and convergence rates.
NETWORKS AND HETEROGENEOUS MEDIA
(2023)
Article
Computer Science, Interdisciplinary Applications
Tian Liang, Lin Fu
Summary: In this work, a new shock-capturing framework is proposed based on a new candidate stencil arrangement and the combination of infinitely differentiable non-polynomial RBF-based reconstruction in smooth regions with jump-like non-polynomial interpolation for genuine discontinuities. The resulting scheme achieves high order accuracy and resolves genuine discontinuities with sub-cell resolution.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Lukas Lundgren, Murtazo Nazarov
Summary: In this paper, a high-order accurate finite element method for incompressible variable density flow is introduced. The method addresses the issues of saddle point system and stability problem through Schur complement preconditioning and artificial compressibility approaches, and it is validated to have high-order accuracy for smooth problems and accurately resolve discontinuities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Gabriele Ciaramella, Laurence Halpern, Luca Mechelli
Summary: This paper presents a novel convergence analysis of the optimized Schwarz waveform relaxation method for solving optimal control problems governed by periodic parabolic PDEs. The analysis is based on a Fourier-type technique applied to a semidiscrete-in-time form of the optimality condition, which enables a precise characterization of the convergence factor at the semidiscrete level. The behavior of the optimal transmission condition parameter is also analyzed in detail as the time discretization approaches zero.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jonas A. Actor, Xiaozhe Hu, Andy Huang, Scott A. Roberts, Nathaniel Trask
Summary: This article introduces a scientific machine learning framework that uses a partition of unity architecture to model physics through control volume analysis. The framework can extract reduced models from full field data while preserving the physics. It is applicable to manifolds in arbitrary dimension and has been demonstrated effective in specific problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Nozomi Magome, Naoki Morita, Shigeki Kaneko, Naoto Mitsume
Summary: This paper proposes a novel strategy called B-spline based SFEM to fundamentally solve the problems of the conventional SFEM. It uses different basis functions and cubic B-spline basis functions with C-2-continuity to improve the accuracy of numerical integration and avoid matrix singularity. Numerical results show that the proposed method is superior to conventional methods in terms of accuracy and convergence.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Timothy R. Law, Philip T. Barton
Summary: This paper presents a practical cell-centred volume-of-fluid method for simulating compressible solid-fluid problems within a pure Eulerian setting. The method incorporates a mixed-cell update to maintain sharp interfaces, and can be easily extended to include other coupled physics. Various challenging test problems are used to validate the method, and its robustness and application in a multi-physics context are demonstrated.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Xing Ji, Fengxiang Zhao, Wei Shyy, Kun Xu
Summary: This paper presents the development of a third-order compact gas-kinetic scheme for compressible Euler and Navier-Stokes solutions, constructed particularly for an unstructured tetrahedral mesh. The scheme demonstrates robustness in high-speed flow computation and exhibits excellent adaptability to meshes with complex geometrical configurations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Alsadig Ali, Abdullah Al-Mamun, Felipe Pereira, Arunasalam Rahunanthan
Summary: This paper presents a novel Bayesian statistical framework for the characterization of natural subsurface formations, and introduces the concept of multiscale sampling to localize the search in the stochastic space. The results show that the proposed framework performs well in solving inverse problems related to porous media flows.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jacob Rains, Yi Wang, Alec House, Andrew L. Kaminsky, Nathan A. Tison, Vamshi M. Korivi
Summary: This paper presents a novel method called constrained optimized DMD with Control (cOptDMDc), which extends the optimized DMD method to systems with exogenous inputs and can enforce the stability of the resulting reduced order model (ROM). The proposed method optimally places eigenvalues within the stable region, thus mitigating spurious eigenvalue issues. Comparative studies show that cOptDMDc achieves high accuracy and robustness.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Andrea La Spina, Jacob Fish
Summary: This work introduces a hybridizable discontinuous Galerkin formulation for simulating ideal plasmas. The proposed method couples the fluid and electromagnetic subproblems monolithically based on source and employs a fully implicit time integration scheme. The approach also utilizes a projection-based divergence correction method to enforce the Gauss laws in challenging scenarios. Numerical examples demonstrate the high-order accuracy, efficiency, and robustness of the proposed formulation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Junhong Yue, Peijun Li
Summary: This paper proposes two numerical methods (IP-FEM and BP-FEM) to study the flexural wave scattering problem of an arbitrary-shaped cavity on an infinite thin plate. These methods successfully decompose the fourth-order plate wave equation into the Helmholtz and modified Helmholtz equations with coupled conditions on the cavity boundary, providing an effective solution to this challenging problem.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
William Anderson, Mohammad Farazmand
Summary: We develop fast and scalable methods, called RONS, for computing reduced-order nonlinear solutions. These methods have been proven to be highly effective in tackling challenging problems, but become computationally prohibitive as the number of parameters grows. To address this issue, three separate methods are proposed and their efficacy is demonstrated through examples. The application of RONS to neural networks is also discussed.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Marco Caliari, Fabio Cassini
Summary: In this paper, a second order exponential scheme for stiff evolutionary advection-diffusion-reaction equations is proposed. The scheme is based on a directional splitting approach and uses computation of small sized exponential-like functions and tensor-matrix products for efficient implementation. Numerical examples demonstrate the advantage of the proposed approach over state-of-the-art techniques.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Sebastiano Boscarino, Seung Yeon Cho, Giovanni Russo
Summary: This work proposes a high order conservative semi-Lagrangian method for the inhomogeneous Boltzmann equation of rarefied gas dynamics. The method combines a semi-Lagrangian scheme for the convection term, a fast spectral method for computation of the collision operator, and a high order conservative reconstruction and a weighted optimization technique to preserve conservative quantities. Numerical tests demonstrate the accuracy and efficiency of the proposed method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jialei Li, Xiaodong Liu, Qingxiang Shi
Summary: This study shows that the number, centers, scattering strengths, inner and outer diameters of spherical shell-structured sources can be uniquely determined from the far field patterns. A numerical scheme is proposed for reconstructing the spherical shell-structured sources, which includes a migration series method for locating the centers and an iterative method for computing the inner and outer diameters without computing derivatives.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
