Article
Mathematics, Applied
Z. Dong, L. Mascotto
Summary: This paper proves the effectiveness of hp-optimal error estimates for interior penalty discontinuous Galerkin methods (IPDG) in solving the biharmonic problem with homogeneous essential boundary conditions. The study considers both tensor product-type meshes in two and three dimensions, as well as triangular meshes in two dimensions. A key aspect of the analysis is the construction of a global H-2 piecewise polynomial approximants with hp-optimal approximation properties over the given meshes. The paper also discusses the hp-optimality of C-0-IPDG in two and three dimensions, as well as the stream formulation of the Stokes problem in two dimensions. Numerical experiments validate the theoretical predictions and show that p-suboptimality occurs in the presence of singular essential boundary conditions.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Mathematics, Applied
H. H. Kim, C-Y Jung, T. B. Nguyen
Summary: This article presents a staggered discontinuous Galerkin (SDG) approximation for elliptic problems on rectangular meshes, with theoretical proofs of optimal convergence results. Numerical evidence and examples demonstrate the effectiveness, stability, and accuracy of the proposed method. The simplicity of rectangular meshes allows for easy definition of discrete gradients, making numerical implementation easier, and there are plans to extend this approach to curved domains in future research.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
Liuqiang Zhong, Liangliang Zhou, Chunmei Liu, Jie Peng
Summary: This paper studies the two-grid interior penalty discontinuous Galerkin (IPDG) method for mildly nonlinear second-order elliptic partial differential equations. The well-posedness of the IPDG finite element discretizations is established by introducing the equivalent weak formulation and combining Brouwer's fixed point theorem. Error estimates for the discrete solution in various norms are derived, and a two-grid method is designed for solving the IPDG discretization scheme with corresponding error estimates provided. Numerical experiments confirm the efficiency of the proposed approach.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Mathematics, Applied
Paola F. Antonietti, Michele Botti, Ilario Mazzieri, Simone Nati Poltri
Summary: This work introduces and analyzes a finite element discontinuous Galerkin method for the numerical discretization of acoustic waves propagation in poroelastic materials. The method couples acoustic equations in the acoustic domain with Biot's equations in the poroelastic domain using physically consistent transmission conditions. The high-order discontinuous Galerkin method on polygonal and polyhedral meshes is used for spatial discretization, and it is coupled with Newmark-\beta time integration schemes. Stability analysis and error estimates are presented, and numerical results validate the error analysis. Examples of physical interest are also provided.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Yao Cheng, Xuesong Wang
Summary: This paper considers a local discontinuous Galerkin (LDG) method for a one-dimensional singularly perturbed convection-diffusion problem with an exponential boundary layer. Based on the technique of discrete Green's function, the optimal pointwise convergence (up to a logarithmic factor) of the LDG method is established on three typical families of layer-adapted meshes: Shishkin-type, Bakhvalov-Shishkin-type, and Bakhvalov-type. Numerical experiments are also provided.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics, Applied
Yao Cheng
Summary: In this study, the local discontinuous Galerkin method is applied to a singularly perturbed problem with two parameters. The use of layer-adapted mesh and various projections results in robust or almost robust convergence in different norms. Careful approximation error estimation on anisotropic meshes leads to different error estimates in various norms, with numerical experiments conducted to validate the theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Zhen Wang
Summary: In this paper, a multiterm time-fractional initial-boundary value problem is studied. Numerical schemes are constructed and their stability and convergence are analyzed. A numerical experiment is conducted to verify the effectiveness of the proposed method.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2022)
Article
Mathematics, Applied
Lin Mu, Xiu Ye, Shangyou Zhang
Summary: Pressure-robustness is crucial for incompressible fluid simulations. Enhancements to the discontinuous Galerkin finite element methods in the primary velocity-pressure formulation for solving Stokes equations have been developed to achieve pressure-robustness. The new schemes show improvements in source term modifications and have been validated through numerical experiments. Optimal-order error estimates have been established for the numerical approximations in various norms.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Piotr Krzyzanowski
Summary: This article considers a composite H-divided discontinuous Galerkin finite element discretization of a diffusion problem with subdomains separated by thin membranes, modeled by the Kedem-Katchalsky transmission condition. It is proved that a preconditioner based on the additive Schwarz method has a bounded condition number, independent of the mesh size, membrane permeability, and diffusion coefficient, provided that the condition numbers of the subspace solvers are also bounded. Numerical experiments confirm these findings and suggest that the convergence rate is weakly dependent on the degree of the approximating polynomials.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Mathematics, Applied
Jiansong Zhang, Rong Qin, Yun Yu, Jiang Zhu, Yue Yu
Summary: A new combined hybrid mixed finite element method is proposed to solve the propagation problem of incompressible wormholes. The method can maintain local mass balance while ensuring the boundedness of porosity. The convergence of the proposed method is analyzed and the optimal error estimate in L-2-norm is derived. Numerical examples are provided to verify the validity of the algorithm and the correctness of the theoretical results using the first-order backward Euler scheme in time.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Physics, Mathematical
Jie Du, Eric Chung
Summary: The proposed method utilizes mortar technique and staggered hybridization to allow the use of fine mesh near the free surface, significantly reducing computational cost and preserving the strong symmetry of the stress tensor. The resulting scheme is explicit in time and only requires solving local saddle point system for each time step.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Xuesong Wang, Yao Cheng
Summary: The local discontinuous Galerkin (LDG) method on a Shishkin mesh is investigated for a one-dimensional singularly perturbed reaction-diffusion problem. Improved pointwise error estimates are derived based on the discrete Green's function in the regular and layer regions. The convergence rates of the pointwise error for both the LDG approximation to the solution and its derivative are analyzed, showing optimal rates in different domains. Moreover, optimal pointwise error estimates are established when the regular component of the exact solution belongs to the finite element space. Numerical experiments are conducted to validate the theoretical findings.
APPLIED NUMERICAL MATHEMATICS
(2024)
Article
Mathematics, Applied
Mustafa Engin Danis, Jue Yan
Summary: In this study, a unified and general framework for direct discontinuous Galerkin methods is proposed. The framework eliminates the need for the antiderivative of the nonlinear diffusion matrix, allowing for a simple definition of the numerical flux. Nonlinear stability analyses and numerical experiments validate the performance of the new methods, showing that the symmetric and interface correction versions achieve optimal convergence and outperform the nonsymmetric version. Furthermore, the new direct discontinuous Galerkin methods accurately capture singular or blow up solutions.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Mathematics, Applied
Rohit Khandelwal, Kamana Porwal, Ritesh Singla
Summary: We perform a posteriori error analysis for the quadratic discontinuous Galerkin method for the elliptic obstacle problem, and discuss the pointwise reliability and efficiency of the proposed error estimator. We define two discrete sets and use a linear averaging function to transfer the DG finite element space to standard conforming finite element space. We also construct upper and lower barrier functions for the continuous solution using the Green's function of the Poisson's problem.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
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
Mathematics, Applied
Eric Chung, Kazufumi Ito, Masahiro Yamamoto
Summary: This paper proposes a least squares formulation for ill-posed inverse problems in partial differential equations, establishing the existence, uniqueness, and continuity of the inverse solution for noisy data in L-2. The method can be applied to a general class of non-linear inverse problems, and a stability analysis is developed. Numerical tests show the applicability and performance of the proposed method.
APPLICABLE ANALYSIS
(2022)
Article
Mathematics, Applied
Laura Bagur, Stephanie Chaillat, Patrick Ciarlet
Summary: Standard hierarchical matrix (H-matrix)-based methods are not optimal for oscillatory kernels, but still significant in mechanical engineering. This study investigates the effect of complex wavenumber on H-matrix-based fast methods and proposes an improvement for solving dense linear systems.
ADVANCES IN COMPUTATIONAL MATHEMATICS
(2022)
Article
Mathematics, Applied
Siu Wun Cheung, Eric Chung, Yalchin Efendiev, Wing Tat Leung, Sai-Mang Pun
Summary: This paper develops an iterative scheme within the framework of CEM-GMsFEM to construct multiscale basis functions for the mixed formulation. The iterative procedure starts with constructing an energy minimizing snapshot space and performing spectral decomposition to form global multiscale space, where each global basis function can be split into non-decaying and decaying parts. The decaying part is approximated using a modified Richardson scheme with an appropriately defined preconditioner, leading to first-order convergence with respect to the coarse mesh size under suitable regularization parameters.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Engineering, Multidisciplinary
Camille Carvalho, Patrick Ciarlet, Claire Scheid
Summary: The paper investigates the limiting amplitude principle in a case where it may not hold, providing numerical evidence and identifying clear characteristics of critical pulsations. The results are connected to physical plasmonic resonances in the lossy metallic case.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
Lina Zhao, Dohyun Kim, Eun-Jae Park, Eric Chung
Summary: In this paper, a staggered discontinuous Galerkin method for Darcy flows in fractured porous media is presented and analyzed. The method uses a staggered discontinuous Galerkin method and a standard conforming finite element method with appropriate inclusion of interface conditions. The optimal convergence estimates for all the variables are proved, and the error estimates are shown to be fully robust with respect to the heterogeneity and anisotropy of the permeability coefficients.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Lina Zhao, Eric Chung, Eun-Jae Park
Summary: This paper proposes and analyzes a staggered discontinuous Galerkin method for a five-field formulation of the Biot system of poroelasticity on general polygonal meshes. The method is locking-free and can handle highly distorted grids, and a fixed stress splitting scheme is introduced to reduce the size of the global system.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2023)
Article
Computer Science, Software Engineering
Changqing Ye, Eric T. Chung
Summary: This paper studies the convergences of several FFT-based discretization schemes in computational micromechanics, including Moulinec-Suquet's scheme, Willot's scheme, and the FEM scheme. It proves that the effective coefficients obtained by these schemes converge to the theoretical ones under reasonable assumptions. Convergence rate estimates are provided for the FEM scheme under additional regularity assumptions.
BIT NUMERICAL MATHEMATICS
(2023)
Article
Mathematics, Applied
Denis Spiridonov, Maria Vasilyeva, Min Wang, Eric T. Chung
Summary: In this paper, a class of Mixed Generalized Multiscale Finite Element Methods is proposed for solving elliptic problems in thin two-dimensional domains. The method utilizes multiscale basis functions and local snapshot space to construct a lower dimensional model and achieve multiscale approximation.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Uygulaana Kalachikova, Maria Vasilyeva, Isaac Harris, Eric T. Chung
Summary: This paper investigates the scattering problem in a heterogeneous domain using the Helmholtz equation and absorbing boundary conditions. A fine unstructured grid that resolves grid-level perforation is constructed for the finite element method solution. The large system of equations resulting from these approximations is reduced using the Generalized Multiscale Finite Element Method. The method constructs a multiscale space using the solution of local spectral problems on the snapshot space in each local domain, and two types of multiscale basis functions are presented and studied. Numerical results for the Helmholtz problem in a heterogeneous domain with obstacles of varying properties are provided, examining different wavenumbers and numbers of multiscale basis functions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Damien Chicaud, Patrick Ciarlet
Summary: This study focuses on the time-harmonic Maxwell's equations in anisotropic media. The problem addressed is an approximation of the diffraction problem or scattering from bounded objects that are usually located in an exterior domain in R3. The study considers perfectly conducting objects and imposes a Dirichlet boundary condition on those objects and an impedance condition on an artificial boundary to model an approximate radiation condition. The research examines the mathematical meaning of the impedance condition and determines the well-posedness of the model, as well as the a priori regularity of the fields in the domain and on the boundaries.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
(2023)
Article
Mathematics, Applied
Patrick Ciarlet Jr., David Lassounon, Mahran Rihani
Summary: In this work, a new numerical method for solving the scalar transmission problem with sign-changing coefficients is presented. This method is based on an optimal control reformulation of the problem and has proven convergence without any restrictive condition. It is applicable to situations where the domain of interest is a combination of dielectric material and metal or metamaterial. Experimental results in two dimensions are provided to illustrate the effectiveness of the method.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2023)
Article
Mathematics, Applied
Patrick Ciarlet, Minh Hieu Do, Francois Madiot
Summary: We analyse error estimates for the discretization of the neutron diffusion equations with mixed finite elements. We provide guaranteed and locally efficient estimators on the base block equation, namely the one-group neutron diffusion equation. Our focus is on AMR strategies on Cartesian meshes, which are commonly used in nuclear reactor core applications. We propose a robust marker strategy, the direction marker strategy, for this specific constraint.
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
(2023)
Article
Mathematics, Applied
Leonardo A. Poveda, Shubin Fu, Eric T. Chung, Lina Zhao
Summary: This paper presents a new Finite Element Method called CEM-GMsFEM for solving single-phase non-linear compressible flows in highly heterogeneous media. The method constructs basis functions by solving local spectral problems and local energy minimization problems. The convergence of the method is shown to only depend on the coarse grid size and the method is enhanced with an online enrichment guided by an a posteriori error estimator. Numerical experiments confirm the theoretical findings and demonstrate the efficiency and accuracy of the method.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
Jie Du, Eric Chung, Yang Yang
Summary: This paper studies the classical Allen-Cahn equations and investigates the maximum-principle-preserving (MPP) techniques. It discusses the application of the local discontinuous Galerkin (LDG) method and the use of conservative modified exponential Runge-Kutta methods. Numerical experiments are used to demonstrate the effectiveness of the MPP LDG scheme.
COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Lina Zhao, Ming Fai Lam, Eric Chung
Summary: This paper proposes a uniformly robust staggered DG method for the unsteady Darcy-Forchheimer-Brinkman problem, based on velocity gradient-velocity-pressure formulation for general polygonal meshes. The relaxation of tangential continuity for velocity is essential in achieving uniform robustness, and error analysis shows velocity error estimates are independent of pressure. Numerical experiments confirm the theoretical findings.
COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
M. S. Bruzon, T. M. Garrido, R. de la Rosa
Summary: We study a family of generalized Zakharov-Kuznetsov modified equal width equations in (2+1)-dimensions involving an arbitrary function and three parameters. By using the Lie group theory, we classify the Lie point symmetries of these equations and obtain exact solutions. We also show that this family of equations admits local low-order multipliers and derive all local low-order conservation laws through the multiplier approach.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Dohee Jung, Changbum Chun
Summary: The paper presents a general approach to enhance the Pade iterations for computing the matrix sign function by selecting an arbitrary three-point family of methods based on weight functions. The approach leads to a multi-parameter family of iterations and allows for the discovery of new methods. Convergence and stability analysis as well as numerical experiments confirm the improved performance of the new methods.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Abhishek Yadav, Amit Setia, M. Thamban Nair
Summary: In this paper, we propose a Galerkin's residual-based numerical scheme for solving a system of Cauchy-type singular integral equations using Chebyshev polynomials. We prove the well-posedness of the system and derive a theoretical error bound and convergence order. The numerical examples validate the theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Fernando Chacon-Gomez, M. Eugenia Cornejo, Jesus Medina, Eloisa Ramirez-Poussa
Summary: The use of decision rules allows for reliable extraction of information and inference of conclusions from relational databases, but the concepts of decision algorithms need to be extended in fuzzy environments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Ilhame Amirali, Gabil M. Amiraliyev
Summary: This paper considers the one-dimensional initial-boundary problem for a pseudoparabolic equation with a time delay. To solve this problem numerically, a higher-order difference method is constructed and the error estimate for its solution is obtained. Based on the method of energy estimates, the fully discrete scheme is shown to be convergent of order four in space and of order two in time. The given numerical results illustrate the convergence and effectiveness of the numerical method.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Tong-tong Shang, Guo-ji Tang, Wen-sheng Jia
Summary: The goal of this paper is to investigate a class of linear complementarity problems over tensor-spaces, denoted by TLCP, which is an extension of the classical linear complementarity problem. First, two classes of structured tensors over tensor-spaces (i.e., T-R tensor and T-RO tensor) are introduced and some equivalent characterizations are discussed. Then, the lower bound and upper bound of the solutions in the sense of the infinity norm of the TLCP are obtained when the problem has a solution.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Fabio Difonzo, Pawel Przybylowicz, Yue Wu
Summary: This paper focuses on the existence, uniqueness, and approximation of solutions of delay differential equations (DDEs) with Caratheodory type right-hand side functions. It presents the construction of the randomized Euler scheme for DDEs and investigates its error. Furthermore, the paper reports the results of numerical experiments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Priyanka Roy, Geetanjali Panda, Dong Qiu
Summary: In this article, a gradient based descent line search scheme is proposed for solving interval optimization problems under generalized Hukuhara differentiability. The innovation and importance of these concepts are presented from practical and computational perspectives. The necessary condition for existence of critical point is presented in inclusion form of interval-valued gradient. Suitable efficient descent direction is chosen based on the monotonic property of the interval-valued function and specific interval ordering. Mathematical convergence of the scheme is proved under the assumption of Inexact line search. The theoretical developments are implemented with a set of interval test problems in different dimensions. A possible application in finance is provided and solved by the proposed scheme.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Zhongqian Wang, Changqing Ye, Eric T. Chung
Summary: In this paper, the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with mixed boundary conditions for elasticity equations in high contrast media is developed. The method offers advantages such as independence of target region's contrast from precision and significant impact of oversampling domain sizes on numerical accuracy. Furthermore, this is the first proof of convergence of CEM-GMsFEM with mixed boundary conditions for elasticity equations. Numerical experiments demonstrate the method's performance.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Samaneh Soradi-Zeid, Maryam Alipour
Summary: The Laguerre polynomials are a new set of basic functions used to solve a specific class of optimal control problems specified by integro-differential equations, namely IOCP. The corresponding operational matrices of derivatives are calculated to extend the solution of the problem in terms of Laguerre polynomials. By considering the basis functions and using the collocation method, the IOCP is simplified into solving a system of nonlinear algebraic equations. The proposed method has been proven to have an error bound and convergence analysis for the approximate optimal value of the performance index. Finally, examples are provided to demonstrate the validity and applicability of this technique.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Almudena P. Marquez, Maria L. Gandarias, Stephen C. Anco
Summary: A generalization of the KP equation involving higher-order dispersion is studied. The Lie point symmetries and conservation laws of the equation are obtained using Noether's theorem and the introduction of a potential. Sech-type line wave solutions are found and their features, including dark solitary waves on varying backgrounds, are discussed.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Susanne Saminger-Platz, Anna Kolesarova, Adam Seliga, Radko Mesiar, Erich Peter Klement
Summary: In this article, we study real functions defined on the unit square satisfying basic properties and explore the conditions for generating bivariate copulas using parameterized transformations and other constructions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Lulu Tian, Nattaporn Chuenjarern, Hui Guo, Yang Yang
Summary: In this paper, a new local discontinuous Galerkin (LDG) algorithm is proposed to solve the incompressible Euler equation in two dimensions on overlapping meshes. The algorithm solves the vorticity, velocity field, and potential function on different meshes. The method employs overlapping meshes to ensure continuity of velocity along the interfaces of the primitive meshes, allowing for the application of upwind fluxes. The article introduces two sufficient conditions to maintain the maximum principle of vorticity.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Cheng Wang, Jilu Wang, Steven M. Wise, Zeyu Xia, Liwei Xu
Summary: In this paper, a temporally second-order accurate numerical scheme for the Cahn-Hilliard-Magnetohydrodynamics system of equations is proposed and analyzed. The scheme utilizes a modified Crank-Nicolson-type approximation for time discretization and a mixed finite element method for spatial discretization. The modified Crank-Nicolson approximation allows for mass conservation and energy stability analysis. Error estimates are derived for the phase field, velocity, and magnetic fields, and numerical examples are presented to validate the proposed scheme's theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Mingyu He, Wenyuan Liao
Summary: This paper presents a numerical method for solving reaction-diffusion equations in spatially heterogeneous domains, which are commonly used to model biological applications. The method utilizes a fourth-order compact alternative directional implicit scheme based on Pade approximation-based operator splitting techniques. Stability analysis shows that the method is unconditionally stable, and numerical examples demonstrate its high efficiency and high order accuracy in both space and time.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
