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Semantic units: organizing knowledge graphs into semantically meaningful units of representation
BackgroundIn today’s landscape of data management, the importance of knowledge graphs and ontologies is escalating as critical mechanisms aligned...
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Subdivision Schemes Based on Weighted Local Polynomial Regression: A New Technique for the Convergence Analysis
The generation of curves and surfaces from given data is a well-known problem in Computer-Aided Design that can be approached using subdivision...
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A Stable High-Order Perturbation of Surfaces/Asymptotic Waveform Evaluation Method for the Numerical Solution of Grating Scattering Problems
The scattering of electromagnetic radiation by a layered periodic diffraction grating is an important model in engineering and the sciences. The...
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Time Reparametrization and Event Location for Discontinuous Differential Algebraic Equations
In this paper, we consider numerical methods for the event location of differential algebraic equations. The event corresponds to cross a...
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A Divergence-Free Petrov–Galerkin Immersed Finite Element Method for Stokes Interface Problem
The paper proposes a Petrov–Galerkin immersed finite element (PGIFE) method for solving Stokes interface problems. We employ the uniform mesh which...
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Coupled and Decoupled Stabilized Finite Element Methods for the Stokes–Darcy-Transport Problem
In this paper, we propose and analyze two stabilized finite element schemes for the Stokes–Darcy-transport model. The first stabilized method is a...
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Efficient WENO Schemes for Nonuniform Grids
A set of arbitrarily high-order WENO schemes for reconstructions on nonuniform grids is presented. These non-linear interpolation methods use simple...
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Numerical Analysis of the Plateau Problem by the Method of Fundamental Solutions
Toward identifying the number of minimal surfaces sharing the same boundary from the geometry of the boundary, we propose a numerical scheme with...
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Second Order Unconditionally Convergent Fully Discrete Scheme for Incompressible Vector Potential MHD System
In this paper, we present and analyze a second order unconditionally convergent mixed finite element method for solving incompressible...
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An Isoparametric Finite Element Method for Time-fractional Parabolic Equation on 2D Curved Domain
This paper provides an efficient numerical scheme for approximating the solution of the time-fractional parabolic equation on 2D curved domain. Here,...
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A Proximal Alternating Direction Method of Multipliers for DC Programming with Structured Constraints
In this paper, we consider a class of structured DC programming, where the objective function is the difference of two (possibly nonsmooth) convex...
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A Hybridizable Discontinuous Galerkin Method for Magnetic Advection–Diffusion Problems
We propose and analyze a hybridizable discontinuous Galerkin (HDG) method for solving a mixed magnetic advection–diffusion problem within a more...
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An \(\alpha \)-Robust and Second-Order Accurate Scheme for a Subdiffusion Equation
We investigate a second-order accurate time-step** scheme for solving a time-fractional diffusion equation with a Caputo derivative of order
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A High-Order Shifted Boundary Virtual Element Method for Poisson Equations on 2D Curved Domains
We consider a high-order virtual element method for Poisson problems with non-homogeneous Dirichlet boundary condition on 2D domains with curved...
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Discrete-Velocity-Direction Models of BGK-Type with Minimum Entropy: II—Weighted Models
In this series of works, we develop a discrete-velocity-direction model (DVDM) with collisions of BGK-type for simulating gas flows, where the...
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Global Convergence in Learning Fully-Connected ReLU Networks Via Un-rectifying Based on the Augmented Lagrangian Approach
Most learning algorithms for deep neural networks (DNNs) employ gradient descent or block coordinate descent, which involves the direct application...
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A Local Approach to Parameter Space Reduction for Regression and Classification Tasks
Parameter space reduction has been proved to be a crucial tool to speed-up the execution of many numerical tasks such as optimization, inverse...
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Analysis of a Parallel Grad-Div Stabilized Method for the Navier–Stokes Problem with Friction Boundary Conditions
By combining grad-div stabilization used for improving pressure-robustness and full domain partition used for parallelization, a new parallel finite...
