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07/19/2023
A simple and efficient convex optimization based bound-preserving high order accurate limiter for Cahn-Hilliard-Navier-Stokes system
For time-dependent PDEs, the numerical schemes can be rendered bound-pre...
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04/05/2023
FMG-Net and W-Net: Multigrid Inspired Deep Learning Architectures For Medical Imaging Segmentation
Accurate medical imaging segmentation is critical for precise and effect...
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02/27/2023
Numerical analysis of a hybridized discontinuous Galerkin method for the Cahn-Hilliard problem
The mixed form of the Cahn-Hilliard equations is discretized by the hybr...
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02/08/2023
A Weighted Normalized Boundary Loss for Reducing the Hausdorff Distance in Medical Imaging Segmentation
Within medical imaging segmentation, the Dice coefficient and Hausdorff-...
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10/11/2022
Convergence of a Decoupled Splitting Scheme for the Cahn-Hilliard-Navier-Stokes System
This paper is devoted to the analysis of an energy-stable discontinuous ...
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07/18/2022
Discontinuous Galerkin Approximations to Elliptic and Parabolic Problems with a Dirac Line Source
The analyses of interior penalty discontinuous Galerkin methods of any o...
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01/21/2022
A Sequential Discontinuous Galerkin Method for Two-Phase Flow in Deformable Porous Media
We formulate a numerical method for solving the two-phase flow poroelast...
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12/07/2021
Improved a priori error estimates for a discontinuous Galerkin pressure correction scheme for the Navier-Stokes equations
The pressure correction scheme is combined with interior penalty discont...
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10/15/2021
Existence and convergence of a discontinuous Galerkin method for the compressible three-phase flow problem in porous media
This paper presents and analyzes a discontinuous Galerkin method for the...
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09/22/2021
A discontinuous Galerkin pressure correction scheme for the incompressible Navier-Stokes equations: stability and convergence
A discontinuous Galerkin pressure correction numerical method for solvin...
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04/21/2021
PocketNet: A Smaller Neural Network for 3D Medical Image Segmentation
Overparameterized deep learning networks have shown impressive performan...
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10/30/2020
A pressure-correction and bound-preserving discretization of the phase-field method for variable density two-phase flows
In this paper, we present an efficient numerical algorithm for solving t...
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10/04/2020