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05/24/2023
A new discretely divergence-free positivity-preserving high-order finite volume method for ideal MHD equations
This paper proposes and analyzes a novel efficient high-order finite vol...
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05/24/2023
Provably convergent Newton-Raphson methods for recovering primitive variables with applications to physical-constraint-preserving Hermite WENO schemes for relativistic hydrodyn
The relativistic hydrodynamics (RHD) equations have three crucial intrin...
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04/15/2023
Critical Sampling for Robust Evolution Operator Learning of Unknown Dynamical Systems
Given an unknown dynamical system, what is the minimum number of samples...
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02/07/2023
Deep-OSG: A deep learning approach for approximating a family of operators in semigroup to model unknown autonomous systems
This paper proposes a novel deep learning approach for approximating evo...
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12/09/2022
On Optimal Cell Average Decomposition for High-Order Bound-Preserving Schemes of Hyperbolic Conservation Laws
This paper presents the first systematic study on the fundamental proble...
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12/06/2022
A New Locally Divergence-Free Path-Conservative Central-Upwind Scheme for Ideal and Shallow Water Magnetohydrodynamics
We develop a new second-order unstaggered path-conservative central-upwi...
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11/30/2022
High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers
In this paper, a high-order semi-implicit (SI) asymptotic preserving (AP...
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07/19/2022
Positivity-Preserving Well-Balanced Central Discontinuous Galerkin Schemes for the Euler Equations under Gravitational Fields
This paper designs and analyzes positivity-preserving well-balanced (WB)...
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07/19/2022
A Physical-Constraint-Preserving Finite Volume WENO Method for Special Relativistic Hydrodynamics on Unstructured Meshes
This paper presents a highly robust third-order accurate finite volume w...
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07/18/2022
Is the Classic Convex Decomposition Optimal for Bound-Preserving Schemes in Multiple Dimensions?
Since proposed in [X. Zhang and C.-W. Shu, J. Comput. Phys., 229: 3091–3...
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03/28/2022
Provably Positive Central DG Schemes via Geometric Quasilinearization for Ideal MHD Equations
In the numerical simulation of ideal MHD, keeping the pressure and densi...
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01/17/2022
On Energy Laws and Stability of Runge–Kutta Methods for Linear Seminegative Problems
This paper presents a systematic theoretical framework to derive the ene...
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11/08/2021
Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes
Solutions to many partial differential equations satisfy certain bounds ...
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06/07/2021
Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space
We present a numerical framework for deep neural network (DNN) modeling ...
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02/07/2021
Minimum Principle on Specific Entropy and High-Order Accurate Invariant Region Preserving Numerical Methods for Relativistic Hydrodynamics
This paper explores Tadmor's minimum entropy principle for the relativis...
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05/14/2020
Uniformly High-Order Structure-Preserving Discontinuous Galerkin Methods for Euler Equations with Gravitation: Positivity and Well-Balancedness
This paper presents a class of novel high-order accurate discontinuous G...
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03/05/2020
Methods to Recover Unknown Processes in Partial Differential Equations Using Data
We study the problem of identifying unknown processes embedded in time-d...
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02/11/2020
A Non-Intrusive Correction Algorithm for Classification Problems with Corrupted Data
A novel correction algorithm is proposed for multi-class classification ...
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02/09/2020
Provably Physical-Constraint-Preserving Discontinuous Galerkin Methods for Multidimensional Relativistic MHD Equations
We propose and analyze a class of robust, uniformly high-order accurate ...
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10/15/2019
Data-Driven Deep Learning of Partial Differential Equations in Modal Space
We present a framework for recovering/approximating unknown time-depende...
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07/17/2019
Entropy Symmetrization and High-Order Accurate Entropy Stable Numerical Schemes for Relativistic MHD Equations
This paper presents entropy symmetrization and high-order accurate entro...
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05/24/2019
Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Data
We present a numerical approach for approximating unknown Hamiltonian sy...
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11/13/2018
Data Driven Governing Equations Approximation Using Deep Neural Networks
We present a numerical framework for approximating unknown governing equ...
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09/24/2018
Numerical Aspects for Approximating Governing Equations Using Data
We present effective numerical algorithms for locally recovering unknown...
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08/22/2018