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05/31/2023
A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type
Nonlocal models allow for the description of phenomena which cannot be c...
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06/15/2022
A Multifidelity Monte Carlo Method for Realistic Computational Budgets
A method for the multifidelity Monte Carlo (MFMC) estimation of statisti...
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04/17/2022
Energetically Consistent Model Reduction for Metriplectic Systems
The metriplectic formalism is useful for describing complete dynamical s...
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03/15/2022
An asymptotically compatible coupling formulation for nonlocal interface problems with jumps
We introduce a mathematically rigorous formulation for a nonlocal interf...
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10/05/2021
A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling
The popularity of deep convolutional autoencoders (CAEs) has engendered ...
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05/27/2021
High-Order Multirate Explicit Time-Stepping Schemes for the Baroclinic-Barotropic Split Dynamics in Primitive Equations
In order to treat the multiple time scales of ocean dynamics in an effic...
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04/29/2021
Nonlinear Level Set Learning for Function Approximation on Sparse Data with Applications to Parametric Differential Equations
A dimension reduction method based on the "Nonlinear Level set Learning"...
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08/26/2020
A general framework for substructuring-based domain decomposition methods for models having nonlocal interactions
A rigorous mathematical framework is provided for a substructuring-based...
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05/21/2020
A cookbook for finite element methods for nonlocal problems, including quadrature rules and approximate Euclidean balls
The implementation of finite element methods (FEMs) for nonlocal models ...
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04/29/2020
On a nonlocal Cahn-Hilliard model permitting sharp interfaces
A nonlocal Cahn-Hilliard model with a nonsmooth potential of double-well...
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02/04/2020
Numerical methods for nonlocal and fractional models
Partial differential equations (PDEs) are used, with huge success, to mo...
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01/11/2020
An energy-based coupling approach to nonlocal interface problems
Nonlocal models provide accurate representations of physical phenomena r...
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10/05/2019
Exponential Time Differencing for the Tracer Equations Appearing in Primitive Equation Ocean Models
The tracer equations are part of the primitive equations used in ocean m...
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06/26/2019
Piecewise polynomial approximation of probability density functions with application to uncertainty quantification for stochastic PDEs
The probability density function (PDF) associated with a given set of sa...
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06/28/2018