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08/29/2023
MCMS-RBM: Multi-Component Multi-State Reduced Basis Method toward Efficient Transition Pathway Identification for Crystals and Quasicrystals
Due to quasicrystals having long-range orientational order but without t...
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03/27/2023
GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEs
Physics-Informed Neural Network (PINN) has proven itself a powerful tool...
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11/10/2022
A new conservative discontinuous Galerkin method via implicit penalization for the generalized KdV equation
We design, analyze, and implement a new conservative Discontinuous Galer...
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11/09/2022
A micro-macro decomposed reduced basis method for the time-dependent radiative transfer equation
Kinetic transport equations are notoriously difficult to simulate becaus...
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12/03/2021
Fast L^2 optimal mass transport via reduced basis methods for the Monge-Ampère equation
Repeatedly solving the parameterized optimal mass transport (pOMT) probl...
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10/21/2021
A hyper-reduced MAC scheme for the parametric Stokes and Navier-Stokes equations
The need for accelerating the repeated solving of certain parametrized s...
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03/12/2021
A reduced basis method for radiative transfer equation
Linear kinetic transport equations play a critical role in optical tomog...
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01/14/2021
An EIM-degradation free reduced basis method via over collocation and residual hyper reduction-based error estimation
The need for multiple interactive, real-time simulations using different...
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09/08/2020
L1-based reduced over collocation and hyper reduction for steady state and time-dependent nonlinear equations
The task of repeatedly solving parametrized partial differential equatio...
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11/06/2019
Multi-level adaptive greedy algorithms for the reduced basis method
The reduced basis method (RBM) empowers repeated and rapid evaluation of...
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06/18/2019
L1-ROC and R2-ROC: L1- and R2-based Reduced Over-Collocation methods for parametrized nonlinear partial differential equations
The onerous task of repeatedly resolving certain parametrized partial di...
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03/19/2015