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04/24/2023
Matrix-free GPU-accelerated saddle-point solvers for high-order problems in H(div)
This work describes the development of matrix-free GPU-accelerated solve...
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10/21/2022
End-to-end GPU acceleration of low-order-refined preconditioning for high-order finite element discretizations
In this paper, we present algorithms and implementations for the end-to-...
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03/04/2022
Low-order preconditioning for the high-order finite element de Rham complex
In this paper we present a unified framework for constructing spectrally...
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02/01/2022
Subcell limiting strategies for discontinuous Galerkin spectral element methods
We present a general family of subcell limiting strategies to construct ...
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11/24/2021
A Family of Independent Variable Eddington Factor Methods with Efficient Linear Solvers
We present a family of discretizations for the Variable Eddington Factor...
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09/10/2021
Efficient Exascale Discretizations: High-Order Finite Element Methods
Efficient exploitation of exascale architectures requires rethinking of ...
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04/16/2021
A short note on the accuracy of the discontinuous Galerkin method with reentrant faces
We study the convergence of the discontinuous Galerkin (DG) method appli...
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03/09/2021
Conservative and accurate solution transfer between high-order and low-order refined finite element spaces
In this paper we introduce general transfer operators between high-order...
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02/27/2021
Spline parameterization of neural network controls for deep learning
Based on the continuous interpretation of deep learning cast as an optim...
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01/05/2021
Fast parallel solution of fully implicit Runge-Kutta and discontinuous Galerkin in time for numerical PDEs, Part II: nonlinearities and DAEs
Fully implicit Runge-Kutta (IRK) methods have many desirable accuracy an...
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01/02/2021
Fast parallel solution of fully implicit Runge-Kutta and discontinuous Galerkin in time for numerical PDEs, Part I: the linear setting
Fully implicit Runge-Kutta (IRK) methods have many desirable properties ...
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09/02/2020
Uniform subspace correction preconditioners for discontinuous Galerkin methods with hp-refinement
In this paper, we develop subspace correction preconditioners for discon...
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04/18/2020
Sparse invariant domain preserving discontinuous Galerkin methods with subcell convex limiting
In this paper, we develop high-order nodal discontinuous Galerkin (DG) m...
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11/20/2019
MFEM: a modular finite element methods library
MFEM is an open-source, lightweight, flexible and scalable C++ library f...
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10/07/2019
High-order matrix-free incompressible flow solvers with GPU acceleration and low-order refined preconditioners
We present a matrix-free flow solver for high-order finite element discr...
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09/03/2019
High-order partitioned spectral deferred correction solvers for multiphysics problems
We present an arbitrarily high-order, conditionally stable, partitioned ...
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08/19/2019