Dylan Copeland
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View article: Machine-precision energy conservative quadrature hyperreduction of Lagrangian hydrodynamics
Machine-precision energy conservative quadrature hyperreduction of Lagrangian hydrodynamics Open
We present an energy conservative, quadrature based model reduction framework for the compressible Euler equations of Lagrangian hydrodynamics. Building on a high order finite element discretization of the governing equations, we develop a…
View article: Defining Foundation Models for Computational Science: A Call for Clarity and Rigor
Defining Foundation Models for Computational Science: A Call for Clarity and Rigor Open
The widespread success of foundation models in natural language processing and computer vision has inspired researchers to extend the concept to scientific machine learning and computational science. However, this position paper argues tha…
View article: S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models
S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models Open
While projection-based reduced order models can reduce the dimension of full order solutions, the resulting reduced models may still contain terms that scale with the full order dimension. Hyper-reduction techniques are sampling-based meth…
View article: High-performance finite elements with MFEM
High-performance finite elements with MFEM Open
The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for finite element discretizations. MFEM supports numerous types of finite element methods and is the discretization engine powering many computational phy…
View article: High-performance finite elements with MFEM
High-performance finite elements with MFEM Open
The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for finite element discretizations. MFEM supports numerous types of finite element methods and is the discretization engine powering many computational phy…
View article: Energy conserving quadrature based dimensionality reduction for nonlinear hydrodynamics problems
Energy conserving quadrature based dimensionality reduction for nonlinear hydrodynamics problems Open
Projection based dimensionality reduction is used to approximate the full discretiza tion of a PDE problem in order to reduce the cost of its numerical simulation while staying faithful to the full dynamics. For nonlinear problems, hyperre…
View article: S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models
S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models Open
While projection-based reduced order models can reduce the dimension of full order solutions, the resulting reduced models may still contain terms that scale with the full order dimension. Hyper-reduction techniques are sampling-based meth…
View article: Local Lagrangian reduced-order modeling for Rayleigh-Taylor instability by solution manifold decomposition
Local Lagrangian reduced-order modeling for Rayleigh-Taylor instability by solution manifold decomposition Open
Rayleigh-Taylor instability is a classical hydrodynamic instability of great interest in various disciplines of science and engineering, including astrophyics, atmospheric sciences and climate, geophysics, and fusion energy. Analytical met…
View article: Reduced order models for Lagransian hydrodynamics
Reduced order models for Lagransian hydrodynamics Open
As a mathematical model of high-speed flow and shock wave propagation in a complex multimaterial setting, Lagrangian hydrodynamics is characterized by moving meshes, advection-dominated solutions, and moving shock fronts with sharp gradien…
View article: Variable Precision Computing
Variable Precision Computing Open
This report summarizes the activities and major accomplishments of the Variable Precision Computing Strategic Initiative project. The overarching goal of this project was to initiate and promote a new paradigm in High Performance Computing…
View article: libROM
libROM Open
libROM is a collection of C++ classes that compute reduced order models and hyperreduced order models for systems of ordinary differential equations. libROM includes parallel, adaptive methods for proper orthogonal decomposition, and paral…