33.1k citations
- Sandia National Laboratories CaliforniaUS256 papers
- Center for Integrated NanotechnologiesUS116 papers
- University of New MexicoUS94 papers
- Los Alamos National LaboratoryUS75 papers
- Princeton UniversityUS59 papers
- Massachusetts Institute of TechnologyUS48 papers
- Oak Ridge National LaboratoryUS45 papers
- Lawrence Livermore National LaboratoryUS43 papers
- Purdue University West LafayetteUS40 papers
- Lawrence Berkeley National LaboratoryUS38 papers
- The University of Texas at AustinUS37 papers
- University of Maryland, College ParkUS37 papers
6 papers · 2 filters
Second-order invariant domain preserving approximation of the compressible Navier--Stokes equations
Jean-Luc Guermond, Matthias Maier, Bojan Popov +1
We present a fully discrete approximation technique for the compressible Navier-Stokes equations that is second-order accurate in time and space, semi-implicit, and guaranteed to b…
A cookbook for finite element methods for nonlocal problems, including quadrature rules and approximate Euclidean balls
Marta D'Elia, Max Gunzburger, Christian Vollmann
The implementation of finite element methods (FEMs) for nonlocal models with a finite range of interaction poses challenges not faced in the partial differential equations (PDEs) s…
A unified, stable and accurate meshfree framework for peridynamic correspondence modeling. Part I: core methods
Masoud Behzadinasab, Nathaniel Trask, Yuri Bazilevs
The overarching goal of this work is to develop an accurate, robust, and stable methodology for finite deformation modeling using strong-form peridynamics (PD) and the corresponden…
A local basis approximation approach for nonlinear parametric model order reduction
Konstantinos Vlachas, Konstantinos Tatsis, Konstantinos Agathos +2
The efficient condition assessment of engineered systems requires the coupling of high fidelity models with data extracted from the state of the system `as-is'. In enabling this ta…
Numerical methods for nonlocal and fractional models
Marta D'Elia, Qiang Du, Christian Glusa +3
Partial differential equations (PDEs) are used, with huge success, to model phenomena arising across all scientific and engineering disciplines. However, across an equally wide swa…
Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation
Yu Leng, Xiaochuan Tian, Nathaniel A. Trask +1
In this work, we study the reproducing kernel (RK) collocation method for the peridynamic Navier equation. We first apply a linear RK approximation on both displacements and dilata…