scholarly journals A higher-order Lagrangian discontinuous Galerkin hydrodynamic method for solid dynamics and reactive materials

2019 ◽  
Author(s):  
Evan Lieberman ◽  
Xiaodong Liu ◽  
Nathaniel Ray Morgan ◽  
Darby Jon Luscher ◽  
Donald E. Burton
Keyword(s):  
Discontinuous Galerkin ◽  
Higher Order ◽  
Reactive Materials ◽  
Hydrodynamic Method ◽  
Solid Dynamics ◽  
Higher Order Lagrangian

scholarly journals A higher-order Lagrangian discontinuous Galerkin hydrodynamic method for solid dynamics

2019 ◽  
Vol 353 ◽  
pp. 467-490 ◽  
Author(s):  
Evan J. Lieberman ◽  
Xiaodong Liu ◽  
Nathaniel R. Morgan ◽  
Darby J. Luscher ◽  
Donald E. Burton
Keyword(s):  
Discontinuous Galerkin ◽  
Higher Order ◽  
Hydrodynamic Method ◽  
Solid Dynamics ◽  
Higher Order Lagrangian

scholarly journals A higher-order Lagrangian discontinuous Galerkin hydrodynamic method for elastic–plastic flows

2019 ◽  
Vol 78 (2) ◽  
pp. 318-334 ◽  
Author(s):  
Evan J. Lieberman ◽  
Nathaniel R. Morgan ◽  
Darby J. Luscher ◽  
Donald E. Burton
Keyword(s):  
Discontinuous Galerkin ◽  
Higher Order ◽  
Elastic Plastic ◽  
Hydrodynamic Method ◽  
Higher Order Lagrangian

scholarly journals Block Generalized Locally Toeplitz Sequences: From the Theory to the Applications

Axioms ◽  
2018 ◽  
Vol 7 (3) ◽  
pp. 49 ◽  
Author(s):  
Carlo Garoni ◽  
Mariarosa Mazza ◽  
Stefano Serra-Capizzano
Keyword(s):  
Finite Element ◽  
Differential Equations ◽  
Discontinuous Galerkin ◽  
Spectral Distribution ◽  
Galerkin Approximation ◽  
Higher Order ◽  
Numerical Discretization

The theory of generalized locally Toeplitz (GLT) sequences is a powerful apparatus for computing the asymptotic spectral distribution of matrices An arising from virtually any kind of numerical discretization of differential equations (DEs). Indeed, when the mesh fineness parameter n tends to infinity, these matrices An give rise to a sequence {An}n, which often turns out to be a GLT sequence or one of its “relatives”, i.e., a block GLT sequence or a reduced GLT sequence. In particular, block GLT sequences are encountered in the discretization of systems of DEs as well as in the higher-order finite element or discontinuous Galerkin approximation of scalar DEs. Despite the applicative interest, a solid theory of block GLT sequences has been developed only recently, in 2018. The purpose of the present paper is to illustrate the potential of this theory by presenting a few noteworthy examples of applications in the context of DE discretizations.

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