Results 91 to 100 of about 121,260 (302)

Generalized Multiscale Finite Element Method for Elastic Wave Propagation in the Frequency Domain

Computation, 2020
In this work, we consider elastic wave propagation in fractured media. The mathematical model is described by the Helmholtz problem related to wave propagation with specific interface conditions (Linear Slip Model, LSM) on the fracture in the frequency ...
Uygulana Gavrilieva, Maria Vasilyeva, Eric T. Chung   +2 more
doaj   +1 more source

Parallelization of Faber Polynomial Based Propagators for Laser Applications

International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Volume 38, Issue 4, July/August 2025.
ABSTRACT In order to simulate a laser system, the evaluation of a complex semilinear master equation is needed, including the description of the wave propagation by Maxwell's equations and appropriate rate equations. The denser the spatial discretization, the slower the computation time of the time‐dependent propagator.
Wladimir Plotnikov, Dirk Schulz
wiley   +1 more source

The Development of Discontinuous Galerkin Methods [PDF]

, 2000
In this paper, we present an overview of the evolution of the discontinuous Galerkin methods since their introduction in 1973 by Reed and Hill, in the framework of neutron transport, until their most recent developments. We show how these methods made their way into the main stream of computational fluid dynamics and how they are quickly finding use in
Bernardo Cockburn, Chi-Wang Shu, George Em Karniadakis   +2 more
openaire   +1 more source

Parameterized Local Reduced Order Model of Stimulated Volume Evolution in Reservoirs

International Journal for Numerical and Analytical Methods in Geomechanics, Volume 49, Issue 10, Page 2357-2375, July 2025.
ABSTRACT Real‐time simulation of large‐scale geomechanics problems, such as hydraulic dilation stimulation, is computationally expensive as they must span multiple spatial and temporal length scales, often including nonlinearities and thermo‐hydromechanical processes.
Saeed Hatefi Ardakani, Robert Gracie
wiley   +1 more source

A convergent nonconforming finite element method for compressible Stokes flow [PDF]

, 2009
We propose a nonconforming finite element method for isentropic viscous gas flow in situations where convective effects may be neglected. We approximate the continuity equation by a piecewise constant discontinuous Galerkin method. The velocity (momentum)
Karlsen, Kenneth H., Karper, Trygve K.
core   +1 more source

An Entropy Stable Discontinuous Galerkin Finite-Element Moment Method for the Boltzmann Equation

, 2016
This paper presents a numerical approximation technique for the Boltzmann equation based on a moment system approximation in velocity dependence and a discontinuous Galerkin finite-element approximation in position dependence.
Abdelmalik, M. R. A., van Brummelen, E. H.   +1 more
core   +2 more sources

On 2D elliptic discontinuous Galerkin methods [PDF]

International Journal for Numerical Methods in Engineering, 2005
AbstractWe discuss the discretization using discontinuous Galerkin (DG) formulation of an elliptic Poisson problem. Two commonly used DG schemes are investigated: the original average flux proposed by Bassi and Rebay (J. Comput. Phys. 1997; 131:267) and the local discontinuous Galerkin (LDG) (SIAM J. Numer. Anal. 1998; 35:2440–2463) scheme.
Sherwin, SJ, Kirby, RM, Peiro, J, Taylor, RL, Zienkiewicz, OC   +4 more
openaire   +4 more sources

Structure‐Preserving Approximations of the Serre‐Green‐Naghdi Equations in Standard and Hyperbolic Form

Numerical Methods for Partial Differential Equations, Volume 41, Issue 4, July 2025.
ABSTRACT We develop structure‐preserving numerical methods for the Serre–Green–Naghdi equations, a model for weakly dispersive free‐surface waves. We consider both the classical form, requiring the inversion of a nonlinear elliptic operator, and a hyperbolic approximation of the equations, allowing fully explicit time stepping.
H. Ranocha, M. Ricchiuto
wiley   +1 more source

High order exactly divergence-free Hybrid Discontinuous Galerkin Methods for unsteady incompressible flows

, 2015
In this paper we present an efficient discretization method for the solution of the unsteady incompressible Navier-Stokes equations based on a high order (Hybrid) Discontinuous Galerkin formulation.
Lehrenfeld, Christoph, Schöberl, Joachim   +1 more
core   +1 more source

-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations

Journal of Inequalities and Applications, 2010
We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations.
Lee HyunYoung, Shin JunYong, Ohm MiRay
doaj