Results 61 to 70 of about 2,893 (187)

Local Discontinuous Galerkin Methods Coupled with Implicit Integration Factor Methods for Solving Reaction-Cross-Diffusion Systems

Discrete Dynamics in Nature and Society, 2016
We present a new numerical method for solving nonlinear reaction-diffusion systems with cross-diffusion which are often taken as mathematical models for many applications in the biological, physical, and chemical sciences.
Na An, Xijun Yu, Chaobao Huang, Maochang Duan   +3 more
doaj   +1 more source

Numerical analysis of an implicit fully discrete local discontinuous Galerkin method for the fractional Zakharov–Kuznetsov equation

Mathematical Modelling and Analysis, 2012
In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for a time-fractional Zakharov–Kuznetsov equation.
Zongxiu Ren, Leilei Wei, Yinnian He, Shaoli Wang   +3 more
doaj   +1 more source

On the Extension of Mesh‐Distortion‐Insensitive Petrov‐Galerkin Finite Element Formulations to Linear Elastodynamics

International Journal for Numerical Methods in Engineering, Volume 127, Issue 14, 30 July 2026.
ABSTRACT Numerous mesh‐distortion‐insensitive Petrov‐Galerkin finite element formulations have been developed for the simulation of elastostatic problems. This contribution presents initial results on how these formulations can be extended to linear elastodynamics. In this context, three different approaches are examined, building upon an established 8‐
Felix Zähringer, Peter Betsch
wiley   +1 more source

Comparison of DDFV and DG Methods for Flow in Anisotropic Heterogeneous Porous Media

Oil & Gas Science and Technology, 2014
We present a preliminary work to simulate gas injection in deep aquifers. Unsteady single-phase flows are considered. We compare Discrete Duality Finite Volume (DDFV, Discrete Duality Finite Volume) and Discontinuous Galerkin (DG, Discontinuous Galerkin)
Baron V., Coudière Y., Sochala P.
doaj   +1 more source

A Matrix‐Free, Scalable, and Robust Implicit Material Point Method

International Journal for Numerical Methods in Engineering, Volume 127, Issue 14, 30 July 2026.
ABSTRACT An implicit material point method is presented using a new dynamic relaxation solver, allowing for a simple and efficient quasi‐static formulation that may be readily implemented in existing explicit‐dynamic codes. The use of dynamic relaxation and aggregation is shown to produce an extremely robust material point method scheme, with good ...
Sam J. V. Sutcliffe, William M. Coombs, Wangcheng Zhang, Ravindra Duddu, Giuliano Pretti, Charles E. Augarde   +5 more
wiley   +1 more source

A NUMERICAL METHOD AND A PARALLEL ALGORITHM FOR SOLVING THE PROBLEM OF ELECTROMAGNETIC WAVE DIFFRACTION ON A NON-PLANAR PERFECTLY CONDUCTING SCREEN

Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2020
Background. The purpose of the work is to develop and implement the parallel algorithm for numerical solving the problem of electromagnetic wave diffraction by non-planar perfectly conducting screens. Materials and methods. Vector integro-differential
A. A. Tsupak
doaj   +1 more source

Overcoming Computational Bottlenecks in Quantum Hydrodynamics: A Volume‐Based Integral Formalism for Spherical Nanoparticles

Nanophotonics, Volume 15, Issue 13, 13 July 2026.
Numerical modeling of mesoscopic material response models that capture the quantum dynamics of electrons does not have to come with discouraging computational bottlenecks. The main message is that through a shift in perspective in modeling toward integral equation methods and exploiting symmetry‐based arguments, it is possible to capture complicated ...
Christos Mystilidis, Christos Tserkezis, Guy A. E. Vandenbosch, N. Asger Mortensen, Xuezhi Zheng   +4 more
wiley   +1 more source

Normalized Bernstein polynomials in solving space-time fractional diffusion equation

Advances in Difference Equations, 2017
In this paper, we solve a time-space fractional diffusion equation. Our methods are based on normalized Bernstein polynomials. For the space domain, we use a set of normalized Bernstein polynomials and for the time domain, which is a semi-infinite domain,
A Baseri, E Babolian, S Abbasbandy
doaj   +1 more source

The Discontinuous Galerkin Method with Diffusion [PDF]

Mathematics of Computation, 1992
Let \(\Omega\subset \mathbb{R}^ 2\) be a bounded polygon and \(\alpha=(\alpha_ 1,\alpha_ 2)\) a unit vector. The author considers the following class of constant-coefficient convection-diffusion equations: (1) \(u_ \alpha-\sigma_ 1u_{xx}-\sigma_ 2u_{yy}=f\), where \((x,y)\in \Omega\), \(u_ \alpha=\alpha\cdot\bigtriangledown u\) and \(\sigma_ 1\) and \(\
openaire   +1 more source

On the convergence of Galerkin method for solving hypersingular integral equations in special classes of functions

Известия высших учебных заведений. Поволжский регион: Физико-математические науки
Background. The numerical method for solving hypersingular integral equations on a segment that arise in many problems of mathematical physics is considered. Materials and methods.
Yu.G. Smirnov
doaj   +1 more source