Results 71 to 80 of about 4,597 (168)

A fast second-order block-centered finite difference method for the fractional Cattaneo equation

AIMS Mathematics
In this paper, a fast second-order block-centered finite difference method based on the $ \mathcal {FL} $2-$ 1_{\sigma} $ formula and a weighted approach was proposed for the time fractional Cattaneo equation. Using the special properties of the discrete
Xianqiang Zhang
doaj   +1 more source

FFT‐based computational micromechanics with Dirichlet boundary conditions on the rotated staggered grid

International Journal for Numerical Methods in Engineering, Volume 125, Issue 21, 15 November 2024.
Abstract Imposing nonperiodic boundary conditions for unit cell analyses may be necessary for a number of reasons in applications, for example, for validation purposes and specific computational setups. The work at hand discusses a strategy for utilizing the powerful technology behind fast Fourier transform (FFT)‐based computational micromechanics ...
Lennart Risthaus, Matti Schneider
wiley   +1 more source

Collocation Solutions of a Weakly Singular Volterra Integral Equation

Trends in Computational and Applied Mathematics, 2007
The discrete superconvergence properties of spline collocation solutions for a certain Volterra integral equation with weakly singular kernel are analyzed.
T. Diogo, P. Lima
doaj   +1 more source

Orthogonal polynomial bases in the mixed virtual element method

Numerical Methods for Partial Differential Equations, Volume 40, Issue 6, November 2024.
Abstract The use of orthonormal polynomial bases has been found to be efficient in preventing ill‐conditioning of the system matrix in the primal formulation of Virtual Element Methods (VEM) for high values of polynomial degree and in presence of badly‐shaped polygons.
Stefano Berrone, Stefano Scialò, Gioana Teora   +2 more
wiley   +1 more source

Iterated Crank–Nicolson Method for Peridynamic Models

Dynamics
In this paper, we explore the iterated Crank–Nicolson (ICN) algorithm for the one-dimensional peridynamic model. The peridynamic equation of motion is an integro-differential equation that governs structural deformations such as fractures. The ICN method
Jinjie Liu, Samuel Appiah-Adjei, Moysey Brio   +2 more
doaj   +1 more source

Multidomain spectral approach to rational‐order fractional derivatives

Studies in Applied Mathematics, Volume 152, Issue 4, Page 1110-1132, May 2024.
Abstract We propose a method to numerically compute fractional derivatives (or the fractional Laplacian) on the whole real line via Riesz fractional integrals. The compactified real line is divided into a number of intervals, thus amounting to a multidomain approach; after transformations in accordance with the underlying Zq$Z_{q}$ curve ensuring ...
Christian Klein, Nikola Stoilov
wiley   +1 more source

Imposing different boundary conditions for thermal computational homogenization problems with FFT‐ and tensor‐train‐based Green's operator methods

International Journal for Numerical Methods in Engineering, Volume 125, Issue 7, 15 April 2024.
Abstract To compute the effective properties of random heterogeneous materials, a number of different boundary conditions are used to define the apparent properties on cells of finite size. Typically, depending on the specific boundary condition, different numerical methods are used.
Lennart Risthaus, Matti Schneider
wiley   +1 more source

The Best Fit Bayesian Hierarchical Generalized Linear Model Selection Using Information Complexity Criteria in the MCMC Approach

Journal of Mathematics, Volume 2024, Issue 1, 2024.
Both frequentist and Bayesian statistics schools have improved statistical tools and model choices for the collected data or measurements. Model selection approaches have advanced due to the difficulty of comparing complicated hierarchical models in which linear predictors vary by grouping variables, and the number of model parameters is not distinct ...
Endris Assen Ebrahim, Mehmet Ali Cengiz, Erol Terzi, Antonio Di Crescenzo   +3 more
wiley   +1 more source

Extrapolation methods for solving the hypersingular integral equation of the first kind

AIMS Mathematics
Hypersingular integral equations have garnered extensive attention in the context of boundary element methods, particularly within natural boundary element methods.
Qian Ge, Jin Li
doaj   +1 more source

Superconvergence of a Nonconforming Interface Penalty Finite Element Method for Elliptic Interface Problems

Axioms
In our previous works, we developed the superconvergence of a nonconforming finite element method based on unfitted meshes for an elliptic interface problem and elliptic problem, respectively.
Xiaoxiao He
doaj   +1 more source