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A robust and fast solver for the fractional differential equation (FDEs) involving the Riesz fractional derivative is developed using an adaptive finite element method on non-uniform meshes. It is based on the utilization of hierarchical…

Numerical Analysis · Mathematics 2017-10-11 Xuan Zhao , Xiaozhe Hu , Wei Cai , George Em Karniadakis

Dynamical mean-field theory (DMFT) provides an optimal local approximation for correlated lattice systems by mapping the lattice onto a self-consistent effective impurity model. To account for the missing long-range correlations, we propose…

Strongly Correlated Electrons · Physics 2026-03-04 S. D. Semenov , A. I. Lichtenstein , A. N. Rubtsov

In Trefftz discontinuous Galerkin methods a partial differential equation is discretized using discontinuous shape functions that are chosen to be elementwise in the kernel of the corresponding differential operator. We propose a new…

Numerical Analysis · Mathematics 2023-04-27 Christoph Lehrenfeld , Paul Stocker

In this paper, the authors devise a new discretization scheme for div-curl systems defined in connected domains with heterogeneous media by using the weak Galerkin finite element method. Two types of boundary value problems are considered…

Numerical Analysis · Mathematics 2015-01-20 Chunmei Wang , Junping Wang

Frequency-domain full-waveform inversion (FWI) is suitable for long-offset stationary-recording acquisition, since reliable subsurface models can be reconstructed with a few frequencies and attenuation is easily implemented without…

Computational Physics · Physics 2020-04-15 Victorita Dolean , Pierre Jolivet , Stéphane Operto , Pierre-Henri Tournier

In this paper, we introduce the Phantom Domain Finite Element Method (PDFEM), a novel computational approach tailored for the efficient analysis of heterogeneous and composite materials. Inspired by fictitious domain methods, this method…

Numerical Analysis · Mathematics 2025-05-06 Tianlong He , Philippe Karamian-Surville , Daniel Choï

The simulation of high-dimensional problems with manageable computational resource represents a long-standing challenge. In a series of our recent work [25, 17, 18, 24], a class of sparse grid DG methods has been formulated for solving…

Numerical Analysis · Mathematics 2019-06-27 Wei Guo

A novel numerical approach to analyze the mechanical behavior within composite materials including the inelastic regime up to final failure is presented. Therefore, a second-gradient theory is combined with phase-field methods to fracture.…

Computational Engineering, Finance, and Science · Computer Science 2021-04-20 Maik Dittman , Jonathan Schult , Felix Schmidt , Christian Hesch

This paper introduces a new local plastic correction algorithm that is aimed at accelerating elasto-plastic finite element (FE) simulations for structural problems exhibiting localised plasticity (around e.g. notches, geometrical defects).…

Computational Engineering, Finance, and Science · Computer Science 2024-09-26 Abhishek Palchoudhary , Simone Peter , Vincent Maurel , Cristian Ovalle , Pierre Kerfriden

The Lip-field approach is a new way to regularize softening material models. It has already been tested in 1D quasistatic and 2D quasistatic: this paper extends it to 1D dynamics, on the challenging problem of dynamic fragmentation. The…

Computational Engineering, Finance, and Science · Computer Science 2022-03-10 Nicolas Moës , Benoît Lé , Andrew Stershic

We present a novel image-based adaptive domain decomposition FEM framework to accelerate the solution of continuum damage mechanics problems. The key idea is to use image-processing techniques in order to identify the moving interface…

Computational Engineering, Finance, and Science · Computer Science 2024-11-08 Panos Pantidis , Cornelius Otchere , Mostafa E. Mobasher

We analyze numerical approximation of the fractional elliptic problem $L^{\beta}u=f$, ${\beta>0}$, where $L$ is a second-order self-adjoint elliptic operator with homogeneous Dirichlet or Neumann boundary conditions. The paper develops a…

Numerical Analysis · Mathematics 2026-05-13 Kelvin J. R. Almeida-Sousa , David Bolin , Alexandre B. Simas

FFT-based solvers introduced in the 1990s for the numerical homogenization of heterogeneous elastic materials have been extended to a wide range of physical properties. In parallel, alternative algorithms and modified discrete Green…

Materials Science · Physics 2015-05-20 Lionel Gélébart , Franck Ouaki

The quasistatic rate-independent damage combined with linearized plasticity with hardening at small strains is investigated. The fractional-step time discretisation is devised with the purpose to obtain a numerically efficient scheme…

Numerical Analysis · Mathematics 2015-06-05 Tomáš Roubíček , Jan Valdman

In this work, we develop a localized numerical scheme with low regularity requirements for solving time-fractional integro-differential equations. First, a fully discrete numerical scheme is constructed. Specifically, for temporal…

Numerical Analysis · Mathematics 2025-12-02 Lijing Zhao , Rui Zhao , Wenyi Tian , Yufeng Nie

The method of the fundamental solutions (MFS) is used to construct an approximate solution for a partial differential equation in a bounded domain. It is demonstrated by combining the fundamental solutions shifted to the points outside the…

Numerical Analysis · Mathematics 2020-09-30 Shin-Ichiro Ei , Hiroyuki Ochiai , Yoshitaro Tanaka

We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy…

Numerical Analysis · Mathematics 2021-05-14 Juan Pablo Borthagaray , Wenbo Li , Ricardo H. Nochetto

The present work deals with the numerical resolution of coupled 3D-2D problems arising from the simulation of fluid flow in fractured porous media modeled via the Discrete Fracture and Matrix (DFM) model. According to the DFM model,…

Numerical Analysis · Mathematics 2024-01-18 Stefano Scialò

Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…

Numerical Analysis · Mathematics 2021-08-10 Fabrizio Greco , Lorenzo Leonetti , Paolo Lonetti , Raimondo Luciano , Andrea Pranno

Fracture is a very challenging and complicated problem with various applications in engineering and physics. Although it has been extensively studied within the context of mesh-based numerical techniques, such as the finite element method…

Numerical Analysis · Mathematics 2022-06-28 Mohammad Naqib Rahimi , Georgios Moutsanidis