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In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…

Optics · Physics 2024-12-03 Fan Xiao , Jingwei Wang , Zhongfei Xiong , Yuntian Chen

In this paper, we proposed two new types of edge multiscale methods motivated by \cite{GL18} to solve Partial Differential Equations (PDEs) with high-contrast heterogeneous coefficients: Edge spectral multiscale Finte Element method…

Numerical Analysis · Mathematics 2019-09-04 Shubin Fu , Eric Chung , Guanglian Li

This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the…

Quantum Physics · Physics 2025-04-01 Abhishek Arora , Benjamin M. Ward , Caglar Oskay

In this paper, the first large-scale application of multiscale-spectral generalized finite element methods (MS-GFEM) to composite aero-structures is presented. The crucial novelty lies in the introduction of A-harmonicity in the local…

Numerical Analysis · Mathematics 2023-03-03 Jean Bénézech , Linus Seelinger , Peter Bastian , Richard Butler , Timothy Dodwell , Chupeng Ma , Robert Scheichl

In this paper we propose a general framework for the uncertainty quantification of quantities of interest for high-contrast single-phase flow problems. It is based on the generalized multiscale finite element method (GMsFEM) and multilevel…

Numerical Analysis · Mathematics 2015-06-18 Yalchin Efendiev , Bangti Jin , Michael Presho , Xiaosi Tan

We propose a hybrid method, the Neural Enrichment Finite Element Method (NEFEM), designed for problems involving strong oscillations or interface problems with weak discontinuities. This method is based on the stable generalized finite…

Numerical Analysis · Mathematics 2026-05-12 Shihan Guo , Thomas Richter

We study the numerical approximation of advection-diffusion equations with highly oscillatory coefficients and possibly dominant advection terms by means of the Multiscale Finite Element Method. The latter method is a now classical, finite…

Numerical Analysis · Mathematics 2024-11-12 Rutger A. Biezemans , Claude Le Bris , Frédéric Legoll , Alexei Lozinski

In this article, we present a new unified finite element method (UFEM) for simulation of general Fluid-Structure interaction (FSI) which has the same generality and robustness as monolithic methods but is significantly more computationally…

Computational Engineering, Finance, and Science · Computer Science 2016-08-18 Yongxing Wang , Peter Jimack , Mark Walkley

In this paper, we propose a novel iterative multiscale framework for solving high-contrast contact problems of Signorini type. The method integrates the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM)…

Numerical Analysis · Mathematics 2025-10-28 Zishang Li , Changqing Ye , Eric T. Chung

Despite the increasing use of the Particle Finite Element Method (PFEM) in fluid flow simulation and the outstanding success of the Generalized-alpha time integration method, very little discussion has been devoted to their combined…

In this paper, we discuss multiscale methods for nonlinear problems. The main idea of these approaches is to use local constraints and solve problems in oversampled regions for constructing macroscopic equations. These techniques are…

Numerical Analysis · Mathematics 2019-04-01 Wing T. Leung , Eric T. Chung , Yalchin Efendiev , Mary F. Wheeler

In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the…

Numerical Analysis · Mathematics 2022-09-14 Kuokuo Zhang , Weibing Deng , Haijun Wu

The numerical simulation of physical processes in the underground frequently entails challenges related to the geometry and/or data. The former are mainly due to the shape of sedimentary layers and the presence of fractures and faults,…

Numerical Analysis · Mathematics 2020-02-28 Alessio Fumagalli , Anna Scotti , Luca Formaggia

We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are…

Numerical Analysis · Mathematics 2018-08-28 August Johansson , Benjamin Kehlet , Mats G. Larson , Anders Logg

In this work, we introduce a time memory formalism in poroelasticity model that couples the pressure and displacement. We assume this multiphysics process occurs in multicontinuum media. The mathematical model contains a coupled system of…

Numerical Analysis · Mathematics 2022-01-20 Aleksei Tyrylgin , Maria Vasilyeva , Anatoly Alikhanov , Dongwoo Sheen

Complex mechanic systems simulation is important in many real-world applications. The de-facto numeric solver using Finite Element Method (FEM) suffers from computationally intensive overhead. Though with many progress on the reduction of…

Machine Learning · Computer Science 2024-09-04 Jiasheng Shi , Fu Lin , Weixiong Rao

In this paper, we propose a new formulation and a suitable finite element method for the steady coupling of viscous flow in deformable porous media using divergence-conforming filtration fluxes. The proposed method is based on the use of…

Numerical Analysis · Mathematics 2025-10-23 Ruben Caraballo , Chansophea Wathanak In , Alberto F. Martín , Ricardo Ruiz-Baier

We propose and analyze a mixed formulation for the Brinkman-Forchheimer equations for unsteady flows. Our approach is based on the introduction of a pseudostress tensor related to the velocity gradient, leading to a mixed formulation where…

Numerical Analysis · Mathematics 2020-09-01 Sergio Caucao , Ivan Yotov

The purpose of this work is to investigate the behavior of Multiscale Finite Element type methods for advection-diffusion problems in the advection-dominated regime. We present, study and compare various options to address the issue of the…

Numerical Analysis · Mathematics 2015-11-30 Claude Le Bris , Frederic Legoll , François Madiot

We propose an extrinsic, continuous-Galerkin (CG), extended finite element method (XFEM) that generalizes the work of Hansbo and Hansbo to allow multiple Heaviside enrichments within a single element in a hierarchical manner. This approach…

Computational Engineering, Finance, and Science · Computer Science 2021-11-24 M. Keith Ballard , Roman Amici , Varun Shankar , Lauren A. Ferguson , Michael Braginsky , Robert M. Kirby