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A new and effective computational approach is presented for analyzing transient heat conduction problems. The approach consists of a meshless Fragile Points Method (FPM) being utilized for spatial discretization, and a Local Variational…

Computational Engineering, Finance, and Science · Computer Science 2020-01-27 Yue Guan , Rade Grujicic , Xuechuan Wang , Leiting Dong , Satya N. Atluri

An iterative coupling algorithm based on restricted additive Schwarz domain decomposition is investigated to co-simulate electrical circuits with hybrid electromagnetic (EMT) and transient stability (TS) modeled using dynamic phasors. This…

Numerical Analysis · Mathematics 2022-12-13 Héléna Shourick , Damien Tromeur-Dervout , Laurent Chédot

An improved approach to updating the electric field in simulations of Coulomb gases using the local lattice technique introduced by Maggs and Rossetto, is described and tested. Using the Fast Fourier Transform (FFT) an independent…

Other Condensed Matter · Physics 2009-11-11 A. Duncan , R. D. Sedgewick , R. D. Coalson

In this paper, we propose a time-marching multi-level Variational Multiscale-Tensor Decomposition (VMS-TD) algorithm to solve the heat equation with a moving heat source model that arises from additive manufacturing. First, we take a…

Numerical Analysis · Mathematics 2025-10-02 Xinyi Guan , Jiayi Hu , Lei Zhang , Shaoqiang Tang , Wing Kam Liu

Electromagnetic transient (EMT) simulation is a crucial tool for power system dynamic analysis because of its detailed component modeling and high simulation accuracy. However, it suffers from computational burdens for large power grids…

Systems and Control · Electrical Eng. & Systems 2023-12-21 Min Xiong , Kaiyang Huang , Yang Liu , Rui Yao , Kai Sun , Feng Qiu

Enhanced geothermal systems (EGS) involve strongly coupled, advection-dominated flow and heat transfer in fractured porous media. Conventional models typically assume local thermal equilibrium with a single effective fluid temperature or,…

Numerical Analysis · Mathematics 2026-04-23 Yi-Yung Yang , Sanghyun Lee , Dmitri Kuzmin

We present a cut finite element method for the heat equation on two overlapping meshes: a stationary background mesh and an overlapping mesh that moves around inside/"on top" of it. Here the overlapping mesh is prescribed a simple…

Numerical Analysis · Mathematics 2023-03-02 Mats G. Larson , Anders Logg , Carl Lundholm

This paper proposes a single-domain dual-reciprocity inclusion-based boundary element method (DR-iBEM) for a three-dimensional fully bonded bi-layered composite embedded with ellipsoidal inhomogeneities under transient/harmonic thermal…

Numerical Analysis · Mathematics 2025-12-11 Chunlin Wu , Liangliang Zhang , Tengxiang Wang , Huiming Yin

We propose a multiscale spectral generalized finite element method (MS-GFEM) for discontinuous Galerkin (DG) discretizations. The method builds local approximations on overlapping subdomains as the sum of a local source solution and a…

Numerical Analysis · Mathematics 2026-01-15 Christian Alber , Lukas Holbach

Linear-scaling electronic structure methods based on the calculation of moments of the underlying electronic Hamiltonian offer a computationally efficient and numerically robust scheme to drive large-scale atomistic simulations, in which…

Materials Science · Physics 2017-01-09 Eunan J. McEniry , Ralf Drautz

We extend the FE-DMN method to fully coupled thermomechanical two-scale simulations of composite materials. In particular, every Gauss point of the macroscopic finite element model is equipped with a deep material network (DMN). Such a DMN…

Computational Engineering, Finance, and Science · Computer Science 2021-11-30 Sebastian Gajek , Matti Schneider , Thomas Böhlke

This paper presents a computational model, based on the Finite Element Method (FEM), that simulates the thermal response of laser-irradiated tissue. This model addresses a gap in the current ecosystem of surgical robot simulators, which…

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

For electromagnetic transient (EMT) simulation of a power system, a state-space-based approach needs to solve state-space EMT equations by using numerical integration methods, e.g., the Euler method, Runge-Kutta methods, and…

Systems and Control · Electrical Eng. & Systems 2023-02-21 Min Xiong , Rui Yao , Yang Liu , Kai Sun , Feng Qiu

In this work, we present a numerical method that remedies the instabilities of the conventional FDTD approach for solving Maxwell's equations in a space-time dependent magneto-electric medium with direct application to the simulation of the…

Optics · Physics 2015-06-18 Jason Cornelius , Jinjie Liu , Moysey Brio

The Finite Element Method (FEM) is the gold standard for spatial discretization in numerical simulations for a wide spectrum of real-world engineering problems. Prototypical areas of interest include linear heat transfer and linear…

Numerical Analysis · Mathematics 2022-01-10 Marcelo Forets , Daniel Freire Caporale , Jorge M. Pérez Zerpa

Innovative numerical scheme studied in this work enables to overcome two main limitations of Building Performance Simulation (BPS) programs as high computational cost and the choice of a very fine numerical grid. The method, called…

Computational Engineering, Finance, and Science · Computer Science 2020-01-07 Madina Abdykarim , Julien Berger , Denys Dutykh , Amen Agbossou

We present the implementation and application of a multiphysics simulation technique to carrier dynamics under electromagnetic excitation in supported two-dimensional electronic systems. The technique combines ensemble Monte Carlo (EMC) for…

Mesoscale and Nanoscale Physics · Physics 2014-05-21 N. Sule , K. J. Willis , S. C. Hagness , I. Knezevic

In this paper we study the thermal effective behaviour for 3D multiphase composite material consisting of three isotropic phases which are the matrix, the inclusions and the coating media. For this purpose we use an accelerated FFT-based…

Computational Engineering, Finance, and Science · Computer Science 2015-04-29 Sophie Lemaitre , Vladimir Salnikov , Daniel Choi , Philippe Karamian

Design of modern nanostructured semiconductor devices often calls for simulation tools capable of modeling arbitrarily-shaped multiscale geometries. In this work, to this end, a discontinuous Galerkin (DG) method-based framework is…

Computational Physics · Physics 2020-02-03 Liang Chen , Hakan Bagci