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We formulate, analyse, and implement a discontinuous Galerkin finite element method (DG-FEM) for the approximation of the solution of an elliptic boundary value problem in a domain with fractal boundary. We consider the case of the Poisson…

Numerical Analysis · Mathematics 2026-04-30 Sergio Gómez , David Hewett , Andrea Moiola

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

Combined Transmission and Distribution Systems (CoTDS) simulation for power systems requires development of algorithms and software that are numerically stable and at the same time accurately simulate dynamic events that can occur in…

Systems and Control · Computer Science 2018-01-08 Ramakrishnan Venkatraman , Siddhartha Kumar Khaitan , Venkataramana Ajjarapu

We establish a simple, rigorous, and easy to implement connection between the classical continuous finite element method (FEM) and the discontinuous Galerkin (DG) method for Poisson's problem. The key idea is to insert a vanishing-thickness…

This work focuses on model preparation for electrostatic simulations of CAD designs to realize a rapid virtual prototyping concept. We present a boundary element method (BEM) allowing discontinuous fields between surfaces. The corresponding…

Computational Engineering, Finance, and Science · Computer Science 2024-12-13 Benjamin Marussig , Thomas Rüberg , Jürgen Zechner , Lars Kielhorn , Thomas-Peter Fries

Piezoelectric Micromachined Ultrasonic Transducers (PMUTs) are essential for next-generation ultrasonic sensing and imaging due to their bidirectional electromechanical behavior, compact design, and compatibility with low-voltage…

Real-time analysis of bio-heat transfer is very beneficial in improving clinical outcomes of hyperthermia and thermal ablative treatments but challenging to achieve due to large computational costs. This paper presents a fast numerical…

Computational Engineering, Finance, and Science · Computer Science 2021-12-30 Jinao Zhang , Sunita Chauhan

This paper presents the development of a real-time T&D co-simulation testbed for simulating large grids under high DER penetration. By integrating bulk power system, distribution feeders, and distributed energy resources (DER) models into…

Systems and Control · Electrical Eng. & Systems 2023-02-03 Victor Paduani , Rahul Kadavil , Hossein Hooshyar , Aboutaleb Haddadi , AHM Jakaria , Aminul Huque

We consider in this paper a challenging problem of simulating fluid flows, in complex multiscale media possessing multi-continuum background. As an effort to handle this obstacle, model reduction is employed. In \cite{rh2}, homogenization…

Numerical Analysis · Mathematics 2022-05-31 Jun Sur Richard Park , Siu Wun Cheung , Tina Mai , Viet Ha Hoang

In this paper, we present an Online Generalized Multiscale Finite Element Method(Online GMsFEM) for heat and mass transfer problem in heterogeneous media with artificial ground freezing pipes. The mathematical model of the process is based…

Numerical Analysis · Mathematics 2022-05-31 Denis Spiridonov , Sergei Stepanov , Vasil`ev Vasiliy

The XDEM multi-physics and multi-scale simulation platform roots in the Ex- tended Discrete Element Method (XDEM) and is being developed at the In- stitute of Computational Engineering at the University of Luxembourg. The platform is an…

Computational Engineering, Finance, and Science · Computer Science 2018-08-27 Bernhard Peters , Maryam Baniasadi , Mehdi Baniasadi , Xavier Besseron , Alvaro Estupinan Donoso , Mohammad Mohseni , Gabriele Pozzetti

In this paper, we present results of a discontinuous Galerkin (DG) scheme applied to deterministic computations of the transients for the Boltzmann-Poisson system describing electron transport in semiconductor devices. The collisional term…

Numerical Analysis · Mathematics 2015-05-13 Yingda Cheng , Irene M. Gamba , Armando Majorana , Chi-Wang Shu

The coupling effects in multiphysics processes are often neglected in designing multiscale methods. The coupling may be described by a non-positive definite operator, which in turn brings significant challenges in multiscale simulations. In…

Numerical Analysis · Mathematics 2024-01-05 Xiaofei Guan , Lijian Jiang , Yajun Wang

This paper presents a space-time finite element method (FEM) based on an unfitted mesh for solving parabolic problems on moving domains. Unlike other unfitted space-time finite element approaches that commonly employ the discontinuous…

Numerical Analysis · Mathematics 2026-04-03 Ruizhi Wang , Weibing Deng

We propose an energy-stable parametric finite element method (ES-PFEM) for simulating solid-state dewetting of thin films in two dimensions via a sharp-interface model, which is governed by surface diffusion and contact line (point)…

Numerical Analysis · Mathematics 2020-06-08 Quan Zhao , Wei Jiang , Weizhu Bao

This study presents a finite element and virtual element (FE-VE) coupled method for thermomechanical analysis in electronic packaging structures. The approach partitions computational domains strategically, employing FEM for regular…

Numerical Analysis · Mathematics 2026-01-14 Yanpeng Gong , Sishuai Li , Yue Mei , Bingbing Xu , Fei Qin , Xiaoying Zhuang , Timon Rabczuk

The aim of this paper is to deal with multi-physics simulation of micro-electro-mechanical systems (MEMS) based on an advanced numerical methodology. MEMS are very small devices in which electric as well as mechanical and fluid phenomena…

Other Computer Science · Computer Science 2007-11-29 V. Rochus , J. -C. Golinval , C. Louis , C. Mendez , I. Klapka

Transient grating spectroscopy (TGS) is a material characterization technique based on laser-induced thermoelastic excitation of thermal and acoustic gratings. On opaque samples, these gratings are dynamic surface displacements that reflect…

Materials Science · Physics 2026-05-01 Jakub Kušnír , Tomáš Grabec , Petr Sedlák , Pavla Stoklasová , Hanuš Seiner

This study proposes a high-order multi-scale method tailored for time-dependent nonlinear thermo-electro-mechanical coupling problems of composite structures with highly spatial heterogeneity, which incorporate temperature-dependent…

Numerical Analysis · Mathematics 2026-04-22 Hao Dong

This paper presents a very straightforward method to compute the transient thermal response to arbitrary power dissipation profiles in electronic devices with multiple heat sources. Using cubic spline interpolation of simulated or measured…

Materials Science · Physics 2007-09-13 D. Schweitzer