Continuous Finite Element Method Research Articles

Pressure and convection robust bounds for continuous interior penalty divergence-free finite element methods for the incompressible Navier–Stokes equations

Abstract In this paper, we analyze a pressure-robust method based on divergence-free mixed finite element methods with continuous interior penalty stabilization. The main goal is to prove an $O(h^{k+1/2})$ error estimate for the $L^2$ norm of the velocity in the convection dominated regime. This bound is pressure robust (the error bound of the velocity does not depend on the pressure) and also convection robust (the constants in the error bounds are independent of the Reynolds number).

Finite element solution of crack-tip fields for an elastic porous solid with density-dependent material moduli and preferential stiffness

In this paper, the finite element solutions of crack-tip fields for an elastic porous solid with density-dependent material moduli are presented. Unlike the classical linearized case in which material parameters are globally constant under a small strain regime, the stiffness of the model presented in this paper can depend upon the density with a modeling parameter. The proposed constitutive relationship appears linear in the Cauchy stress and linearized strain independently. From a subclass of the implicit constitutive relation, the governing equation is bestowed via the balance of linear momentum, resulting in a quasi-linear partial differential equation (PDE) system. Using the classical damped Newton’s method, the sequence of linear problems is then obtained, and the linear PDEs are discretized through a bilinear continuous Galerkin-type finite element method. We perform a series of numerical simulations for material bodies with a single edge-crack subject to a variety of loading types (i.e. the pure mode-I, II, and mixed-mode). Numerical solutions demonstrate that the modeling parameter in our proposed model can control preferential mechanical stiffness with its sign and magnitude along with the change of volumetric strain. This study can provide a mathematical and computational foundation to further model the quasi-static and dynamic evolution of cracks, utilizing the density-dependent moduli model and its modeling framework.

Numerical simulation of CO2-enhanced oil recovery in fractured shale reservoirs using discontinuous and continuous Galerkin finite element methods

Introduction: This study explores the potential of enhancing shale oil recovery and reducing CO2 emissions through CO2 injection in fractured shale reservoirs. The importance of this approach lies in its dual benefit: improving oil extraction efficiency and addressing environmental concerns associated with CO2 emissions.Method: We employed a discrete fracture-matrix model to simulate CO2 flooding in fractured shale reservoirs, utilizing both discontinuous Galerkin (DG) and continuous Galerkin (CG) finite element methods. The DG-CG FEM’s accuracy was validated against the McWhorter problem, ensuring the reliability of the simulation results. Our model also considered various factors, including reservoir heterogeneity, fracture permeability, CO2 injection volume, and gas injection patterns, to analyze their impact on shale oil recovery.Result: Our simulations revealed that fractured reservoirs significantly enhance shale oil production efficiency compared to homogeneous reservoirs, with an approximate 48.9% increase in production. A notable increase in shale oil production, by 15.8%, was observed when fracture permeability was increased by two orders of magnitude. Additionally, a fourfold increase in CO2 injection rate resulted in a 31.5% rise in shale oil production. Implementing a step-by-step reduction in injection volume while maintaining the total CO2 injection constant proved to be more effective than constant-rate injections.Discussion: The study demonstrates the effectiveness of CO2 flooding in fractured shale reservoirs for enhancing shale oil recovery.

FEMFFUSION and its verification using the C5G7 benchmark

FEMFFUSION is an open source code that solves the multigroup neutron transport equation using the diffusion and the SPN approximations. This code uses the continuous Galerkin finite element method to be able to deal with any type of geometry, structured or unstructured, and problem dimension. To verify the program, a research study of the two-dimensional C5G7 benchmark has been performed, including the static, time-dependent and neutron noise computations. Numerical results include the effective multiplication factor, keff, the spatial neutron fluxes, and neutron power distributions for the static computations. The total neutron power evolution of a given transient and the neutron flux distribution evolution for the different energy groups. In addition, neutron noise frequency domain calculation were completed for perturbations of some cross-section in the reactor core. All computation have been performed using different SPN approximations. FEMFFUSION results are verified against the official OECD/NEA benchmark results.

A SAV finite element method for the Cahn–Hilliard equation with dynamic boundary conditions

In this paper, we propose a SAV method for the Cahn–Hilliard type phase field model with new dynamic boundary conditions. By using the continuous finite element method in space and the backward difference method in time, the fully discrete numerical schemes preserving the energy law are constructed. Numerical examples show that the proposed scheme can simulate the phase field model well even in a relatively rough grid.

A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume / finite element scheme for the incompressible MHD equations

We present a new exactly divergence-free and well-balanced hybrid finite volume/finite element scheme for the numerical solution of the incompressible viscous and resistive magnetohydrodynamics (MHD) equations on staggered unstructured mixed-element meshes in two and three space dimensions. The equations are split into several subsystems, each of which is then discretized with a particular scheme that allows to preserve some fundamental structural features of the underlying governing PDE system also at the discrete level. The pressure is defined on the vertices of the primary mesh, while the velocity field and the normal components of the magnetic field are defined on an edge-based/face-based dual mesh in two and three space dimensions, respectively. This allows to account for the divergence-free conditions of the velocity field and of the magnetic field in a rather natural manner. The non-linear convective and the viscous terms in the momentum equation are solved at the aid of an explicit finite volume scheme, while the magnetic field is evolved in an exactly divergence-free manner via an explicit finite volume method based on a discrete form of the Stokes law in the edges/faces of each primary element. The latter method is stabilized by the proper choice of the numerical resistivity in the computation of the electric field in the vertices/edges of the 2D/3D elements. To achieve higher order of accuracy, a piecewise linear polynomial is reconstructed for the magnetic field, which is guaranteed to be exactly divergence-free via a constrained L2 projection. Finally, the pressure subsystem is solved implicitly at the aid of a classical continuous finite element method in the vertices of the primary mesh and making use of the staggered arrangement of the velocity, which is typical for incompressible Navier-Stokes solvers. In order to maintain non-trivial stationary equilibrium solutions of the governing PDE system exactly, which are assumed to be known a priori, each step of the new algorithm takes the known equilibrium solution explicitly into account so that the method becomes exactly well-balanced. We show numerous test cases in two and three space dimensions in order to validate our new method carefully against known exact and numerical reference solutions. In particular, this paper includes a very thorough study of the lid-driven MHD cavity problem in the presence of different magnetic fields and the obtained numerical solutions are provided as free supplementary electronic material to allow other research groups to reproduce our results and to compare with our data. We finally present long-time simulations of Soloviev equilibrium solutions in several simplified 3D tokamak configurations, showing that the new well-balanced scheme introduced in this paper is able to maintain stationary equilibria exactly over very long integration times even on very coarse unstructured meshes that, in general, do not need to be aligned with the magnetic field.

A numerical solver for investigating the space charge effect on theelectric field in liquid argon time projection chambers

This paper reports the development of a numerical solver aimed to simulate the interaction between the space charge (i.e. ions) distribution and the electric field in liquid argon time projection chamber (LArTPC) detectors. The ion transport equation is solved by a time-accurate, cell-centered finite volume method and the electric potential equation by a continuous finite element method. The electric potential equation updates the electric field which provides the drift velocity to the ion transport equation. The ion transport equation updates the space charge density distribution which appears as the source term in the electric potential equation. The interaction between the space charge distribution and the electric field is numerically simulated within each physical time step. The convective velocity in the ion transport equation can include the background flow velocity in addition to the electric drift velocity. The numerical solver has been parallelized using the Message Passing Interface (MPI) library. Numerical tests show and verify the capability and accuracy of the current numerical solver. It is planned that the developed numerical solver, together with a Computational Fluid Dynamics (CFD) package which provides the flow velocity field, can be used to investigate the space charge effect on the electric field in large-scale particle detectors.

Dispersion Analysis of CIP-FEM for the Helmholtz Equation

When solving the Helmholtz equation numerically, the accuracy of numerical solution deteriorates as the wave number increases, which is known as “pollution effect” and which is directly related to the phase difference between the exact and numerical solutions, caused by the numerical dispersion. In this paper, we propose a dispersion analysis for the continuous interior penalty finite element method (CIP-FEM) and derive an explicit formula of the penalty parameter for the th order CIP-FEM on tensor product (Cartesian) meshes, with which the phase difference is reduced from to . Extensive numerical tests show that the pollution error of the CIP-FE solution is also reduced by two orders in with the same penalty parameter.

Solution of Neutron Diffusion Problems by Discontinuous Galerkin Finite Element Method With Consideration of Discontinuity Factors

Abstract Neutronics calculations are the basis of reactor analysis and design. Finite element methods (FEM) have gained increasing attention in solving neutron transport problems for the rigorous mathematical formulation and the flexibility of handling complex geometric domains and boundary conditions. In order to reduce the computational errors caused by the homogenization of cross sections, this paper adopts the discontinuous Galerkin finite element method (DG-FEM) to solve the generalized eigenvalue problem formulated by the neutron diffusion theory and compensates the homogenization error by incorporating discontinuity factors. The results show that the discontinuous Galerkin finite element method can introduce the discontinuity factors with clear mathematical and physical meanings. The computational results of the discontinuous Galerkin finite element method are slightly better than those of the continuous Galerkin finite element method. However, the computation cost of the former is higher than that of the latter. Although good parallel efficiency can be achieved, the discontinuous Galerkin finite element method is not preferable for large-scale problems unless the effect of the discontinuity factors is significant.

Some Observations on the Interaction Between Linear and Nonlinear Stabilization for Continuous Finite Element Methods Applied to Hyperbolic Conservation Laws

We discuss stability and accuracy of stabilized finite element methods for hyperbolic problems. In particular we focus on the interaction between linear and nonlinear stabilizations. First we show that the combination of linear and nonlinear stabilization can be designed to be invariant preserving. Then we show that such a combined method allows for the classical error estimates for smooth solutions of space semidiscretized formulations of the linear transport equation. Based on these ideas we propose a Runge–Kutta finite element method for the compressible Euler equations using entropy viscosity to ensure stability at shocks and gradient jump penalty to prevent propagation of high frequency content into the smooth part of the solution. In a numerical example we show that the method predicts the shock structure accurately, without high frequency pollution of the smooth parts.

Adaptive FEM for Helmholtz Equation with Large Wavenumber

A posteriori upper and lower bounds are derived for the linear finite element method (FEM) for the Helmholtz equation with large wavenumber. It is proved rigorously that the standard residual type error estimator seriously underestimates the true error of the FE solution for the mesh size h in the preasymptotic regime, which is first observed by Babuška et al. (Int J Numer Methods Eng 40:3443–3462, 1997) for a one dimensional problem. By establishing an equivalence relationship between the error estimators for the FE solution and the corresponding elliptic projection of the exact solution, an adaptive algorithm is proposed and its convergence and quasi-optimality are proved under the condition that \(k^3h_0^{1+\alpha }\) is sufficiently small, where k is the wavenumber, \(h_0\) is the initial mesh size, and \(\frac{1}{2}<\alpha \le 1\) is a regularity constant depending on the maximum reentrant angle of the domain. Numerical tests are given to verify the theoretical findings and to show that the adaptive continuous interior penalty finite element method (CIP-FEM) with appropriately selected penalty parameters can greatly reduce the pollution error and hence the residual type error estimator for this CIP-FEM is reliable and efficient even in the preasymptotic regime.

A Priori and a Posteriori Error Analysis for Generic Linear Elliptic Problems

In this paper, a priori error analysis has been examined for the continuous Galerkin finite element method which is used for solving a generic scalar and a generic system of linear elliptic equations. We derived optimal order a priori error bounds in (energy) norm utilising standard a priori error analysis techniques and tools. Also, a posteriori error analysis is investigated for a generic scalar linear elliptic equation and for a generic system of linear elliptic equations. We derived optimal residual-based a posteriori error estimates energy technique in  norm

A family of independent Variable Eddington Factor methods with efficient preconditioned iterative solvers

We present a family of discretizations for the Variable Eddington Factor (VEF) equations that have high-order accuracy on curved meshes and efficient preconditioned iterative solvers. The VEF discretizations are combined with the Discontinuous Galerkin transport discretization from [1] to form effective high-order, linear transport methods. The VEF discretizations are derived by extending the unified analysis of Discontinuous Galerkin methods for elliptic problems presented by Arnold et al. [2] to the VEF equations. This framework is used to define analogs of the interior penalty, second method of Bassi and Rebay, minimal dissipation local Discontinuous Galerkin, and continuous finite element methods. The analysis of subspace correction preconditioners [3], which use a continuous operator to iteratively precondition the discontinuous discretization, is extended to the case of the non-symmetric VEF system. Numerical results demonstrate that the VEF discretizations have arbitrary-order accuracy on curved meshes, preserve the thick diffusion limit, and are effective on a proxy problem from thermal radiative transfer in both outer transport iterations and inner preconditioned linear solver iterations. We demonstrate that the VEF solution converges to the SN transport solution as the mesh is refined on both problems with smooth and non-smooth behavior in angle. Parallel performance studies show that the interior penalty VEF discretization's linear solve weak scales out to 1024 processors and strong scales well on a single node. Particular attention is paid to the parallel performance of the VEF algorithm when used in combination with a parallel block Jacobi transport sweep.

Meet the Editors

In this editorial, I would like to introduce you to our Senior Editor and eighteen Associate Editors. First of all, I wish to express my gratitude and thanks to our retiring Associate Editors Dr. Tianjian Lu (Google Inc., USA) and Prof. Tao Zheng (North China Electric Power University, China) for their expertise and dedicated service to IJNM. Meanwhile, I am delighted to welcome our new Associate Editor Prof. Zlatica Marinković (University of Niš, Serbia). She brings her great expertise on neural modeling and machine learning applications in the field of microwaves, telecommunications, and electronics. As part of our continuous commitment to promote diversity, equality, and inclusion, our team of Editors comprises researchers from various countries (i.e., China, Finland, Iceland, India, Italy, Poland, Serbia, Singapore, and USA) and with gender diversity (i.e., three female Associate Editors) and complementary expertise. Given the strong multidisciplinary nature of IJNM, our team consists of highly skilled and motivated researches from diverse scientific backgrounds. They are all well-recognized researchers in their respective areas of expertise. Their biographies and photos are given below, in alphabetical order. In closing, my warmest thanks to the entire team of Editors for their outstanding work and dedication to IJNM. They are truly the very backbone of this journal, whose success is based on a great teamwork! NAME: Slawomir SURNAME: Koziel AFFILIATION: Reykjavik University, Iceland EMAIL: koziel@ru.is SHORT BIO: Slawomir Koziel received the M.Sc. and Ph.D. degrees in electronic engineering from Gdansk University of Technology, Poland, in 1995 and 2000, respectively. He also received the M.Sc. degrees in theoretical physics and in mathematics, in 2000 and 2002, respectively, as well as the PhD in mathematics in 2003, from the University of Gdansk, Poland. He is currently a Professor with the Department of Engineering, Reykjavik University, Iceland. His research interests include CAD and modeling of microwave and antenna structures, simulation-driven design, surrogate-based optimization, space mapping, circuit theory, analog signal processing, evolutionary computation and numerical analysis. NAME: Guido SURNAME: Ala AFFILIATION: University of Palermo, Italy EMAIL: guido.ala@unipa.it SHORT BIO: Guido Ala is currently Full Professor in Electrical Engineering - SC 09/E1, at the “Dipartimento di Ingegneria” of the University of Palermo. Since 2012, he has been the director of the laboratory for Modelling and Electromagnetic Simulation – MOSEM-lab. His main research interests are in the fields of computational electromagnetics (including MoM, FDTD, application of wavelets, mesh-free innovative numerical approach), electromagnetic transient analysis, lightning, electromagnetic compatibility, optimized design of EMI filters and power electronics converters, partial discharge detection, biomedical engineering (including magnetoencephalography and electroencephalography innovative numerical modelling, and electromagnetic fields effect on humans), electrical systems design for fusion engineering, innovative solutions for sustainable mobility in the smart cities context, electrical analogies in material's viscoelasticity behavior. He has coauthored several scientific papers in peer reviewed international journals, in peer reviewed international volumes and in proceedings and abstract of international conferences, in proceedings of national conferences. NAME: Yogendra SURNAME: Arya AFFILIATION: J.C. Bose University of Science and Technology, YMCA, India EMAIL: yarya@jcboseust.ac.in SHORT BIO: Yogendra Arya is currently an Associate Professor at J.C. Bose University of Science & Technology, YMCA, India. He has published 50+ research papers in reputed National/International journals and conferences. He has published 35+ SCIE papers, out of which 13 are written as a sole author. He has received “MSIT Best Faculty Award” in 2018 and “MSIT Certificate of Excellence in Research” in 2018 & 2019. He has been placed among “Top 2% of Researchers in the World” for 2019 & 2020 by Stanford University, USA. He is a regular reviewer of leading journals. He has Google Scholar citations of 1700+ and h-index of 25. He has received “Best Associate Editor Award-2021” from Journal of Electrical Engineering & Technology. He is Fellow of IETE, Senior Member of IEEE, AMIE(I) and Life Member of ISTE. His major areas of research interests include instrumentation, measurement, control, AGC/LFC in smart grid, fuzzy control, optimization techniques, energy storage systems and renewable energy systems. NAME: Ruisheng SURNAME: Diao AFFILIATION: Zhejiang University - University of Illinois Urbana-Champaign Institute, Haining, China EMAIL: ruishengdiao@intl.zju.edu.cn SHORT BIO: Ruisheng Diao obtained his Ph.D. degree in Electrical Engineering from Arizona State University in 2009. He has been managing and supporting a portfolio of research projects in the area of power system modeling, dynamic simulation, online security assessment and control, dynamic state estimation, integration of renewable energy, AI and HPC implementation in power systems, etc. The project funds range from $30 K to $4 M. Dr. Diao has published more than 100 peer reviewed journal and conference papers. He is the co-applicant for 20 U.S. patents. Dr. Diao is the recipient of the 2018 R&D 100 Awards, 2018 IEEE PES Conference Prize Paper Award, and multiple IEEE PES best paper awards. He is a senior member of IEEE and a registered Professional Engineer (PE) in Washington State. Dr. Diao is now with ZJU-UIUC Institute as Director, Renewable Power System Simulation & Intelligent Control, and a tenured associate professor, leading the development of a number of AI-based applications in power systems (autonomous voltage control, line flow control, intelligent maintenance scheduling and others for power utilities and control centers). NAME: Xinda SURNAME: Ke AFFILIATION: Pacific Northwest National Laboratory (PNNL), Richland, USA EMAIL: xke@pnnl.gov SHORT BIO: Xinda Ke received the Ph.D. at North Carolina State University, Raleigh, NC in 2016. He has been a senior power system engineer at Pacific Northwest National Laboratory (PNNL) since 2016. Xinda has been managing and supporting multiple research projects that funded by DOE, EERE, ARPA-E, and other industrial collaborators. His research interests involves power grid operation and planning tool development, renewable integration and production cost study. NAME: Qi SURNAME: Li AFFILIATION: Southwest Jiaotong University, China EMAIL: liqi0800@163.com SHORT BIO: Qi Li is currently a Full Professor at the Southwest Jiaotong University, China. He did research as Visiting Scholar with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, from 2009 and 2011. His main research interests include optimization and control of integrated energy system, energy storage system management in transportation and power grid, hydrogen and fuel cell generation technology. He has authored or coauthored more than 200 publications in international journals. He has authorized for 45 Chinese patents. He is IET Fellow and IEEE Senior member, and he is the Associate Editor of IEEE Transactions on Transportation Electrification, CSEE Journal of Power and Energy Systems and IEEE Access. He was nominated in 2019 as the Sub-committee Chair of Technical Committee on Transportation Electrification of the IEEE Industrial Electronics Society. NAME: Zlatica SURNAME: Marinković AFFILIATION: University of Niš, Serbia EMAIL: zlatica.marinkovic@elfak.ni.ac.rs SHORT BIO: Zlatica Marinković is currently an Associate Professor with the University of Niš, Faculty of Electronic Engineering Serbia. Her main research areas are neural modeling of microwave transistors and machine learning applications in the field of microwaves, telecommunications and electronics. She was a visiting researcher with the University of Messina, Italy and the University of L'Aquila, Italy. She authored/coauthored more than 150 scientific papers in international journals and conferences and three book chapters. Dr. Marinković serves as the IEEE MTT-S Undergraduate Scholarship Chair and as the Chair of IEEE MTT-S Chapter of Serbia and Montenegro. She also serves as the vice-chair of the IEEE Serbia and Montenegro Women in Engineering Affinity Group. NAME: Anna SURNAME: Pietrenko-Dabrowska AFFILIATION: Gdansk University of Technology, Poland EMAIL: anna.dabrowska@pg.edu.pl SHORT BIO: Anna Pietrenko-Dabrowska received the M.Sc. and Ph.D. degrees in electronic engineering from Gdansk University of Technology, Poland, in 1998 and 2007, respectively. Currently, she is an Associate Professor with Gdansk University of Technology, Poland. Her research interests include simulation-driven design, design optimization, control theory, modeling of microwave and antenna structures, numerical analysis. NAME: Antonio SURNAME: Raffo AFFILIATION: University of Ferrara, Italy EMAIL: antonio.raffo@unife.it SHORT BIO: Antonio Raffo was born in Taranto, Italy, in 1976. He received the M.S. degree cum laude in electronic engineering and Ph.D. degree in information engineering from the University of Ferrara, Ferrara, Italy, in 2002 and 2006, respectively. Since 2002, he has been with the Department of Engineering, University of Ferrara, where he is currently an Associate Professor teaching the courses of circuit theory and high-frequency electronics. He has co-authored more than 150 publications in international journals and conferences and co-edited “Microwave Wireless Communications: From Transistor to System Level” (Elsevier, 2016). His current research interests include nonlinear electron device characterization and modeling and circuit-design techniques for nonlinear microwave and millimeter-wave applications. Prof. Raffo has been the Chair of the IEEE Microwave Measurements Technical Committee and serves as Technical Program Committee member of the most important international conferences on microwave electronics. NAME: Ping Jack SURNAME: Soh AFFILIATION: University of Oulu, Finland EMAIL: pingjack.soh@oulu.fi SHORT BIO: Ping Jack Soh was born in Sabah, Malaysia. He is an Associate Professor in the Centre for Wireless Communications (CWC), University of Oulu, Finland, and the coordinator for the “Devices and Circuit Technology” strategic research area within the national Finnish 6G Flaghip program. His research interests include antennas and their applications in wearables/body area communication; metasurfaces and reflectors; 6G communications; compact satellites; and wireless healthcare techniques. He was the recipient of the URSI Young Scientist Award in 2015, the IEEE MTT-S Graduate Fellowship in 2013 and the IEEE AP-S Doctoral Research Award in 2012. He was also the Second Place Winner of the IEEE Presidents' Change the World Competition in 2013. He is a Chartered Engineer registered with the UK Engineering Council; a Senior Member of the IEEE, and Members of the IET and URSI. He also serves in the IEEE MTT-S Undergraduate Scholarships and Graduate Fellowships committee. NAME: Valeria SURNAME: Vadalà AFFILIATION: University of Milano-Bicocca, Italy EMAIL: valeria.vadala@unimib.it SHORT BIO: Valeria Vadalà received the M.S. degree cum laude in electronic engineering from the “Mediterranea” University of Reggio Calabria, Reggio Calabria, Italy, in 2006 and the Ph.D. degree in information engineering from the University of Ferrara, Ferrara, Italy, in 2010. In 2013 she was invited to spend a period as Visiting Fellow at the Telecommunication and Microwave Laboratory (TELEMIC) at the Engineering department of KU Leuven University in Belgium. She is currently Assistant Professor at the University of Milano-Bicocca where she teaches the course of electronic instrumentation and measurement in the MS degree at the Department of Physics. Her current research interests include nonlinear electron-device characterization and modeling and circuit-design techniques for nonlinear microwave and millimeter wave applications. NAME: Chao-Fu SURNAME: Wang AFFILIATION: National University of Singapore, Singapore EMAIL: cfwang@nus.edu.sg SHORT BIO: Chao-Fu Wang is currently a Principal Research Scientist and an Associate Professor at the National University of Singapore, Singapore. From 1996 to 1999, he was a Postdoctoral Research Fellow at the University of Illinois at Urbana-Champaign, USA. He coauthored Characteristic Modes: Theory and Applications in Antenna Engineering (Wiley, 2015). He was a co-recipient of the 2009 Best Applied Computational Electromagnetics Society (ACES) Journal Paper Award. He served as the Chairperson for the IEEE Singapore MTT/AP Chapter in 2013. He has been actively involved in organizing many conferences, including the General Chair of IEEE ICCEM 2020 and the Special Session and Short Course Chair of 2021 IEEE AP-S/URSI 2021. He is currently an Associate Editor of the IEEE Transactions on Microwave Theory and Techniques, IEEE Journal on Multiscale and Multiphysics Computational Techniques, International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, and Electronics Letters. NAME: Su SURNAME: Xu AFFILIATION: Jilin University, China EMAIL: xusu@jlu.edu.cn SHORT BIO: Su Xu is currently an Associate Professor at Jilin University, China. His main research interests include design, modeling and characterization of microwave and terahertz devices with nanoscale artificial structures. He has authored or coauthored more than 40 publications in international journals and conferences. He is currently collaborating with worldwide-known companies for the potentially industrial application of artificial structure-based electromagnetic devices. NAME: Yuehang SURNAME: Xu AFFILIATION: University of Electronic Science and Technology of China, China EMAIL: yuehangxu@uestc.edu.cn SHORT BIO: Yuehang Xu is currently a Professor at University of Electronic Science and Technology of China (UESTC),China. He was a visiting scholar of Columbia University, New York, NY, USA, in 2010. And he was a Visiting Associate Professor of Case Western Reserve University, Cleveland, OH, USA, in 2016. He is the first author of “Equivalent circuit modeling of Microwave GaN power transistors” (China Science Press, 2017) and the second author of “Microwave integrated circuits” (Electronic Industry press,2018). He has authored or co-authored more than 150 scientific papers in international journals and conferences. His current research interests include transistor modeling, microwave integrated circuits, RF GaN circuits, and diamond electronics. He has served as one of two General Chairs of MOS-AK in 2019, and Session Chair of “Modeling, CAD and Testing” in IEEE ICTA since 2019. NAME: Su SURNAME: Yan AFFILIATION: Howard University, USA EMAIL: su.yan@howard.edu SHORT BIO: Su Yan is an Assistant Professor at Howard University, Washington, DC, USA, and serves as the Director of Graduate Studies in the Department of Electrical Engineering and Computer. His research interests include nonlinear electromagnetic (EM) and multiphysics problems, EM scattering and radiation, numerical methods in computational EM, especially continuous and discontinuous Galerkin finite element methods, integral-equation-based methods, domain decomposition methods, fast algorithms, and preconditioning techniques. He has authored or coauthored over 110 papers in refereed journals and conferences and two book chapters. Dr. Yan is a Senior Member of the IEEE, and a Life Member of the Applied Computational Electromagnetics Society (ACES). He was a recipient of the ACES Early Career Award in 2020 and a recipient of the Edward E. Altschuler AP-S Magazine Prize Paper Award by IEEE Antennas and Propagation Society in 2020. NAME: Abdulkadir C. SURNAME: Yucel AFFILIATION: Nanyang Technological University, Singapore EMAIL: acyucel@ntu.edu.sg SHORT BIO: Abdulkadir C. Yucel is an Assistant Professor at Nanyang Technology University (NTU), Singapore. He received his M.S. and Ph.D. degrees in electrical engineering from the University of Michigan, Ann Arbor, MI, USA, in 2008 and 2013, respectively. He pursued his postdoctoral studies in various institutions, including the Massachusetts Institute of Technology, MA, USA. Dr. Yucel was the recipient of Fulbright Fellowship in 2006, EECS Departmental Fellowship of University of Michigan in 2007, and Honorable Mention Award at IEEE Int. Symp. AP-S in 2009. He is the author/co-author of more than 110 journal papers and conference papers/abstracts. He is a Senior Member of IEEE. He is currently serving as an Associate Editor for IEEE Antennas and Propagation Magazine and the International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, as a reviewer for various technical journals, and as a reviewer and organizing committee member of several IEEE conferences. NAME: Ata SURNAME: Zadehgol AFFILIATION: University of Idaho, USA EMAIL: azadehgol@uidaho.edu SHORT BIO: Ata Zadehgol received the B.S. degree in electrical engineering (EE) from the University of Washington, in 1996, the M.S. degree in EE from the University of California at Davis, in 2006, and the Ph.D. degree in EE from the University Illinois at Urbana, in 2011. With more than a decade of experience in advanced microelectronics industry, in 2014 he joined the University of Idaho where he is currently an Associate Professor in ECE, and the director of the Applied Computational Electromagnetics and Signal/Power Integrity (ACEM-SPI) group. His research interests include computational electromagnetics and its various applications in low-frequency to THz electronic systems. His work has been recognized through research grants from the NSF, NASA, Micron Technology, and SEL, the IEEE TCPMT best poster-paper award, and University of Idaho's Presidential Mid-Career Award. He has served on the Editorial Board of IJNM since 2016. Dr. Zadehgol is a professional engineer licensed in Idaho State. NAME: Hualiang SURNAME: Zhang AFFILIATION: University of Massachusetts Lowell, USA EMAIL: hualiang_zhang@uml.edu SHORT BIO: Hualiang Zhang is currently a Professor with the Electrical and Computer Engineering Department, University of Massachusetts Lowell. He received the B.S. degree in Electrical Engineering from the University of Science and Technology of China in 2003, and his Ph.D. degree in Electrical and Computer Engineering from the Hong Kong University of Science and Technology in 2007. From 2007 to 2009 he was a postdoctoral research associate at the University of Arizona. From 2009 to Jan. 2016, he was an Assistant Professor and then Associate Professor at the University of North Texas. He has coauthored over 250 journal and conference papers. His research interests include RF/microwave/millimeter-wave circuits and systems, antennas, metasurfaces and metamaterials, nano-photonics and optoelectronics in both rigid and flexible substrates, as well as their applications, covering the frequency range from RF/microwave and THz to infrared and visible. He has served as the Sub-Committee Chair of the IEEE International Microwave Symposium and Technical Committee Members of several major technical conferences. NAME: Zhenyuan SURNAME: Zhang AFFILIATION: University of Electronic Science and Technology of China, China EMAIL: zhangzhenyuan@uestc.edu.cn SHORT BIO: Zhenyuan Zhang is currently a Professor with the Department of Mechanical and Electrical Engineering, at the University of Electronic Science and Technology of China (UESTC), Chengdu, China. His focus lies in power system analysis and modeling, electrical safety, smart grids, renewable energy, and power market researches. He has published more than 100 technical papers, where more than 60 SCI journal papers, and has participated in more than 30 research projects as Principal Investigator or Co-Principal Investigator. He served as the Secretary of IEEE IAS ESC/DER Committee, Associate Editor of IEEE TIA, IJNM, and Editor of PCMP. He was the General Chair of 2021 AEEES, Secretary in General of 2019 IEEE ISGT ASIA and 2021 IEEE I&CPS ASIA. He is of receipt of several IEEE awards, such as Prize Paper Award of IEEE TIA, IEEE IAS Ralph Lee Award, IEEE IAS I&CPS Department Prize Paper Awards, IEEE ESW award, etc.

An Arbitrary-Lagrangian-Eulerian hybrid finite volume/finite element method on moving unstructured meshes for the Navier-Stokes equations

This paper presents a novel semi-implicit hybrid finite volume / finite element (FV/FE) scheme for the numerical solution of the incompressible and weakly compressible Navier-Stokes equations on moving unstructured meshes using a direct Arbitrary-Lagrangian-Eulerian (ALE) formulation. The scheme is based on a suitable splitting of the governing partial differential equations into subsystems and employs a staggered grid arrangement, where the pressure is defined on the primal simplex mesh, while the velocity and the remaining flow quantities are defined on an edge-based staggered dual mesh. The key idea of the scheme presented in this paper is to discretize the nonlinear convective and viscous terms at the aid of an explicit finite volume scheme that employs the space-time divergence form of the governing equations on moving space-time control volumes. For the convective terms, an ALE extension of the Ducros flux on moving meshes is introduced, which can be proven to be kinetic energy preserving and stable in the energy norm when adding suitable numerical dissipation terms. The use of closed space-time control volumes inside the finite volume scheme guarantees that the important geometric conservation law (GCL) of Lagrangian schemes is verified by construction. Finally, the pressure equation of the Navier-Stokes system is solved on the new mesh configuration at the aid of a classical continuous finite element method, using traditional P1 Lagrange elements.A numerical convergence study confirms that the scheme is second order accurate in space. Subsequently, the ALE hybrid FV/FE method is applied to several incompressible test problems ranging from non-hydrostatic free surface flows over a rising bubble to flows over an oscillating cylinder and an oscillating ellipse. Via the simulation of a circular explosion problem on a moving mesh, we show that the scheme applied to the weakly compressible Navier-Stokes equations is able to capture also weak shock waves, rarefactions and moving contact discontinuities. We also provide numerical evidence which shows that compared to a fully explicit ALE scheme, the semi-implicit ALE method proposed in this paper is particularly efficient for the simulation of weakly compressible flows in the low Mach number limit.

Numerical Solutions of Quasilinear Parabolic Problems by a Continuous Space-Time Finite Element Scheme

In this paper, continuous space-time finite element methods are developed for approximating a class of quasilinear parabolic problems in space and in time, simultaneously. The basis of the whole approach is on a space-time variational formulation where streamline upwind terms and interface jump terms are further added for stabilizing the discretization in the direction of time. Error estimates are shown and are verified numerically through a series of numerical tests. Emphasis is placed on investigating the asymptotic convergence of the error parts, which are related to the time discretization.

A quasi-static contact model for global dynamic simulation of multibody system with contact-impact

The global impact dynamics of multibody system is challenging due to the multi-scale characteristics of slow-changing non-contact process and fast-changing impact process. To solve the contradiction between the impact accuracy and the global simulation efficiency, a novel quasi-static contact model is proposed where the local contact domain is finely discretized and the energy loss caused by elastoplasticity is considered, and the real-time force-displacement interaction is established to execute the global integration capably. Through the experimental case of flexible pendulum impact, the proposed model is compared with measurements and existing methods, including impulse method, continuous contact force method and nonlinear finite element method. It is shown that the impulse method and continuous contact force method are both sensitive to the coefficient of restitution, yielding uncertain results. The nonlinear finite element method can accurately describe the impact process, but its calculation scale is too large to apply to the global simulation. The quasi-static model can accurately describe the response of the global process and does not rely on artificial selection of any parameters, and the calculation efficiency is greatly improved compared with the nonlinear finite element method.

From computed tomography to finite element space: A unified bone material mapping strategy

BackgroundThe spatially varying mechanical properties in finite element models of bone are most often derived from bone density data obtained via quantitative computed tomography. The key step is to accurately and efficiently map the density given in voxels to the finite element mesh. MethodsThe density projection is first formulated in least-squares terms and then discretized using a continuous and discontinuous variant of the finite element method. Both discretization variants are compared with the nodal and element approaches known from the literature. FindingsIn terms of accuracy in the L2 norm, energy distance and efficiency, the discontinuous zero-order variant appears to be the most advantageous. The proposed variant sufficiently preserves the spectrum of density at the edges, while keeping computational cost low. InterpretationThe continuous finite element method is analogous to the nodal formulation in the literature, while the discontinuous finite element method is analogous to the element formulation. The two variants differ in terms of implementation, computational cost and ability to preserve the density spectrum. These differences cannot be described and measured by known indirect methods from the literature.

A new continuous finite element SN method for solving first-order neutron transport equation

A continuous finite element method (FEM) based on B-spline wavelet on the interval (BSWI) is proposed to solve the first-order neutron transport equation with discrete ordinate (SN) angular discretization. Two technologies are applied in this method, one of technologies is that the streamline upwind Petrov-Galerkin (SUPG) method is utilized to stabilize the first-order neutron transport equation when the FEM is used. Another is that the scaling functions of BSWI are applied to replace the usual Lagrange basis function. Based on the above two technologies, the stabilized weak form of neutron transport equation applying the SUPG technology based on BSWI is derived. Finally, some numerical examples are utilized to verify the proposed method. The results demonstrate that the method can treat the void region problem, and compared the FEM with SUPG technology, it can obtain fast convergence and numerical precision under the condition of much less grid. Overall, this method has good accuracy, high computational efficiency and wide application.

A Continuous Finite Element Method with Homotopy Vanishing Viscosity for Solving the Static Eikonal Equation

A Continuous Finite Element Method with Homotopy Vanishing Viscosity for Solving the Static Eikonal Equation