Article
Engineering, Multidisciplinary
Daniel Appelo, Fortino Garcia, Allen Alvarez Loya, Olof Runborg
Summary: This paper considers the application of the WaveHoltz iteration to time-harmonic elastic wave equations with energy conserving boundary conditions. Two time-stepping schemes, explicit and implicit, are presented to eliminate time discretization error from the WaveHoltz solution. Numerical experiments demonstrate the effectiveness of the proposed methods.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Multidisciplinary Sciences
Romik Khajehtourian, Mahmoud Hussein
Summary: The theory presents a method for predicting the collective harmonics spectrum in traveling nonlinear waves through the use of harmonics dispersion relation, valid for both evolving unbalanced waves and steady propagation of balanced waves with waveform invariance. It has been tested on various cases of one-dimensional elastic waves, demonstrating its applicability regardless of initial wave profile, nonlinearity type, and dispersion level in the linear limit. Additionally, the theory provides an analytical condition for soliton synthesis.
Article
Engineering, Electrical & Electronic
Yulong Xia, Qi Zhu
Summary: This article theoretically analyzes absorbers with open boundary conditions, obtaining integration relationships for reflection and transmission, and deducing theoretical limitations. It provides complete analytic limitations for single-layer nonmagnetic absorbers, and presents optimal design methods. Several absorbers are designed as examples.
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
(2021)
Article
Mathematics
Weimin Peng, Dongbing Zha
Summary: In this paper, we investigate the Cauchy problem of nonlinear elastic wave equations for two-dimension isotropic, homogeneous and hyperelastic materials with small initial data, and provide lifespan estimates for classical solutions.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mechanics
Takahito Iida, Ahmad Zareei, Mohammad-Reza Alam
Summary: The trajectory of surface gravity waves is influenced by gravitational acceleration, water density, and sea bed depth. In order to create an omnidirectional cylindrical cloaking device for finite-depth/deep-water waves, an elastic composite plate floating on the surface is proposed. The physical parameters of the plate are optimized to reduce scattered wave energy and wave drift force exerted on the object.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Optics
Matias Koivurova, Charles W. Robson, Marco Ornigotti
Summary: Research on time-varying media, particularly in photonics, has gained renewed interest recently. However, previous research has mainly focused on electromagnetic waves and a comprehensive framework describing the influence of time-varying media on wave phenomena has not been fully developed yet. This study investigates the implications of time-varying wave mechanics and modifies the standard wave equation to account for non-constant wave speed. It demonstrates that waves experiencing longitudinal acceleration exhibit relativistic properties and only propagate forward in time. The research also addresses the Abraham-Minkowski controversy in electromagnetic waves, showing that it is caused by relativistic effects and confirming the conservation of light momentum between different media. Furthermore, it presents examples of accelerating waves that conserve energy when moving along geodesics.
Article
Engineering, Electrical & Electronic
Beibei Kong, Pasi Yla-Oijala, Ari Sihvola
Summary: A surface integral equation (SIE) method has been developed for analyzing electromagnetic scattering by 3-D objects with soft-and-hard/DB (SHDB) boundary conditions. By expressing the SHDB boundary condition in vector form and combining it with tangential field integral equations, a more stable system is obtained for numerical simulations and comparisons. The proposed nonsquare integral equation solutions have been verified using physical optics approximations.
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
(2021)
Article
Mathematics, Applied
Symeon Papadimitropoulos, Dan Givoli
Summary: The study adapts and applies the Double Absorbing Boundary (DAB) to the 2D Helmholtz equation, utilizing a high-order spectral finite element scheme for numerical experiments. The results demonstrate the good performance of the DAB scheme.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Mart Borsboom, Niels G. Jacobsen
Summary: Efficient boundary conditions with low spurious reflection are essential for modeling free-surface waves, and this study introduces a new depth-varying coefficient adaptation of the classical Sommerfeld condition. The improved boundary condition is implemented in OpenFoam(R) and shown to be effective for various types of waves.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2021)
Article
Computer Science, Interdisciplinary Applications
Xavier Adriaens, Francois Henrotte, Christophe Geuzaine
Summary: This paper presents a computationally efficient method, the adjoint state method, for studying acoustic, electromagnetic, and elastic wave scattering problems, which quantifies the influence of medium properties and boundary conditions. The method is applied to various scattering problems with impedance boundary conditions, demonstrating its validity through numerical examples solved using the finite element method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Geochemistry & Geophysics
Qinghua Lei, Didier Sornette
Summary: This study presents numerical simulations of elastic wave transport in two-dimensional fractured media, finding that the dimensionless angular frequency plays a crucial role in governing wave transport. Waves exhibit different behaviors when the angular frequency is below or above a critical value, with strong attenuation occurring in well-connected fracture systems.
JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH
(2021)
Article
Computer Science, Interdisciplinary Applications
Vianey Villamizar, Jacob C. Badger, Sebastian Acosta
Summary: This paper presents derived high order and local absorbing boundary conditions (ABC) for solving multiple acoustic scattering problems in two- and three-dimensional settings. By considering continuities and utilizing the superposition of outgoing waves, a novel ABC is defined at artificial boundaries, exhibiting both accuracy and computational efficiency in dealing with complex-shaped obstacles.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Multidisciplinary Sciences
A. Roohezamin, R. Kalatehjari, M. Hajihassani, M. Kharghani, D. Dias
Summary: Understanding the acoustic behavior of buried tunnels in multilayer soil structures is crucial for locating and monitoring their structure health. This study presents a 3D finite element model of a tunnel system and investigates the variations in reflected and transmitted acoustic wave pressure for a multilayer soil buried tunnel. The effects of soil layers, tunnel buried depths, and lining concrete types on the acoustic wave behavior of the tunnel are evaluated. The findings can be applied to interpret recorded signals for structural health monitoring and locating underground structures, especially in media with multilayer soil structures.
SCIENTIFIC REPORTS
(2022)
Article
Energy & Fuels
Song -Ling Li, Ying Shi, Ning Wang, Wei-Hong Wang, Xuan Ke
Summary: In this study, we develop a hybrid absorbing boundary condition (THABC) based on a transmitting boundary to eliminate artificial boundary reflections in 3D second-order fractional viscoacoustic numerical simulations. We propose an adaptive weighted coefficient to reconcile the transmitting and viscoacoustic wavefields in THABC. Our scheme performs well in the 3D fractional Laplacian viscoacoustic numerical simulation, exhibiting better ability in eliminating boundary reflection and more efficient computation compared to traditional ABC schemes.
Article
Engineering, Multidisciplinary
Arman Shojaei, Alexander Hermann, Pablo Seleson, Stewart A. Silling, Timon Rabczuk, Christian J. Cyron
Summary: The paper focuses on applying peridynamics (PD) to the propagation of elastic waves in unbounded domains. It introduces absorbing boundary conditions (ABCs) that are derived from a semi-analytical solution of the PD governing equation. The proposed ABCs have Dirichlet-type implementation, are constructed in the time and space domains, and offer advantages in terms of simplicity and compatibility with the near-field solution.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
Kaoutar Hazim, Guillaume Parent, Stephane Duchesne, Andre Nicolet, Christophe Geuzaine
Summary: This paper presents a method for modeling the three-dimensional twisted geometry of a twisted pair using two-dimensional finite elements in an electrostatic approximation. By utilizing a change of coordinates, this method offers faster computation time and higher accuracy, demonstrating effectiveness in studying the insulation properties of winding wires in electrical machines according to the IEC 60851-5 standard.
COMPEL-THE INTERNATIONAL JOURNAL FOR COMPUTATION AND MATHEMATICS IN ELECTRICAL AND ELECTRONIC ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Anthony Royer, Christophe Geuzaine, Eric Bechet, Axel Modave
Summary: This work presents a non-overlapping substructured DDM with PML transmission conditions for checkerboard decompositions, considering cross-points. The continuity of Dirichlet traces is enforced at the interfaces between subdomains and PMLs using Lagrange multipliers, allowing for the computation of Neumann traces and the use of PMLs as discrete operators approximating the exact Dirichlet-to-Neumann maps.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
Ruiyang Dai, Axel Modave, Jean-Francois Remacle, Christophe Geuzaine
Summary: This paper explores a family of generalized sweeping preconditioners for Helmholtz problems with non-overlapping checkerboard partition. By using high-order transmission conditions and cross-point treatments in the domain decomposition procedure, combined with the flexible version of GMRES, the rapid transfer of information between different areas and accelerated convergence can be achieved. Experimental results demonstrate the good performance of the preconditioners in different sweeping directions.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Martin Grignard, Christophe Geuzaine, Christophe Phillips
Summary: This paper proposes a tool to assess the uncertainty in the model parameters and calculate parametric forward models for EEG and tDCS.
Article
Mathematics, Applied
David Gasperini, Hans-peter Biese, U. D. O. Schroeder, Xavier Antoine, Christophe Geuzaine
Summary: This paper proposes a finite element method in the frequency domain for solving scattering problems with moving or deforming boundaries. The original problem is rewritten as an equivalent weak formulation in a fixed domain. Then, a simpler weak form is approximated based on asymptotic expansions when the amplitude of the movements or deformations is small. Fourier series expansions are introduced to obtain a coupled multi-harmonic frequency domain formulation. Standard finite element methods can be applied to solve the resulting problem, and a block diagonal preconditioner is proposed to accelerate the Krylov subspace solution for high-frequency problems. The efficiency of the method is demonstrated on a radar sensing application for the automotive industry.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Ismail Badia, Boris Caudron, Xavier Antoine, Christophe Geuzaine
Summary: This paper proposes efficient weak coupling formulations between the boundary element method and the high-order finite element method for solving time-harmonic electromagnetic scattering problems. The approach is based on a nonoverlapping domain decomposition method involving optimal transmission operators, constructing transmission conditions through a localization process based on complex rational Pade' approximants of the nonlocal magnetic-to-electric operators.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Physics, Applied
M. Houbart, J-F Fagnard, J. Dular, A. R. Dennis, D. K. Namburi, J. H. Durrell, C. Geuzaine, B. Vanderheyden, P. Vanderbemden
Summary: This study experimentally investigates the assembly of large grain melt-textured superconductors with orthogonal c-axes to form a Halbach array structure. The experimental distribution of magnetic flux density above the array is compared to a similar array made of permanent magnets, and a simple analytical model is developed to accurately reproduce the main experimental observations. The results show that lowering the distance between the superconductors causes a redistribution of current and affects the magnetic flux density distribution.
SUPERCONDUCTOR SCIENCE & TECHNOLOGY
(2022)
Review
Environmental Sciences
Christian Brabant, Anton Geerinck, Charlotte Beaudart, Ezio Tirelli, Christophe Geuzaine, Olivier Bruyere
Summary: This study conducted a systematic review and meta-analysis to explore the relationship between childhood leukemia and extremely low frequency magnetic fields (ELF-MF). The results indicate that ELF-MF higher than 0.4 mu T may increase the risk of childhood leukemia, particularly acute lymphoblastic leukemia. Prolonged exposure to electric appliances that generate magnetic fields higher than 0.4 mu T like electric blankets is associated with a greater risk of childhood leukemia.
REVIEWS ON ENVIRONMENTAL HEALTH
(2023)
Article
Engineering, Electrical & Electronic
Matteo Cicuttin, Anthony Royer, Peter Binde, Christophe Geuzaine
Summary: This article discusses the implementation of DGTD for Maxwell's equations on modern GPUs and evaluates its performance in simulating electrostatic discharge.
IEEE TRANSACTIONS ON MAGNETICS
(2022)
Article
Engineering, Electrical & Electronic
Florent Purnode, Francois Henrotte, Francois Caire, Joaquim da Silva, Gilles Louppe, Christophe Geuzaine
Summary: This article presents a new approach using neural networks to determine material parameters in magnetodynamic problems with hysteresis. This method saves time and speeds up the modeling process.
IEEE TRANSACTIONS ON MAGNETICS
(2022)
Article
Engineering, Electrical & Electronic
Julien Dular, Kevin Berger, Christophe Geuzaine, Benoit Vanderheyden
Summary: In this paper, we discuss the relevance of various finite-element formulations for handling nonlinear systems containing high-temperature superconductors and ferromagnetic materials in a three-dimensional motor pole model. The formulations are evaluated based on their numerical robustness and efficiency. We propose a coupled h-phi-a formulation as the optimal choice, which successfully addresses the nonlinearities of HTS and FM while maintaining a low number of degrees of freedom (DOFs).
IEEE TRANSACTIONS ON MAGNETICS
(2022)
Article
Mathematics, Applied
D. Gasperini, H-P Beise, U. Schroeder, X. Antoine, C. Geuzaine
Summary: In this paper, the Cauchy integral theorem is utilized to develop the steepest descent method for efficiently computing the three-dimensional acoustic single-layer integral operator for large wave numbers. The explicit formulas for the splitting points are derived and the construction of admissible steepest descent paths is investigated. Based on the theoretical results, the quadrature scheme of the oscillatory integrals is derived in one dimension and extended to three-dimensional planar triangles. Numerical simulations are conducted to demonstrate the accuracy and efficiency of the proposed approach.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2023)
Article
Energy & Fuels
Ali Dashti, Maziar Gholami Korzani, Christophe Geuzaine, Robert Egert, Thomas Kohl
Summary: Evaluation of underground processes requires sophisticated and reliable numerical modeling techniques. The new GeoMeshPy library focuses on discretizing probabilistic geological structures. This study showcases the library's ability to quantify the impact of structural uncertainty through the development of 50 models. These models calculate the recovery time and magnitude of tracer breakthrough in a faulted reservoir with unclear structure, revealing significant differences due to small angular variations in the faults.
Article
Computer Science, Interdisciplinary Applications
Theodore Cherriere, Luc Laurent, Sami Hlioui, Francois Louf, Pierre Duysinx, Christophe Geuzaine, Hamid Ben Ahmed, Mohamed Gabsi, Eduardo Fernandez
Summary: This study utilizes multi-material topology optimization to maximize the torque of a 3-phase permanent magnet synchronous machine, presenting a rational function penalty for meaningful structure convergence. Results show that a hexagonal-based diamond polytope is a better choice for this problem.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Physics, Applied
Sebastien Brialmont, Julien Dular, Laurent Wera, Jean-Francois Fagnard, Benoit Vanderheyden, Christophe Geuzaine, Seungyong Hahn, Anup Patel, Philippe Vanderbemden
Summary: In this study, we demonstrated the magnetic shielding ability of a stack of YBa2Cu3O7 tape annuli. The annuli were cut from a second generation coated conductor deposited on a Ni-5at.%W alloy ferromagnetic substrate. The experiments showed that the stack of annuli could effectively shield both axial and transverse magnetic fields, and the presence of the ferromagnetic substrates played an important role in the shielding mechanism.
SUPERCONDUCTOR SCIENCE & TECHNOLOGY
(2023)
Article
Mathematics, Applied
Junfeng Cao, Ke Chen, Huan Han
Summary: This paper proposes a two-stage image segmentation model based on structure tensor and fractional-order regularization. In the first stage, fractional-order regularization is used to approximate the Hausdorff measure of the MS model. The solution is found using the ADI scheme. In the second stage, thresholding is used for target segmentation. The proposed model demonstrates superior performance compared to state-of-the-art methods.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Dylan J. Oliver, Ian W. Turner, Elliot J. Carr
Summary: This paper discusses a projection-based framework for numerical computation of advection-diffusion-reaction (ADR) equations in heterogeneous media with multiple layers or complex geometric structures. By obtaining approximate solutions on a coarse grid and reconstructing solutions on a fine grid, the computational cost is significantly reduced while accurately approximating complex solutions.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Nathan V. Roberts, Sean T. Miller, Stephen D. Bond, Eric C. Cyr
Summary: In this study, the time-marching discontinuous Petrov-Galerkin (DPG) method is applied to the Vlasov equation for the first time, using backward Euler for a Vlasov-Poisson discretization. Adaptive mesh refinement is demonstrated on two problems: the two-stream instability problem and a cold diode problem.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Yizhi Sun, Zhilin Sun
Summary: This work investigates the convexity of a specific class of positive definite probability measures and demonstrates the preservation of convexity under multiplication and intertwining product. The study reveals that any integrable function on an interval with a polynomial expansion of fast absolute convergence can be decomposed into a pair of positive convex interval probabilities, simplifying the study of interval distributions and discontinuous probabilistic Galerkin schemes.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Bhagwan Singh, Komal Jangid, Santwana Mukhopadhyay
Summary: This paper examines the prediction of bending characteristics of nanoscale materials using the Moore-Gibson-Thompson thermoelasticity theory in conjunction with the nonlocal strain gradient theory. The study finds that the stiffness of the materials can be affected by nonlocal and length-scale parameters, and the aspect ratios of the beam structure play a significant role in bending simulations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Guoliang Wang, Bo Zheng, Yueqiang Shang
Summary: This paper presents and analyzes a parallel finite element post-processing algorithm for the simulation of Stokes equations with a nonlinear damping term, which integrates the algorithmic advantages of the two-level approach, the partition of unity method, and the post-processing technique. The algorithm generates a global continuous approximate solution using the partition of unity method and improves the smoothness of the solution by adding an extra coarse grid correction step. It has good parallel performance and is validated through theoretical error estimates and numerical test examples.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Hao Xu, Zeng-Qi Wang
Summary: Fluid flow control problems are crucial in industrial applications, and solving the optimal control of Navier-Stokes equations is challenging. By using Oseen's approximation and matrix splitting preconditioners, we can efficiently solve the linear systems and improve convergence.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Zhengya Yang, Xuejuan Chen, Yanping Chen, Jing Wang
Summary: This paper focuses on the high-order stable numerical solutions of the time-space fractional diffusion equation. The Fourier spectral method is used for spatial discretization and the Spectral Deferred Correction (SDC) method is used for numerical solutions in time. As a result, a high-precision numerical discretization scheme for solving the fractional diffusion equation is obtained, and the convergence and stability of the scheme are proved. Several numerical examples are presented to demonstrate the effectiveness and feasibility of the proposed numerical scheme.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
