Article
Physics, Fluids & Plasmas
Yao Zhou, N. M. Ferraro, S. C. Jardin, H. R. Strauss
Summary: This study extends the capability of modeling the nonlinear magnetohydrodynamic (MHD) evolution of stellarator plasmas by introducing non-axisymmetric domain geometry into the M3D-C (1) code. Logical coordinates are used for axisymmetric computational domain, with a C (1) coordinate mapping connecting it to the non-axisymmetric physical domain. The approach is verified through numerical simulations of various scenarios like heating, destabilization, and equilibration of stellarator plasma, as well as relaxation of stellarator equilibria to different magnetic field configurations in realistic geometries.
Article
Mathematics, Applied
Jens Markus Melenk, Alexander Rieder
Summary: The study involves a time-dependent problem generated by a nonlocal operator in space. The approach includes spatial discretization using hp-finite elements and a Caffarelli-Silvestre extension, and time discretization using hp-discontinuous Galerkin based time stepping. Exponential convergence is proven in an abstract framework for the spatial domain Omega.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2021)
Article
Engineering, Multidisciplinary
Andrea La Spina, Jacob Fish
Summary: The work proposes a hybridizable discontinuous Galerkin (HDG) method for weakly compressible magnetohydrodynamic (MHD) problems, demonstrating its superior properties and superconvergence characteristics. Different MHD formulations are discussed, and the convergence properties of the proposed methods under various conditions are extensively examined through numerical examples.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
Ivy Weber, Gunilla Kreiss, Murtazo Nazarov
Summary: This paper investigates the stability of a numerical method for solving the wave equation using matrix eigenvalue analysis to calculate time-step restrictions. It is found that the time-step restriction for continuous Lagrange elements is independent of the nodal distribution, while the restriction for symmetric interior penalty DG schemes is tighter. The best time-step restriction is obtained for continuous Hermite finite elements.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Engineering, Multidisciplinary
Christoph Lehrenfeld, Paul Stocker
Summary: A new variant called embedded Trefftz discontinuous Galerkin method is proposed, which is the Galerkin projection of an underlying discontinuous Galerkin method onto a subspace of Trefftz-type. This method allows for convenient extension to general cases, reduces globally coupled unknowns significantly, and improves accuracy in the Helmholtz problem.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
Andrea La Spina, Jacob Fish
Summary: This work introduces a hybridizable discontinuous Galerkin formulation for simulating ideal plasmas. The proposed method couples the fluid and electromagnetic subproblems monolithically based on source and employs a fully implicit time integration scheme. The approach also utilizes a projection-based divergence correction method to enforce the Gauss laws in challenging scenarios. Numerical examples demonstrate the high-order accuracy, efficiency, and robustness of the proposed formulation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Physics, Multidisciplinary
Arnab Basak, Krishna Kumar
Summary: Dynamic models of dynamo action in low-Prandtl-number regime emphasize the role of pure thermal convection in magnetic field generation. The threshold for dynamo decreases with increasing Pm for fixed Pr, while for fixed Pm, it increases with increasing Pr. The induced magnetic energy manifests as irregular bursts for lower Pm values and quasi-periodic or oscillatory behavior for larger Pm values.
Article
Mathematics, Applied
Constantin Bacuta, Leszek Demkowicz, Jaime Mora, Christos Xenophontos
Summary: This work focuses on two problems: analyzing the DPG method in fractional energy spaces, and investigating a non-conforming version of the DPG method for general polyhedral meshes. The ultraweak variational formulation is used for the model Laplace equation, and theoretical estimates are supported by 3D numerical experiments.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
C. Engstrom, S. Giani, L. Grubisic
Summary: This paper introduces the application and performance comparison of discontinuous Galerkin composite finite element methods (DGCFEM) in addressing approximation problems on complicated domains.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Engineering, Multidisciplinary
Kerstin Weinberg, Christian Wieners
Summary: We propose a new numerical approach for wave induced dynamic fracture. The method combines a discontinuous Galerkin approximation of elastic waves and a phase-field approximation of brittle fracture. The algorithm is staggered in time and uses an implicit midpoint rule for wave propagation and an implicit Euler step for phase-field evolution. Examples in two and three dimensions demonstrate the advantages of this approach in computing crack growth and spalling initiated by reflected and superposed waves.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Slimane Adjerid, Ivo Babuska, Ruchi Guo, Tao Lin
Summary: This article introduces the first higher degree immersed finite element method for elliptic interface problems with nonhomogeneous jump conditions, demonstrating optimal convergence. It also provides an analysis of the condition numbers of the resulting systems, including optimal upper bounds with respect to mesh size and robustness with respect to small-cut interface elements. The method involves the approximation of jump conditions using basic and enrichment immersed finite elements, which are constructed by solving local Cauchy problems on interface elements.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mathematics, Applied
M. E. Rubio, F. A. Stasyszyn
Summary: This paper investigates the well-posedness of the initial-value problem for the non-relativistic magnetic dynamo equation and finds that the problem is ill-posed when the electromotive force is linearly dependent on the magnetic field. By introducing a linear relationship between the electromotive forces and the magnetic field derivatives, a well-posed problem is obtained. Finally, the well-posed theory is applied to the force-free regime, and bounds for the corresponding magnetic energy are derived by analyzing the evolution of magnetic helicity.
PHYSICA D-NONLINEAR PHENOMENA
(2022)
Article
Mathematics, Applied
Liuqiang Zhong, Liangliang Zhou, Chunmei Liu, Jie Peng
Summary: This paper studies the two-grid interior penalty discontinuous Galerkin (IPDG) method for mildly nonlinear second-order elliptic partial differential equations. The well-posedness of the IPDG finite element discretizations is established by introducing the equivalent weak formulation and combining Brouwer's fixed point theorem. Error estimates for the discrete solution in various norms are derived, and a two-grid method is designed for solving the IPDG discretization scheme with corresponding error estimates provided. Numerical experiments confirm the efficiency of the proposed approach.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Mathematics, Applied
Andreas Rupp, Moritz Hauck, Vadym Aizinger
Summary: The method introduced in this work generalizes the enriched Galerkin method with an adaptive two-mesh approach, proving stability and error estimates for a linear advection equation. The analysis technique allows for arbitrary degrees of enrichment on both coarse and fine meshes, covering a wide range of methods from continuous finite element to discontinuous Galerkin with local subcell enrichment. Numerical experiments confirm the analytical results and show good robustness of the proposed method.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Engineering, Multidisciplinary
Peter Hansbo, Mats G. Larson
Summary: This article introduces the use of augmented Lagrangian formalism to derive discontinuous Galerkin methods for problems in nonlinear elasticity, and provides examples from plasticity and large deformation hyperelasticity.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
Tian Liang, Lin Fu
Summary: In this work, a new shock-capturing framework is proposed based on a new candidate stencil arrangement and the combination of infinitely differentiable non-polynomial RBF-based reconstruction in smooth regions with jump-like non-polynomial interpolation for genuine discontinuities. The resulting scheme achieves high order accuracy and resolves genuine discontinuities with sub-cell resolution.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Lukas Lundgren, Murtazo Nazarov
Summary: In this paper, a high-order accurate finite element method for incompressible variable density flow is introduced. The method addresses the issues of saddle point system and stability problem through Schur complement preconditioning and artificial compressibility approaches, and it is validated to have high-order accuracy for smooth problems and accurately resolve discontinuities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Gabriele Ciaramella, Laurence Halpern, Luca Mechelli
Summary: This paper presents a novel convergence analysis of the optimized Schwarz waveform relaxation method for solving optimal control problems governed by periodic parabolic PDEs. The analysis is based on a Fourier-type technique applied to a semidiscrete-in-time form of the optimality condition, which enables a precise characterization of the convergence factor at the semidiscrete level. The behavior of the optimal transmission condition parameter is also analyzed in detail as the time discretization approaches zero.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jonas A. Actor, Xiaozhe Hu, Andy Huang, Scott A. Roberts, Nathaniel Trask
Summary: This article introduces a scientific machine learning framework that uses a partition of unity architecture to model physics through control volume analysis. The framework can extract reduced models from full field data while preserving the physics. It is applicable to manifolds in arbitrary dimension and has been demonstrated effective in specific problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Nozomi Magome, Naoki Morita, Shigeki Kaneko, Naoto Mitsume
Summary: This paper proposes a novel strategy called B-spline based SFEM to fundamentally solve the problems of the conventional SFEM. It uses different basis functions and cubic B-spline basis functions with C-2-continuity to improve the accuracy of numerical integration and avoid matrix singularity. Numerical results show that the proposed method is superior to conventional methods in terms of accuracy and convergence.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Timothy R. Law, Philip T. Barton
Summary: This paper presents a practical cell-centred volume-of-fluid method for simulating compressible solid-fluid problems within a pure Eulerian setting. The method incorporates a mixed-cell update to maintain sharp interfaces, and can be easily extended to include other coupled physics. Various challenging test problems are used to validate the method, and its robustness and application in a multi-physics context are demonstrated.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Xing Ji, Fengxiang Zhao, Wei Shyy, Kun Xu
Summary: This paper presents the development of a third-order compact gas-kinetic scheme for compressible Euler and Navier-Stokes solutions, constructed particularly for an unstructured tetrahedral mesh. The scheme demonstrates robustness in high-speed flow computation and exhibits excellent adaptability to meshes with complex geometrical configurations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Alsadig Ali, Abdullah Al-Mamun, Felipe Pereira, Arunasalam Rahunanthan
Summary: This paper presents a novel Bayesian statistical framework for the characterization of natural subsurface formations, and introduces the concept of multiscale sampling to localize the search in the stochastic space. The results show that the proposed framework performs well in solving inverse problems related to porous media flows.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jacob Rains, Yi Wang, Alec House, Andrew L. Kaminsky, Nathan A. Tison, Vamshi M. Korivi
Summary: This paper presents a novel method called constrained optimized DMD with Control (cOptDMDc), which extends the optimized DMD method to systems with exogenous inputs and can enforce the stability of the resulting reduced order model (ROM). The proposed method optimally places eigenvalues within the stable region, thus mitigating spurious eigenvalue issues. Comparative studies show that cOptDMDc achieves high accuracy and robustness.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Andrea La Spina, Jacob Fish
Summary: This work introduces a hybridizable discontinuous Galerkin formulation for simulating ideal plasmas. The proposed method couples the fluid and electromagnetic subproblems monolithically based on source and employs a fully implicit time integration scheme. The approach also utilizes a projection-based divergence correction method to enforce the Gauss laws in challenging scenarios. Numerical examples demonstrate the high-order accuracy, efficiency, and robustness of the proposed formulation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Junhong Yue, Peijun Li
Summary: This paper proposes two numerical methods (IP-FEM and BP-FEM) to study the flexural wave scattering problem of an arbitrary-shaped cavity on an infinite thin plate. These methods successfully decompose the fourth-order plate wave equation into the Helmholtz and modified Helmholtz equations with coupled conditions on the cavity boundary, providing an effective solution to this challenging problem.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
William Anderson, Mohammad Farazmand
Summary: We develop fast and scalable methods, called RONS, for computing reduced-order nonlinear solutions. These methods have been proven to be highly effective in tackling challenging problems, but become computationally prohibitive as the number of parameters grows. To address this issue, three separate methods are proposed and their efficacy is demonstrated through examples. The application of RONS to neural networks is also discussed.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Marco Caliari, Fabio Cassini
Summary: In this paper, a second order exponential scheme for stiff evolutionary advection-diffusion-reaction equations is proposed. The scheme is based on a directional splitting approach and uses computation of small sized exponential-like functions and tensor-matrix products for efficient implementation. Numerical examples demonstrate the advantage of the proposed approach over state-of-the-art techniques.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Sebastiano Boscarino, Seung Yeon Cho, Giovanni Russo
Summary: This work proposes a high order conservative semi-Lagrangian method for the inhomogeneous Boltzmann equation of rarefied gas dynamics. The method combines a semi-Lagrangian scheme for the convection term, a fast spectral method for computation of the collision operator, and a high order conservative reconstruction and a weighted optimization technique to preserve conservative quantities. Numerical tests demonstrate the accuracy and efficiency of the proposed method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jialei Li, Xiaodong Liu, Qingxiang Shi
Summary: This study shows that the number, centers, scattering strengths, inner and outer diameters of spherical shell-structured sources can be uniquely determined from the far field patterns. A numerical scheme is proposed for reconstructing the spherical shell-structured sources, which includes a migration series method for locating the centers and an iterative method for computing the inner and outer diameters without computing derivatives.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)