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Computer Science, Interdisciplinary Applications
Han Zhou, Wenjun Ying
Summary: This work presents a novel kernel-free boundary integral method for solving elliptic PDEs with implicitly defined irregular boundaries and interfaces. The method avoids complex derivations by solving equivalent simple interface problems, and it demonstrates accuracy and efficiency in various numerical examples.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Thomas O'Leary-Roseberry, Peng Chen, Umberto Villa, Omar Ghattas
Summary: Derivative-informed neural operators (DINOs) are a type of neural networks that can approximate operators and their derivatives with high accuracy. They can be used in derivative-based algorithms in various fields, such as Bayesian inverse problems and optimization under parameter uncertainty. By compressing and efficiently utilizing derivative information in neural operator training, DINOs can significantly reduce the costs of data generation and training.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Shivang Agarwal, Amartya S. Banerjee
Summary: We propose and implement a spectral method for solving the Schrodinger equation for quasi-one-dimensional materials and structures. Our method allows for accurate, efficient and systematic computation of the electronic structure of important technological materials such as nanotubes, nanowires, nanoribbons, chiral nanoassemblies, nanosprings and nanocoils. It overcomes the limitations of other discretization strategies and avoids computationally onerous approximations, making it a valuable tool in computational nanomechanics and multiscale modeling.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Remi Bourgeois, Pascal Tremblin, Samuel Kokh, Thomas Padioleau
Summary: In this paper, a modified acoustic-transport operator splitting Lagrange-projection method is proposed for simulating compressible flows with gravity. The modified scheme is a flux-splitting method that is less computationally expensive, more memory efficient, and easier to implement than the original method. The stability and accuracy of the new method are tested through numerical experiments.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Lee Lindblom, Oliver Rinne
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Yuwei Geng, Yuankai Teng, Zhu Wang, Lili Ju
Summary: This paper proposes a novel deep learning method for predicting the dynamics of the classic and conservative Allen-Cahn equations. Two special convolutional neural network models are designed and trained using the residual of the fully-discrete systems as the loss functions. Extensive experiments demonstrate the outstanding performance of the proposed method in dynamics prediction and generalization ability under different scenarios.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Christian Soize, Quy-Dong To
Summary: This paper presents an algorithm for constructing a truncated polynomial chaos expression to describe a vector-valued random output with an unknown probability measure. By utilizing a training set, a highly accurate global surrogate model can be constructed, and an alternative approach based on data subsets is proposed to improve model accuracy. The experimental results applied to atomic collisions of Helium on a graphite substrate demonstrate the accuracy of the proposed method.
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
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
Pau Batlle, Matthieu Darcy, Bamdad Hosseini, Houman Owhadi
Summary: We present a general kernel-based framework for learning operators between Banach spaces. Our approach is competitive in terms of cost-accuracy trade-off and matches or beats the performance of popular neural net methods on most benchmarks. The framework inherits advantages from kernel methods, such as simplicity, interpretability, convergence guarantees, a priori error estimates, and Bayesian uncertainty quantification.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Hyeonbeen Lee, Seongji Han, Hee-Sun Choi, Jin-Gyun Kim
Summary: This study proposes a novel and robust composite neural network called cNN-DP, which is capable of handling impulsive time-transient dynamics. The network divides the prediction tasks into multiple sub-networks to improve the accuracy and performance of the model.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Zhifang Du, Jiequan Li
Summary: This paper presents a method using the volume fraction of fluid (VOF) approach to track the dynamics of free boundaries. It applies a two-stage fourth order accurate time discretization method to solve the VOF equation, aiming to provide a compact diffuse-interface algorithm for simulating multi-material problems with sharp interfaces. The numerical results demonstrate high resolution and high fidelity for interface capturing.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Dianheng Jiang, Sheng Zhang, Yunpeng Li, Biaosong Chen, Na Li
Summary: This paper proposes a hybrid Bloch mode synthesis method, which improves computational efficiency by considering the influence of higher-order modes on periodic boundary structures, and outperforms traditional methods in terms of accuracy and computational efficiency.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Kishan Ramesh Kumar, Matei Tene
Summary: Subsurface flow simulation is crucial for various geoscience applications, and the algebraic multiscale (AMS) solvers have shown promise in improving simulation performance. This study proposes a novel approach using unsupervised learning methods to generate multiscale coarse grids, resulting in improved AMS performance compared to existing methods. The development has the potential to significantly enhance the efficiency of running detailed models in reservoir engineering.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Alberto Padovan, Clarence W. Rowley
Summary: This research proposes a method to numerically estimate reduced-order models for flows with time-periodic behavior by using Gramians in the frequency domain. The desired post transient response can be obtained by solving algebraic equations without the need to track physical transients. The advantages of frequency domain computation are demonstrated in experiments and feedback controllers and state estimators are successfully designed for two different flow cases.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Mathematics, Applied
Shu-hong Xue, Yun-yun Yang, Biao Feng, Hai-long Yu, Li Wang
Summary: This research focuses on the robustness of multiplex networks and proposes a new index to measure their stability under malicious attacks. The effectiveness of this method is verified in real multiplex networks.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Computer Science, Interdisciplinary Applications
Sergii Kutnii
Summary: A software tool for simplification of Dirac matrix polynomials in particle physics problems has been implemented. It uses pseudo-matrices and algebraic calculations to simplify complex problems and enables efficient and accurate computations involving Dirac matrices in particle physics.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Peiyao Liu, Changsheng Huang, Zhaoli Guo
Summary: This paper proposes two GPU parallel algorithms for simulating low-speed isothermal flows using the discrete unified gas kinetic scheme (DUGKS). The performance of the algorithms is evaluated through simulations of benchmark problems, and the results show satisfactory computational efficiency. The algorithms have different performance in different scenarios.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
