Journal of Computational Physics最新文献

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ECLEIRS: Exact conservation law embedded identification of reduced states for parameterized nonlinear conservation laws from sparse and noisy data ECLEIRS：基于稀疏和噪声数据的参数化非线性守恒律的精确守恒嵌入识别

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-04-01 Epub Date: 2026-01-07 DOI: 10.1016/j.jcp.2026.114651

Aviral Prakash, Ben S. Southworth, Marc L. Klasky

Multi-query applications such as parameter estimation, uncertainty quantification and design optimization for parameterized partial differential equation (PDE) systems are expensive. While reduced/latent state dynamics approaches for parameterized PDEs offer a viable alternative, these approaches rely on high-quality data and struggle with highly sparse spatiotemporal noisy measurements typically obtained from experiments. Furthermore, there is no guarantee that these models satisfy governing physical conservation laws. In this article, we propose a reduced state dynamics approach, referred to as ECLEIRS, that embeds exact conservation in the solution and flux representation by utilizing a space-time divergence-free neural network formulation. We compare ECLEIRS with other reduced state dynamics approaches, those that do not enforce any physical constraints and those with physics-informed loss functions, for three shock-propagation problems: 1-D advection, 1-D Burgers and 2-D Euler equations. The numerical experiments conducted in this study demonstrate that ECLEIRS provides the most accurate prediction of dynamics for unseen parameters even in the presence of highly sparse and noisy data.

参数化偏微分方程（PDE）系统的参数估计、不确定性量化和设计优化等多查询应用是昂贵的。虽然参数化偏微分方程的简化/潜在状态动力学方法提供了一种可行的替代方法，但这些方法依赖于高质量的数据，并且与通常从实验中获得的高度稀疏的时空噪声测量相斗争。此外，也不能保证这些模型满足基本的物理守恒定律。在本文中，我们提出了一种简化状态动力学方法，称为ECLEIRS，它通过利用无时空发散的神经网络公式在解和通量表示中嵌入精确守恒。我们将ECLEIRS与其他简化状态动力学方法（不强制任何物理约束和具有物理通知损失函数的方法）进行比较，以解决三个冲击传播问题：一维平流，一维汉堡和二维欧拉方程。本研究中进行的数值实验表明，即使在高度稀疏和噪声数据存在的情况下，ECLEIRS也能提供最准确的未知参数动力学预测。

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引用次数: 0

Improving Yee’s scheme with asymptotic dispersion correction for time-harmonic Maxwell’s equations 用渐近色散校正改进时谐Maxwell方程组的Yee格式

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-04-01 Epub Date: 2025-12-21 DOI: 10.1016/j.jcp.2025.114602

Pierre-Henri Cocquet , Martin J. Gander

In this paper, we show how to reduce the dispersion error associated to Yee’s finite difference scheme applied to time-harmonic Maxwell’s equations in one, two and three spatial dimensions. Our method, called asymptotic dispersion correction, is based on the introduction of a shifted angular frequency depending on a free parameter in the Yee stencil. The optimal parameter, called the asymptotically optimal shift, is next explicitly determined by minimizing the dispersion error for small enough meshsize or, equivalently, for large enough number of grid points per wavelength. Numerical experiments are provided and show that the relative error is reduced when using the optimal shifted angular frequency as soon as the number of grid points per wavelength is large enough.

在本文中，我们展示了如何减少与Yee有限差分格式相关的色散误差应用于一维、二维和三维的时谐麦克斯韦方程组。我们的方法，称为渐近色散校正，是基于引入一个移位的角频率依赖于Yee模板中的自由参数。最优参数，称为渐近最优位移，接下来明确地通过最小化色散误差来确定足够小的网格尺寸，或者等效地，对于每个波长足够多的网格点。数值实验结果表明，只要每个波长的网格点数量足够大，采用最优位移角频率可以减小相对误差。

引用次数: 0

An optimal transport approach to the far-field reflector problem via Sobolev gradient descent 基于Sobolev梯度下降的远场反射问题的最优输运方法

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-04-01 Epub Date: 2026-01-02 DOI: 10.1016/j.jcp.2025.114643

Yixuan Zhang , Gang Bao

The inverse reflector problem aims to design a freeform reflecting surface that can direct the light from a specified source to produce the desired illumination in the target area, which is significant in the field of geometrical non-imaging optics. Mathematically, it can be formulated as an optimization problem, which is exactly the optimal transportation problem (OT) when the target is in the far field. The gradient of OT is governed by the generalized Monge-Ampère equation that models the far-field reflector system. Based on the gradient, this work presents a Sobolev gradient descent method implemented within a finite element framework to solve the corresponding OT. Local convergence of the method is established and numerical examples are provided to demonstrate the effectiveness of the method.

反反射面问题旨在设计一种自由形状的反射面，使来自指定光源的光在目标区域内产生所需的照明，这在几何非成像光学领域具有重要意义。数学上可以将其表述为优化问题，即目标在远场时的最优运输问题。OT的梯度由模拟远场反射系统的广义monge - ampantere方程控制。基于梯度，本文提出了在有限元框架内实现Sobolev梯度下降法来求解相应的OT。建立了该方法的局部收敛性，并给出了数值算例，验证了该方法的有效性。

引用次数: 0

Solving the inverse source problems for wave equation with final time measurements by a data driven approach 用数据驱动方法求解具有最终时间测量的波动方程逆源问题

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-04-01 Epub Date: 2026-01-02 DOI: 10.1016/j.jcp.2025.114645

Qiling Gu , Wenlong Zhang , Zhidong Zhang

This paper develops a discrete data-driven approach for solving the inverse source problem of the wave equation with final time measurements. Focusing on the L²-Tikhonov regularization method, we analyze its convergence under two different noise models, using noisy discrete spatial observations. By exploiting the spectral decomposition of the forward operator and introducing a noise separation technique into the variational framework, we establish error bounds for the reconstructed solution u and the source term f without requiring classical source conditions. Moreover, an expected convergence rate for the source error is derived in a weaker topology. We also extend the analysis to the fully discrete case with finite element discretization, showing that the overall error depends only on the noise level, regularization parameter, time step size, and spatial mesh size. These estimates provide a basis for selecting the optimal regularization parameter in a data-driven manner, without a priori information. Numerical experiments validate the theoretical results and demonstrate the efficiency of the proposed algorithm.

本文提出了一种离散数据驱动的方法来解决具有最终时间测量的波动方程的逆源问题。以L2-Tikhonov正则化方法为重点，分析了其在两种不同噪声模型下的收敛性。通过利用正演算子的频谱分解，并在变分框架中引入噪声分离技术，我们建立了重构解u和源项f的误差边界，而不需要经典的源条件。此外，在较弱的拓扑结构中推导出源误差的预期收敛速率。我们还将分析扩展到具有有限元离散化的完全离散情况，表明总体误差仅取决于噪声水平，正则化参数，时间步长和空间网格大小。这些估计为在没有先验信息的情况下，以数据驱动的方式选择最优正则化参数提供了基础。数值实验验证了理论结果和算法的有效性。

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引用次数: 0

A variationally consistent and asymptotically convergent phase-field model for solute precipitation and dissolution 溶质析出和溶解的变分一致渐近收敛相场模型

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-04-01 Epub Date: 2026-01-08 DOI: 10.1016/j.jcp.2026.114665

Andrea Lamperti, Laura De Lorenzis

We propose a novel phase-field model for solute precipitation and dissolution in liquid solutions. Unlike in previous studies with similar scope, in our model the two non-linear coupled governing equations of the problem, which deliver the solute ion concentration and the phase-field variable, are derived in a variationally consistent way starting from a free energy functional of Modica-Mortola type. The phase-field variable is assumed to follow the non-conservative Allen-Cahn evolution law, whereas the solute ion concentration obeys the conservative Cahn-Hilliard equation. We also assess the convergence of the new model to the corresponding sharp-interface model via the method of matched asymptotic expansions, and derive a novel expression of the reaction rate of the sharp-interface model. Through a finite element discretization, we present several numerical examples in one, two and three dimensions.

我们提出了溶质在溶液中析出和溶解的相场模型。与以往类似范围的研究不同，在我们的模型中，问题的两个非线性耦合控制方程（传递溶质离子浓度和相场变量）以变分一致的方式从Modica-Mortola型自由能泛函开始推导。假设相场变量遵循非保守的Allen-Cahn演化规律，而溶质离子浓度遵循保守的Cahn-Hilliard方程。通过匹配渐近展开的方法，我们评估了新模型对相应的锐界面模型的收敛性，并推导了锐界面模型反应速率的新表达式。通过有限元离散，给出了一维、二维和三维的数值算例。

引用次数: 0

High-order empirical interpolation methods for real-time solution of parametrized nonlinear PDEs 参数化非线性偏微分方程实时解的高阶经验插值方法

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-04-01 Epub Date: 2026-01-06 DOI: 10.1016/j.jcp.2026.114664

Ngoc Cuong Nguyen

We present novel model reduction methods for rapid solution of parametrized nonlinear partial differential equations (PDEs) in real-time or many-query contexts. Our approach combines reduced basis (RB) space for global approximation of the parametric solution manifold, Galerkin projection of the underlying PDEs onto the RB space for dimensionality reduction, and high-order empirical interpolation for efficient treatment of the nonlinear terms. We propose a class of high-order empirical interpolation methods to derive basis functions and interpolation points by using high-order partial derivatives of the nonlinear terms. We develop error indicator to estimate the interpolation errors and determine parameter points via greedy sampling. Furthermore, we introduce two hyperreduction schemes to construct reduced-order models: one that applies the hyperreduction technique before Newton’s method and another after. The latter scheme significantly reduces hyperreduction errors while maintaining computational efficiency. Numerical results are presented to demonstrate the accuracy and efficiency of our approach.

我们提出了一种新的模型约简方法，用于在实时或多查询环境下快速求解参数化非线性偏微分方程（PDEs）。我们的方法结合了用于参数解流形全局逼近的降基（RB）空间，用于降维的底层偏微分方程的伽辽金投影到RB空间，以及用于有效处理非线性项的高阶经验插值。提出了一类利用非线性项的高阶偏导数来推导基函数和插值点的高阶经验插值方法。我们开发了误差指示器来估计插值误差，并通过贪婪采样确定参数点。此外，我们还介绍了两种构造降阶模型的超约化方案：一种是在牛顿方法之前应用超约化技术，另一种是在牛顿方法之后应用超约化技术。后一种方案在保持计算效率的同时显著降低了超约简误差。数值结果验证了该方法的准确性和有效性。

引用次数: 0

MBNO: Mamba-based neural operators for solving partial differential equations 用于求解偏微分方程的基于mamba的神经算子

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-04-01 Epub Date: 2026-01-05 DOI: 10.1016/j.jcp.2025.114639

Namkyeong Cho , Junseung Ryu , Hyung Ju Hwang

The recently released Mamba model leverages structured state space models (SSMs), incorporating hardware-efficient designs and selection mechanisms. The Mamba architecture demonstrates strong potential as a replacement for Transformer-based models across various tasks. In this work, we employ Mamba to train neural operators on infinite-dimensional spaces derived from partial differential equations. Using well-established theory on the Rough Path and Reproducing Kernel Hilbert Space (RKHS), we theoretically demonstrate that the SSM-based models can replace Transformer-based models for approximating operators. Our empirical findings further show that Mamba consistently outperforms Transformer models across various tasks while achieving faster inference, highlighting the potential of the Mamba architecture to outperform Transformer-based models in various operator learning tasks.

最近发布的Mamba模型利用结构化状态空间模型（ssm），结合了硬件高效设计和选择机制。Mamba体系结构展示了作为跨各种任务的基于transformer的模型的替代品的强大潜力。在这项工作中，我们使用Mamba在由偏微分方程导出的无限维空间上训练神经算子。利用粗糙路径和再现核希尔伯特空间（RKHS）的成熟理论，我们从理论上证明了基于ssm的模型可以取代基于变压器的模型来逼近算子。我们的实证研究结果进一步表明，在实现更快的推理的同时，Mamba在各种任务中始终优于Transformer模型，突出了Mamba架构在各种操作员学习任务中优于基于Transformer模型的潜力。

引用次数: 0

A sharp cartesian grid method for simulating flow past viscous droplets of arbitrary shape and viscosity 一种模拟流过任意形状和粘度的粘性液滴的锐笛卡尔网格方法

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-04-01 Epub Date: 2025-12-27 DOI: 10.1016/j.jcp.2025.114632

Bo-Lin Wei , Jie Zhang , Ming-Jiu Ni

We present a sharp Cartesian grid method for simulating flow past viscous droplets of arbitrary shape and viscosity. The method proposes a height function approach to compute the Weingarten matrix, enabling the accurate estimation of principal curvatures and directions on discretized curved interfaces of the droplet. These geometric quantities are then used to impose space- and time-dependent slip conditions at the interface. The incompressible Navier-Stokes equations are solved separately in the internal and external domains and coupled through the slip conditions using an embedded boundary method coupled with a synchronous iterative approach, ensuring a sharp representation of the interface. A key innovation of this approach is its ability to handle droplets with arbitrary geometries, including complex topologies imported directly from STL files, eliminating the need for analytical interface descriptions. By operating on a Cartesian grid, the method offers enhanced flexibility while preserving sharp interfacial dynamics. Numerical validation demonstrates the method’s accuracy and robustness. The height function approach is shown to reliably compute principal curvatures and directions, while simulations of flow past spheroidal droplets - spanning inviscid bubbles to rigid particles - exhibit excellent agreement with body-fitted benchmark solutions. Further, simulations of popcorn- and blob-shaped droplets highlight the method’s versatility in handling arbitrarily complex interfaces. This solver provides a powerful and flexible tool for investigating interfacial flow phenomena involving droplets with irregular geometries and viscosity variations.

我们提出了一种精确的笛卡尔网格方法来模拟任意形状和粘度的粘性液滴的流动。该方法采用高度函数法计算Weingarten矩阵，能够准确估计液滴离散曲面界面上的主曲率和方向。然后使用这些几何量在界面上施加与空间和时间相关的滑移条件。不可压缩的Navier-Stokes方程在内外域中分别求解，并通过滑移条件进行耦合，采用内嵌边界法与同步迭代法相结合，保证了界面的清晰表示。该方法的一个关键创新之处在于它能够处理任意几何形状的液滴，包括直接从STL文件导入的复杂拓扑，从而消除了对分析接口描述的需求。通过在笛卡尔网格上操作，该方法提供了增强的灵活性，同时保持了尖锐的界面动力学。数值验证验证了该方法的准确性和鲁棒性。高度函数方法被证明可以可靠地计算主曲率和方向，而通过球体液滴的流动模拟-跨越无粘气泡到刚性颗粒-与体贴合基准解表现出极好的一致性。此外，爆米花状和斑点状液滴的模拟突出了该方法在处理任意复杂界面方面的通用性。该求解器为研究具有不规则几何形状和粘度变化的液滴的界面流动现象提供了一个强大而灵活的工具。

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引用次数: 0

Simultaneous reconstruction of the trajectories and strengths for moving acoustic point sources 运动声点源轨迹和强度的同步重建

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-04-01 Epub Date: 2026-01-05 DOI: 10.1016/j.jcp.2025.114644

Keji Liu , Jiaru Wang

This work addresses the inverse problem of simultaneously reconstructing trajectories and strengths of moving acoustic point sources, with applications in gesture recognition, underwater sonar, and sound simulation. Under practical assumptions including co-located source initiation and a few kinematic profiles, we establish uniqueness results for both source trajectories and strengths. The reconstruction of trajectories is formulated through ordinary differential equations, while the recovery of strengths is determined via a matrix-vector system at each time step using at most four sensors. To mitigate numerical instability from ill-conditioned matrices, we introduce a direct imaging method employing an efficient indicator function based solely on Euclidean norm computations, avoiding matrix inversion or iterative optimization. Numerical experiments demonstrate reliable simultaneous recovery of trajectories and strengths for multiple moving sources, confirming the effectiveness of the proposed method and practical utility for real-world acoustic sensing applications.

这项工作解决了同时重建运动声点源的轨迹和强度的逆问题，并应用于手势识别，水下声纳和声音模拟。在实际假设条件下，包括同位源起始和一些运动轮廓，我们建立了源轨迹和强度的唯一性结果。轨迹的重建是通过常微分方程来表述的，而强度的恢复是通过矩阵-向量系统在每个时间步确定的，最多使用四个传感器。为了减轻病态矩阵的数值不稳定性，我们引入了一种直接成像方法，该方法采用基于欧几里得范数计算的有效指示函数，避免了矩阵反演或迭代优化。数值实验表明，该方法可以可靠地同时恢复多个运动声源的轨迹和强度，证实了该方法的有效性和在实际声学传感应用中的实用性。

引用次数: 0

A constrained-transport embedded boundary method for compressible resistive magnetohydrodynamics 可压缩电阻磁流体力学的约束输运嵌入边界法

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-04-01 Epub Date: 2025-12-31 DOI: 10.1016/j.jcp.2025.114641

Samuel W. Jones , Colin P. McNally , Meritt Reynolds

Motivated by the increased interest in pulsed-power magneto-inertial fusion devices in recent years, we present a method for implementing an arbitrarily shaped embedded boundary on a Cartesian mesh while solving the equations of compressible resistive magnetohydrodynamics. The method is built around a finite volume formulation of the equations in which a Riemann solver is used to compute fluxes on the faces between grid cells, and a face-centered constrained transport formulation of the induction equation. The small time step problem associated with the cut cells is avoided by always computing fluxes on the faces and edges of the Cartesian mesh. We extend the method to model a moving interface between two materials with different properties using a ghost-fluid approach, and show some preliminary results including shock-wave-driven and magnetically-driven dynamical compressions of magnetohydrostatic equilibria. We present a thorough verification of the method and show that it converges at second order in the absence of discontinuities, and at first order with a discontinuity in material properties.

由于近年来人们对脉冲功率磁惯性聚变装置的兴趣日益浓厚，我们提出了一种在求解可压缩电阻磁流体动力学方程时在笛卡尔网格上实现任意形状嵌入边界的方法。该方法建立在有限体积方程的基础上，其中黎曼求解器用于计算网格单元之间面的通量，感应方程的面为中心的约束输运公式。通过始终计算笛卡尔网格的面和边的通量，避免了与切割单元相关的小时间步长问题。我们将该方法扩展到使用鬼流体方法模拟具有不同性质的两种材料之间的移动界面，并展示了一些初步结果，包括激波驱动和磁驱动的磁流体静力平衡动态压缩。我们对该方法进行了彻底的验证，并表明它在没有不连续的情况下在二阶收敛，在材料性质具有不连续的情况下在一阶收敛。

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