Journal of Computational Physics最新文献

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Fast prediction of plasma instabilities with sparse-grid-accelerated optimized dynamic mode decomposition 基于稀疏网格加速优化动态模态分解的等离子体不稳定性快速预测

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

Journal of Computational Physics

Pub Date : 2026-01-29 DOI: 10.1016/j.jcp.2026.114718

Kevin Gill , Ionuţ-Gabriel Farcaş , Silke Glas , Benjamin J. Faber

Parametric data-driven reduced-order models (ROMs) that embed dependencies in a large number of input parameters are crucial for enabling many-query tasks in large-scale problems. These tasks, including design optimization, control, and uncertainty quantification, are essential for developing digital twins in real-world applications. However, standard grid-based data generation methods are computationally prohibitive due to the curse of dimensionality, as their cost scales exponentially with the number of inputs. This paper investigates efficient training of parametric data-driven ROMs using sparse grid interpolation with (L)-Leja points, specifically targeting scenarios with higher-dimensional input parameter spaces. (L)-Leja points are nested and exhibit slow growth, resulting in sparse grids with low cardinality in low-to-medium dimensional settings, making them ideal for large-scale, computationally expensive problems. Focusing on gyrokinetic simulations of plasma micro-instabilities in fusion experiments as a representative real-world application, we construct parametric ROMs for the full 5D gyrokinetic distribution function via optimized dynamic mode decomposition (optDMD) and sparse grids based on (L)-Leja points. We perform detailed experiments in two scenarios: First, the Cyclone Base Case benchmark assesses optDMD ROM prediction capabilities beyond training time horizons and across variations in the binormal wave number. Second, for a real-world electron-temperature-gradient-driven micro-instability simulation with six input parameters, we demonstrate that a predictive parametric optDMD ROM that is up to three orders of magnitude cheaper to evaluate can be constructed using only 28 high-fidelity gyrokinetic simulations, enabled by the use of sparse grids. In the broader context of fusion research, these results demonstrate the potential of sparse grid-based parametric ROMs to enable otherwise intractable many-query tasks.

在大量输入参数中嵌入依赖关系的参数化数据驱动降阶模型（ROMs）对于在大规模问题中实现多查询任务至关重要。这些任务，包括设计优化、控制和不确定性量化，对于在实际应用中开发数字孪生至关重要。然而，由于维度的诅咒，标准的基于网格的数据生成方法在计算上是令人望而却步的，因为它们的成本随着输入的数量呈指数级增长。本文研究了使用(L)-Leja点的稀疏网格插值对参数数据驱动rom的有效训练，特别是针对具有高维输入参数空间的场景。(L)-Leja点嵌套且增长缓慢，导致在中低维设置中具有低基数的稀疏网格，使其成为大规模，计算成本高的问题的理想选择。以聚变实验中等离子体微不稳定性的陀螺动力学模拟为代表的现实世界应用，我们通过优化动态模式分解（optDMD）和基于(L)-Leja点的稀疏网格构建了全5D陀螺动力学分布函数的参数rom。我们在两种情况下进行了详细的实验：首先，Cyclone Base Case基准评估了超越训练时间范围和双正态波数变化的optDMD ROM预测能力。其次，对于具有六个输入参数的真实电子温度梯度驱动的微不稳定性模拟，我们证明了仅使用28个高保真陀螺仪动力学模拟就可以构建一个预测参数optDMD ROM，其评估成本降低了三个数量级。在更广泛的融合研究背景下，这些结果证明了基于稀疏网格的参数rom的潜力，可以实现其他难以处理的多查询任务。

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引用次数: 0

High-order structure-preserving schemes for the Schrödinger–Poisson–Slater system Schrödinger-Poisson-Slater系统的高阶保结构方案

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

Journal of Computational Physics

Pub Date : 2026-01-29 DOI: 10.1016/j.jcp.2026.114715

Qing Cheng , Xiaoyun Jiang , Zongze Yang , Hui Zhang

In this paper, we develop a novel class of high-order structure-preserving algorithms for simulating the Schrödinger–Poisson–Slater system. We rewrite the original Schrödinger–Poisson–Slater system into equivalent formulas which warrant exactly the original total mass and energy. Based on the new formulas, a new family of high-order, mass and energy conserving schemes is constructed. We also show that the structure-preserving schemes can be proved to be uniquely solved. Extensive numerical examples in 2D and 3D are provided to demonstrate the high-order convergence rate and the effectiveness of the proposed algorithm in conserving mass and energy. Compared with the existing non-conserved schemes, the advantage of our schemes is that the structure-preserving schemes can also significantly reduce the errors of the numerical solutions in long-time simulations.

在本文中，我们开发了一类新的高阶结构保持算法来模拟Schrödinger-Poisson-Slater系统。我们把原来的Schrödinger-Poisson-Slater系统改写成等价的公式，保证了原来的总质量和能量。在此基础上，构造了一类新的高阶、高质量、节能方案。我们还证明了结构保持方案是唯一可解的。给出了大量二维和三维的数值算例，证明了该算法的高阶收敛速度和节省质量和能量的有效性。与现有的非守恒格式相比，我们的格式的优点是在长时间的模拟中，结构保持格式还可以显著降低数值解的误差。

引用次数: 0

Fast solution of a phase-field model of pitting corrosion 点蚀相场模型的快速求解

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

Journal of Computational Physics

Pub Date : 2026-01-29 DOI: 10.1016/j.jcp.2026.114717

Gianluca Frasca-Caccia, Dajana Conte, Beatrice Paternoster

Excessive computational times represent a major challenge in the solution of corrosion models, limiting their practical applicability, e.g., as a support to predictive maintenance. In this paper, we propose an efficient strategy for solving a phase-field model for metal corrosion. Based on the Kronecker structure of the diffusion matrix in classical finite difference approximations on rectangular domains, time-stepping IMEX methods are efficiently solved in matrix form. However, when the domain is non-rectangular, the lack of the Kronecker structure prevents the direct use of the matrix-based approach. To address this issue, we reformulate the problem on an extended rectangular domain and introduce suitable iterative IMEX methods. The convergence of the iterations and the propagation of the numerical errors are analyzed. Test cases on two and three dimensional domains show that the proposed approach achieves accuracy comparable to existing methods, while significantly reducing the computational time, to the point of allowing actual predictions on standard workstations.

过多的计算时间是腐蚀模型解决方案的主要挑战，限制了它们的实际适用性，例如，作为预测性维护的支持。本文提出了一种求解金属腐蚀相场模型的有效策略。基于经典矩形域有限差分近似中扩散矩阵的Kronecker结构，采用矩阵形式有效地求解了时间步进IMEX方法。然而，当区域是非矩形时，缺乏Kronecker结构阻碍了直接使用基于矩阵的方法。为了解决这个问题，我们在一个扩展的矩形域上重新表述了这个问题，并引入了合适的迭代IMEX方法。分析了迭代的收敛性和数值误差的传播。二维和三维域上的测试用例表明，所提出的方法达到了与现有方法相当的准确性，同时显著减少了计算时间，达到允许在标准工作站上进行实际预测的程度。

引用次数: 0

Complex physics-informed neural network 复杂的物理信息神经网络

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

Journal of Computational Physics

Pub Date : 2026-01-28 DOI: 10.1016/j.jcp.2026.114713

Chenhao Si , Ming Yan , Xin Li , Zhihong Xia

We propose compleX-PINN, a novel physics-informed neural network (PINN) architecture incorporating a learnable activation function inspired by Cauchy’s integral theorem. By optimizing the activation parameters, compleX-PINN achieves high accuracy with just a single hidden layer. Empirically, we demonstrate that compleX-PINN solves high-dimensional problems that pose significant challenges for PINNs. Our results show compleX-PINN consistently achieves substantially greater precision, often improving accuracy by an order of magnitude, on these complex tasks.

我们提出了compleX-PINN，一种新的物理信息神经网络（PINN）架构，其中包含一个受柯西积分定理启发的可学习激活函数。通过优化激活参数，compleX-PINN仅需一个隐藏层即可实现高精度。从经验上，我们证明了compleX-PINN解决了对pinn构成重大挑战的高维问题。我们的结果表明，complex - pinn在这些复杂的任务上始终能够实现更高的精度，通常可以将精度提高一个数量级。

引用次数: 0

Adaptive computation driven by an augmented fully-mixed FEM for double-diffusive natural convection in porous media 多孔介质双扩散自然对流的增广全混合有限元自适应计算

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

Journal of Computational Physics

Pub Date : 2026-01-27 DOI: 10.1016/j.jcp.2026.114711

Mario Álvarez , Eligio Colmenares , Filánder A. Sequeira

This work extends a previous study of ours, established in [M. Álvarez et al., Comput. Math. Appl., 114(2021), 112–131], on a semi-augmented mixed finite element formulation for double-diffusive natural convection in porous media, by developing and analyzing a new augmented fully mixed scheme in both two and three spatial dimensions. The formulation introduces a tensorial pseudo-thermosolutal gradient, depending on the gradients of temperature and concentration, as an additional unknown. This enrichment leads to a mixed system for the coupled equations and brings several computational advantages: the gradients of temperature and concentration can be efficiently recovered from the discrete solution without loss of accuracy; Dirichlet boundary conditions are incorporated naturally, without the need for Lagrange multipliers or extension operators; and the incorporation of parameterized redundant Galerkin terms ensures coercivity and allows the application of the Lax-Milgram theorem, thereby removing the need for inf-sup compatibility conditions and enabling greater flexibility in the selection of finite element subspaces. The scheme admits finite element spaces of arbitrary polynomial degree and achieves optimal-order convergence rates, established through both a priori and a posteriori error analyses. We also propose two computable residual-based a posteriori error estimators, which are entirely local and avoid the nonlocal norms required in previous approaches. These theoretical results are further supported by adaptive numerical experiments in two dimensions, which confirm the efficiency and reliability of the method.

这项工作扩展了我们之前的研究，建立在[M.]Álvarez等，计算。数学。达成。[j],[114(2021), 112-131]，通过在二维和三维空间上开发和分析新的增广完全混合方案，研究了多孔介质中双扩散自然对流的半增广混合有限元公式。该公式引入了一个张量伪热溶质梯度，这取决于温度和浓度的梯度，作为一个额外的未知数。这种富集导致了耦合方程的混合系统，并带来了几个计算优势：温度和浓度的梯度可以有效地从离散解中恢复而不损失精度；Dirichlet边界条件是自然结合的，不需要拉格朗日乘子或扩展算子；参数化冗余伽辽金项的结合确保了矫强力，并允许应用拉克斯-米尔格拉姆定理，从而消除了对内相容条件的需要，并在选择有限元子空间时具有更大的灵活性。该方案允许任意多项式次的有限元空间，并通过先验和后验误差分析建立了最优阶收敛速率。我们还提出了两个可计算的基于残差的后验误差估计器，它们完全是局部的，避免了以前方法中需要的非局部规范。二维自适应数值实验进一步验证了该方法的有效性和可靠性。

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引用次数: 0

Numerical reconstruction of coefficients in elliptic equations using continuous data assimilation 椭圆方程系数的连续同化数值重建

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

Journal of Computational Physics

Pub Date : 2026-01-26 DOI: 10.1016/j.jcp.2026.114708

Peiran Zhang

We consider the numerical reconstruction of the spatially dependent conductivity coefficient and the source term in elliptic partial differential equations in a two-dimensional convex polygonal domain, with homogeneous Dirichlet boundary condition and given interior observations of the solution. Using continuous data assimilation, we derive approximated gradients of the error function to update the reconstructed coefficients, which, in particular, avoids solving adjoint problems. New L² error estimates are provided for the spatially discretized reconstructions. Numerical examples are given to illustrate the effectiveness of the method and demonstrate the error estimates. The numerical results also reveal a notable feature that the reconstruction is very robust to errors in coefficients.

考虑了二维凸多边形区域内椭圆型偏微分方程中空间相关电导率系数和源项的数值重建，并给出了齐次Dirichlet边界条件下解的内部观测值。利用连续数据同化，推导误差函数的近似梯度来更新重构系数，特别避免了伴随问题的求解。为空间离散重建提供了新的L2误差估计。数值算例说明了该方法的有效性，并对误差估计进行了验证。数值结果还显示出重构对系数误差具有很强的鲁棒性。

引用次数: 0

Analysis and elimination of numerical pressure dependency in coupled Stokes-Darcy problem 耦合Stokes-Darcy问题中数值压力依赖性的分析与消除

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

Journal of Computational Physics

Pub Date : 2026-01-26 DOI: 10.1016/j.jcp.2026.114710

Jiachuan Zhang

This paper analyses the classical mixed finite element method (FEM) and a pressure-robust variant with divergence-free reconstruction operators for the coupled Stokes-Darcy problem. Its main contribution is to provide viscosity-explicit a priori error estimates that clearly distinguish the pressure dependence of the two discretizations: the velocity error of the classical scheme depends on both the exact pressure and the viscosity, whereas the pressure-robust method eliminates both entirely. Moreover, we derive pressure error estimates and quantify their dependence on the exact solution and model parameters. Two-dimensional numerical experiments validate the theoretical findings, including higher-order tests up to polynomial degree three and a lid-driven cavity benchmark with a piecewise linear interface. The implementation code is made publicly available to facilitate reproducibility.

本文分析了耦合Stokes-Darcy问题的经典混合有限元法和无发散重构算子的压力鲁棒变体。它的主要贡献是提供粘度显式先验误差估计，清楚地区分了两种离散化的压力依赖性：经典方案的速度误差取决于精确压力和粘度，而压力鲁棒方法完全消除了两者。此外，我们导出了压力误差估计，并量化了它们对精确解和模型参数的依赖。二维数值实验验证了理论结果，包括多项式三次的高阶测试和分段线性界面的盖驱动腔基准测试。实现代码是公开的，以促进再现性。

引用次数: 0

An operator learning method for solving partial differential equations: From transformer to adaptive low-rank resnet-type network 求解偏微分方程的算子学习方法：从变压器到自适应低秩网络

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

Journal of Computational Physics

Pub Date : 2026-01-24 DOI: 10.1016/j.jcp.2026.114705

Jingfei Chen , Minxin Chen , Jingrun Chen

Transformer performs remarkably across a diverse array of natural language processing tasks. Its applicability has been extended to the domain of partial differential equations, giving rise to two novel models: Fourier and Galerkin. However, the self-attention module inherent in Transformers exhibits a quadratic computational complexity with respect to the input sequence length n, as observed in the Fourier model, leading to substantial computational overheads for long input sequences. A detailed analysis illustrates that the correlation matrix in the self-attention mechanism exhibits a low-rank property. We incorporate this structure into the network architecture, where the self-attention mechanism degenerates into an adaptive low-rank ResNet-type network (ALRN). This network can adaptively capture the rank of the correlation matrix. As a consequence, the ALRN model entails a computational complexity of

O (n (2 d^{2} + 4 k d))

in contrast to

O (4 n^{2} d)

for the Fourier model and

O (12 n d^{2})

for the Galerkin model, where k denotes the rank of the correlation matrix and d represents the dimension of the feature space. Concerning parameter space, it is noteworthy that Fourier and Galerkin methods necessitate

O (3 d^{2})

, while the ALRN model demands

O (d^{2} + 2 n k)

. Therefore, the ALRN model offers a clear advantage when

n < O (d^{2})

. Numerical results for Burgers’ equation, Darcy flow, the inverse coefficient identification for the Darcy flow, and the Navier-Stokes equation demonstrate superior efficiency and require fewer parameters while maintaining accuracy.

Transformer在各种自然语言处理任务中表现出色。它的适用性已经扩展到偏微分方程的领域，产生了两个新的模型：傅里叶和伽辽金。然而，正如在傅里叶模型中观察到的那样，变压器中固有的自关注模块表现出相对于输入序列长度n的二次计算复杂性，导致长输入序列的大量计算开销。详细分析表明，自注意机制中的相关矩阵具有低秩性。我们将这种结构整合到网络架构中，其中自关注机制退化为自适应低秩resnet型网络（ALRN）。该网络能够自适应捕获相关矩阵的秩。因此，ALRN模型的计算复杂度为O(n(2d2+4kd))，而傅里叶模型的计算复杂度为O(4n2d)，伽辽金模型的计算复杂度为O(12nd2)，其中k表示相关矩阵的秩，d表示特征空间的维度。在参数空间方面，值得注意的是，Fourier和Galerkin方法需要O(3d2)，而ALRN模型需要O（d2+2nk）。因此，当n<；O（d2）时，ALRN模型具有明显的优势。对于Burgers方程、Darcy流动、Darcy流动的逆系数辨识和Navier-Stokes方程的数值结果表明，该方法具有较高的效率，并且在保持精度的同时需要更少的参数。

{"title":"An operator learning method for solving partial differential equations: From transformer to adaptive low-rank resnet-type network","authors":"Jingfei Chen , Minxin Chen , Jingrun Chen","doi":"10.1016/j.jcp.2026.114705","DOIUrl":"10.1016/j.jcp.2026.114705","url":null,"abstract":"<div><div>Transformer performs remarkably across a diverse array of natural language processing tasks. Its applicability has been extended to the domain of partial differential equations, giving rise to two novel models: Fourier and Galerkin. However, the self-attention module inherent in Transformers exhibits a quadratic computational complexity with respect to the input sequence length <em>n</em>, as observed in the Fourier model, leading to substantial computational overheads for long input sequences. A detailed analysis illustrates that the correlation matrix in the self-attention mechanism exhibits a low-rank property. We incorporate this structure into the network architecture, where the self-attention mechanism degenerates into an adaptive low-rank ResNet-type network (ALRN). This network can adaptively capture the rank of the correlation matrix. As a consequence, the ALRN model entails a computational complexity of <span><math><mrow><mi>O</mi><mo>(</mo><mi>n</mi><mrow><mo>(</mo><mn>2</mn><msup><mi>d</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>k</mi><mi>d</mi><mo>)</mo></mrow><mo>)</mo></mrow></math></span> in contrast to <span><math><mrow><mi>O</mi><mo>(</mo><mn>4</mn><msup><mi>n</mi><mn>2</mn></msup><mi>d</mi><mo>)</mo></mrow></math></span> for the Fourier model and <span><math><mrow><mi>O</mi><mo>(</mo><mn>12</mn><mi>n</mi><msup><mi>d</mi><mn>2</mn></msup><mo>)</mo></mrow></math></span> for the Galerkin model, where <em>k</em> denotes the rank of the correlation matrix and <em>d</em> represents the dimension of the feature space. Concerning parameter space, it is noteworthy that Fourier and Galerkin methods necessitate <span><math><mrow><mi>O</mi><mo>(</mo><mn>3</mn><msup><mi>d</mi><mn>2</mn></msup><mo>)</mo></mrow></math></span>, while the ALRN model demands <span><math><mrow><mi>O</mi><mo>(</mo><msup><mi>d</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>n</mi><mi>k</mi><mo>)</mo></mrow></math></span>. Therefore, the ALRN model offers a clear advantage when <span><math><mrow><mi>n</mi><mo><</mo><mi>O</mi><mo>(</mo><msup><mi>d</mi><mn>2</mn></msup><mo>)</mo></mrow></math></span>. Numerical results for Burgers’ equation, Darcy flow, the inverse coefficient identification for the Darcy flow, and the Navier-Stokes equation demonstrate superior efficiency and require fewer parameters while maintaining accuracy.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"552 ","pages":"Article 114705"},"PeriodicalIF":3.8,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146075599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A multiphase IFED method for fluid-structure interactions 流固耦合的多相IFED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 : 2026-01-22 DOI: 10.1016/j.jcp.2026.114699

Chang Wei , Haotian Liu , Shangming Li

The immersed finite element/difference (IFED) method is a numerical framework for modeling fluid-structure interaction in single-phase flows. In this work, the IFED method is extended to multiphase FSI with emphasis on deformable structures. The proposed approach preserves the geometric flexibility for deformable structures and integrates the level set method to capture phase interfaces. The gas-liquid interface is tracked by advecting a level set, whereas the structural level set is explicitly reconstructed to produce a discrete signed distance field on the Cartesian grid. Once the level set fields are available, fluid density and viscosity are assigned via regularized Heaviside functions to smooth interfacial transitions. Fluid-structure coupling follows the IFED method, in which a force-spreading operator spreads Lagrangian forces onto the Cartesian grid, and a velocity-restriction operator transfers Eulerian velocities back to the structural mesh. These operators are implemented within the multiphase framework. A limitation of the original IFED formulation is the homogeneous time-step coupling that imposes the same time step on fluid and solid subdomains. To address this, a time-splitting scheme is proposed using two Lagrangian representations: the original mesh interacts with the fluid without structural constitutive response, and the auxiliary mesh is coupled to the former via a penalty force formulation. This allows the structural elastodynamic equations to be solved multiple times within each fluid time step using a standard Galerkin finite element method on the auxiliary mesh. The resulting material response is transmitted back to the original mesh as another penalty body force, which is subsequently used to compute the Eulerian force density. The proposed scheme is applicable to both the original IFED method and its multiphase extension. Two 2D dam-break tests indicate that the multiphase IFED method provides accurate predictions for deformable structures with low to moderate stiffness. For high-stiffness structures, the time-splitting scheme achieves achieves a speedup of about 3.8 times in the Turek-Hron test at

G_{s} = 2 \times 10^{7}

Pa relative to the original version, solely by increasing structural substeps. A dam-break impact test involving a deformable body with

E_{s} = 5.0 \times 10^{10}

Pa further demonstrates the effectiveness of the time-splitting scheme. The study provides new insights into the modeling of multiphase FSI problems involving deformable structures.

浸入式有限元差分法（IFED）是一种模拟单相流固相作用的数值框架。在这项工作中，IFED方法扩展到多相FSI，重点是可变形结构。该方法保留了可变形结构的几何灵活性，并集成了水平集方法来捕获相界面。通过平流水平集跟踪气液界面，而结构水平集被显式重构以产生笛卡尔网格上的离散符号距离场。一旦水平集域可用，流体密度和粘度通过正则化Heaviside函数分配，以平滑界面过渡。流固耦合遵循IFED方法，其中力扩散算子将拉格朗日力传播到笛卡尔网格上，速度限制算子将欧拉速度传递回结构网格。这些操作符在多相框架内实现。原始IFED公式的一个限制是均匀的时间步长耦合，对流体和固体子域施加相同的时间步长。为了解决这个问题，提出了一种使用两种拉格朗日表示的时间分裂方案：原始网格与流体相互作用，没有结构本构响应，辅助网格通过罚力公式与前者耦合。这允许在辅助网格上使用标准伽辽金有限元法在每个流体时间步长内多次求解结构弹性动力学方程。产生的材料响应作为另一个罚体力传回原始网格，随后用于计算欧拉力密度。该方案既适用于原IFED方法，也适用于其多相扩展。两个二维溃坝试验表明，多相IFED方法对低刚度到中等刚度的可变形结构提供了准确的预测。对于高刚度结构，在Gs=2×107 Pa的Turek-Hron试验中，仅通过增加结构子步骤，时间分裂方案相对于原始版本的速度提高了约3.8倍。对Es=5.0×1010 Pa的可变形体的溃坝冲击试验进一步证明了时间分裂方案的有效性。该研究为涉及可变形结构的多相FSI问题的建模提供了新的见解。

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引用次数: 0

High-order Hermite optimization: Fast and exact gradient computation in open-loop quantum optimal control using a discrete adjoint approach 高阶Hermite优化：离散伴随方法在开环量子最优控制中的快速精确梯度计算

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

Journal of Computational Physics

Pub Date : 2026-01-22 DOI: 10.1016/j.jcp.2026.114697

Spencer Lee , Daniel Appelo

This work introduces the High-Order Hermite Optimization (HOHO) method, an open-loop discrete adjoint method for quantum optimal control. Our method is the first of its kind to efficiently compute exact (discrete) gradients when using continuous, parameterized control pulses while solving the forward equations (e.g. Schrodinger’s equation or the Linblad master equation) with an arbitrarily high-order Hermite Runge-Kutta method. The HOHO method is implemented in QuantumGateDesign.jl, an open-source software package for the Julia programming language, which we use to perform numerical experiments comparing the method to Juqbox.jl. For realistic model problems we observe speedups up to 775x.

介绍了高阶埃尔米特优化（HOHO）方法，一种量子最优控制的开环离散伴随方法。我们的方法是同类中第一个有效地计算精确（离散）梯度时，使用连续的，参数化的控制脉冲，同时用任意高阶Hermite龙格-库塔方法求解前向方程（如薛定谔方程或林布拉德主方程）。在量子网关设计中实现了HOHO方法。jl是Julia编程语言的开源软件包，我们使用它来进行数值实验，将该方法与Juqbox.jl进行比较。对于实际的模型问题，我们观察到加速高达775倍。

引用次数: 0

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