Pub Date : 2025-12-05DOI: 10.1016/j.jcp.2025.114568
Amr S. Hares , Magdi S. El-Azab , Salah S.A. Obayya
We introduce a Physics-Guided Neural Network (PGNN) for stable and accurate modal analysis of electromagnetic problems, demonstrated on two-dimensional dielectric waveguides. While waveguide problems are traditionally solved using the Finite Differences (FD) method or Finite Elements (FE), which are highly dependent on the resolution of a predefined mesh and often struggle with handling well-defined complex geometries, PGNNs offer a meshless approach with seamless incorporation of available data. However, stability remains a significant challenge when applying PGNNs to practical eigenvalue problems, as misalignments between the loss function minima and the true eigenvalues lead to divergence. We address this issue through a three-component solution: a reformulated loss function, a dynamic eigenvalue-driving term, and a trigonometric basis-powered neural network. Numerical experiments confirm the effectiveness of the proposed approach, demonstrating improved stability, faster convergence, and low relative field-profile errors of 0.9 to 1.7 % compared to a reference FD solver.
{"title":"A stable physics-guided neural networks approach for electromagnetic problems","authors":"Amr S. Hares , Magdi S. El-Azab , Salah S.A. Obayya","doi":"10.1016/j.jcp.2025.114568","DOIUrl":"10.1016/j.jcp.2025.114568","url":null,"abstract":"<div><div>We introduce a Physics-Guided Neural Network (PGNN) for stable and accurate modal analysis of electromagnetic problems, demonstrated on two-dimensional dielectric waveguides. While waveguide problems are traditionally solved using the Finite Differences (FD) method or Finite Elements (FE), which are highly dependent on the resolution of a predefined mesh and often struggle with handling well-defined complex geometries, PGNNs offer a meshless approach with seamless incorporation of available data. However, stability remains a significant challenge when applying PGNNs to practical eigenvalue problems, as misalignments between the loss function minima and the true eigenvalues lead to divergence. We address this issue through a three-component solution: a reformulated loss function, a dynamic eigenvalue-driving term, and a trigonometric basis-powered neural network. Numerical experiments confirm the effectiveness of the proposed approach, demonstrating improved stability, faster convergence, and low relative field-profile errors of 0.9 to 1.7 % compared to a reference FD solver.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"548 ","pages":"Article 114568"},"PeriodicalIF":3.8,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145712078","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}
Pub Date : 2025-12-05DOI: 10.1016/j.jcp.2025.114566
Lei Wei , Qifan Chen , Yinhua Xia
This paper presents a novel class of high-order Runge-Kutta (RK) central discontinuous Galerkin (CDG) schemes for hyperbolic conservation laws. The key feature of the proposed scheme is the hybridization of different spatial discretization operators at different RK stages, which distinguishes it from the traditional method of lines framework. Specifically, we focus on employing the CDG operator without the numerical dissipation term in selected stages while using the standard CDG operator in other stages. This approach can improve efficiency by reducing the number of computational terms and allowing larger time steps. Therefore, the resulting method is referred to as the ECDG method. For smooth problems, the ECDG scheme maintains the same accuracy as the original CDG scheme. For problems involving shocks, it effectively suppresses numerical oscillations and enhances shock-capturing capabilities while being less dissipative. Additionally, we perform Fourier-type stability and error analysis for the ECDG scheme in the context of the one-dimensional linear advection equation. Furthermore, we discuss more possible constructions of ECDG schemes involving other spatial operators. Several numerical examples are presented to demonstrate the improved efficiency and higher resolution of the ECDG scheme for hyperbolic conservation laws.
{"title":"An efficient central discontinuous Galerkin scheme for hyperbolic conservation laws","authors":"Lei Wei , Qifan Chen , Yinhua Xia","doi":"10.1016/j.jcp.2025.114566","DOIUrl":"10.1016/j.jcp.2025.114566","url":null,"abstract":"<div><div>This paper presents a novel class of high-order Runge-Kutta (RK) central discontinuous Galerkin (CDG) schemes for hyperbolic conservation laws. The key feature of the proposed scheme is the hybridization of different spatial discretization operators at different RK stages, which distinguishes it from the traditional method of lines framework. Specifically, we focus on employing the CDG operator without the numerical dissipation term in selected stages while using the standard CDG operator in other stages. This approach can improve efficiency by reducing the number of computational terms and allowing larger time steps. Therefore, the resulting method is referred to as the ECDG method. For smooth problems, the ECDG scheme maintains the same accuracy as the original CDG scheme. For problems involving shocks, it effectively suppresses numerical oscillations and enhances shock-capturing capabilities while being less dissipative. Additionally, we perform Fourier-type stability and error analysis for the ECDG scheme in the context of the one-dimensional linear advection equation. Furthermore, we discuss more possible constructions of ECDG schemes involving other spatial operators. Several numerical examples are presented to demonstrate the improved efficiency and higher resolution of the ECDG scheme for hyperbolic conservation laws.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"548 ","pages":"Article 114566"},"PeriodicalIF":3.8,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145712079","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}
Atmospheric boundary layer (ABL) flows govern surface weather patterns, wind energy forecasting, and urban airflow modeling, making them critical to a wide range of meteorological, engineering and environmental applications. Many ABL flows are characterized by high levels of flow heterogeneity and turbulence anisotropy due to the complex shape of the local terrain, making analysis via large eddy simulation challenging. This study evaluates mixed subgrid-scale models and higher-order numerical schemes formulated in generalized curvilinear coordinates (GCC) aimed at simulating turbulent flows in heterogeneous conditions. The anisotropic minimum-dissipation model, its mixed-model variant, the Bardina-anisotropic minimum dissipation (BAMD) model, and the baseline Bardina–Vreman (BV) model are formulated within GCC, which provides enhanced geometrical flexibility, enabling higher numerical accuracy and stability for resolving heterogeneous turbulent flows compared to traditional Cartesian grids. The mixed formulations combine the dissipative feature of functional subgrid closures with the structural accuracy of scale-similarity-based models. The mixed models are compared with the Lagrangian scale-dependent and localized dynamic Smagorinsky subgrid-scale models using five different convection schemes: second-order central difference, fourth-order central difference, fourth-order central difference with hyper-viscosity (CD4H), third-order upwind-biased, and QUICK. Simulations are conducted for the classical Taylor–Green vortex case, turbulent channel flow at frictional Reynolds number (Reτ) = 395, and a neutral atmospheric boundary layer over heterogeneous terrain. Results consisting of first-, second-, and third-order moments are presented alongside joint probability density functions of the resolved velocity gradient tensor and barycentric maps representing turbulence anisotropy. Among all tested combinations, the BAMD model coupled with the CD4H scheme shows the best balance between accuracy and efficiency, highlighting the effectiveness of combining mixed subgrid-scale models and high-order convective schemes with the geometrical flexibility of finite-volume methods constructed in generalized curvilinear coordinates.
{"title":"Mixed subgrid-scale models in generalized curvilinear coordinates for large-eddy simulations of heterogeneous turbulent flows","authors":"Arjun Ajay , Jagdeep Singh , Sebastiano Stipa , Pierre Bénard , Joshua Brinkerhoff","doi":"10.1016/j.jcp.2025.114554","DOIUrl":"10.1016/j.jcp.2025.114554","url":null,"abstract":"<div><div>Atmospheric boundary layer (ABL) flows govern surface weather patterns, wind energy forecasting, and urban airflow modeling, making them critical to a wide range of meteorological, engineering and environmental applications. Many ABL flows are characterized by high levels of flow heterogeneity and turbulence anisotropy due to the complex shape of the local terrain, making analysis via large eddy simulation challenging. This study evaluates mixed subgrid-scale models and higher-order numerical schemes formulated in generalized curvilinear coordinates (GCC) aimed at simulating turbulent flows in heterogeneous conditions. The anisotropic minimum-dissipation model, its mixed-model variant, the Bardina-anisotropic minimum dissipation (BAMD) model, and the baseline Bardina–Vreman (BV) model are formulated within GCC, which provides enhanced geometrical flexibility, enabling higher numerical accuracy and stability for resolving heterogeneous turbulent flows compared to traditional Cartesian grids. The mixed formulations combine the dissipative feature of functional subgrid closures with the structural accuracy of scale-similarity-based models. The mixed models are compared with the Lagrangian scale-dependent and localized dynamic Smagorinsky subgrid-scale models using five different convection schemes: second-order central difference, fourth-order central difference, fourth-order central difference with hyper-viscosity (CD4H), third-order upwind-biased, and QUICK. Simulations are conducted for the classical Taylor–Green vortex case, turbulent channel flow at frictional Reynolds number (<em>Re<sub>τ</sub></em>) = 395, and a neutral atmospheric boundary layer over heterogeneous terrain. Results consisting of first-, second-, and third-order moments are presented alongside joint probability density functions of the resolved velocity gradient tensor and barycentric maps representing turbulence anisotropy. Among all tested combinations, the BAMD model coupled with the CD4H scheme shows the best balance between accuracy and efficiency, highlighting the effectiveness of combining mixed subgrid-scale models and high-order convective schemes with the geometrical flexibility of finite-volume methods constructed in generalized curvilinear coordinates.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"547 ","pages":"Article 114554"},"PeriodicalIF":3.8,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145733947","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}
Pub Date : 2025-12-04DOI: 10.1016/j.jcp.2025.114557
Boris Martin , Pierre Jolivet , Christophe Geuzaine
Solving large-scale Helmholtz problems discretized with high-order finite elements is notoriously difficult, especially in 3D where direct factorization of the system matrix is very expensive and memory demanding, and robust convergence of iterative methods is difficult to obtain. Domain decomposition methods (DDM) constitute one of the most promising strategies so far, by combining direct and iterative approaches: using direct solvers on overlapping or non-overlapping subdomains, as a preconditioner for a Krylov subspace method on the original Helmholtz system or as an iterative solver on a substructured problem involving field values or Lagrange multipliers on the interfaces between the subdomains. In this work we compare the computational performance of non-overlapping substructured DDM and Optimized Restricted Additive Schwarz (ORAS) preconditioners for solving large-scale Helmholtz problems with multiple sources, as is encountered, e.g., in frequency-domain Full Waveform Inversion. We show on a realistic geophysical test-case that, when appropriately tuned, the non-overlapping methods can reduce the convergence gap sufficiently to significantly outperform the overlapping methods.
{"title":"Comparison of substructured non-overlapping domain decomposition and overlapping additive Schwarz methods for large-scale Helmholtz problems with multiple sources","authors":"Boris Martin , Pierre Jolivet , Christophe Geuzaine","doi":"10.1016/j.jcp.2025.114557","DOIUrl":"10.1016/j.jcp.2025.114557","url":null,"abstract":"<div><div>Solving large-scale Helmholtz problems discretized with high-order finite elements is notoriously difficult, especially in 3D where direct factorization of the system matrix is very expensive and memory demanding, and robust convergence of iterative methods is difficult to obtain. Domain decomposition methods (DDM) constitute one of the most promising strategies so far, by combining direct and iterative approaches: using direct solvers on overlapping or non-overlapping subdomains, as a preconditioner for a Krylov subspace method on the original Helmholtz system or as an iterative solver on a substructured problem involving field values or Lagrange multipliers on the interfaces between the subdomains. In this work we compare the computational performance of non-overlapping substructured DDM and Optimized Restricted Additive Schwarz (ORAS) preconditioners for solving large-scale Helmholtz problems with multiple sources, as is encountered, e.g., in frequency-domain Full Waveform Inversion. We show on a realistic geophysical test-case that, when appropriately tuned, the non-overlapping methods can reduce the convergence gap sufficiently to significantly outperform the overlapping methods.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"548 ","pages":"Article 114557"},"PeriodicalIF":3.8,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145711711","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}
Pub Date : 2025-12-04DOI: 10.1016/j.jcp.2025.114550
Eviatar Bach , Ricardo Baptista , Edoardo Calvello , Bohan Chen , Andrew Stuart
The filtering distribution in hidden Markov models evolves according to the law of a mean-field model in state–observation space. The ensemble Kalman filter (EnKF) approximates this mean-field model with an ensemble of interacting particles, employing a Gaussian ansatz for the joint distribution of the state and observation at each observation time. These methods are robust, but the Gaussian ansatz limits accuracy. Here this shortcoming is addressed by using machine learning to map the joint predicted state and observation to the updated state estimate. The derivation of methods from a mean field formulation of the true filtering distribution suggests a single parametrization of the algorithm that can be deployed at different ensemble sizes. And we use a mean field formulation of the ensemble Kalman filter as an inductive bias for our architecture.
To develop this perspective, in which the mean-field limit of the algorithm and finite interacting ensemble particle approximations share a common set of parameters, a novel form of neural operator is introduced, taking probability distributions as input: a measure neural mapping (MNM). A MNM is used to design a novel approach to filtering, the MNM-enhanced ensemble filter (MNMEF), which is defined in both the mean-field limit and for interacting ensemble particle approximations. The ensemble approach uses empirical measures as input to the MNM and is implemented using the set transformer, which is invariant to ensemble permutation and allows for different ensemble sizes. In practice fine-tuning of a small number of parameters, for specific ensemble sizes, further enhances the accuracy of the scheme. The promise of the approach is demonstrated by its superior root-mean-square-error performance relative to leading methods in filtering the Lorenz ‘96 and Kuramoto-Sivashinsky models.
{"title":"Learning enhanced ensemble filters","authors":"Eviatar Bach , Ricardo Baptista , Edoardo Calvello , Bohan Chen , Andrew Stuart","doi":"10.1016/j.jcp.2025.114550","DOIUrl":"10.1016/j.jcp.2025.114550","url":null,"abstract":"<div><div>The filtering distribution in hidden Markov models evolves according to the law of a mean-field model in state–observation space. The ensemble Kalman filter (EnKF) approximates this mean-field model with an ensemble of interacting particles, employing a Gaussian ansatz for the joint distribution of the state and observation at each observation time. These methods are robust, but the Gaussian ansatz limits accuracy. Here this shortcoming is addressed by using machine learning to map the joint predicted state and observation to the updated state estimate. The derivation of methods from a mean field formulation of the true filtering distribution suggests a single parametrization of the algorithm that can be deployed at different ensemble sizes. And we use a mean field formulation of the ensemble Kalman filter as an inductive bias for our architecture.</div><div>To develop this perspective, in which the mean-field limit of the algorithm and finite interacting ensemble particle approximations share a common set of parameters, a novel form of neural operator is introduced, taking probability distributions as input: a <em>measure neural mapping</em> (MNM). A MNM is used to design a novel approach to filtering, the <em>MNM-enhanced ensemble filter</em> (MNMEF), which is defined in both the mean-field limit and for interacting ensemble particle approximations. The ensemble approach uses empirical measures as input to the MNM and is implemented using the set transformer, which is invariant to ensemble permutation and allows for different ensemble sizes. In practice fine-tuning of a small number of parameters, for specific ensemble sizes, further enhances the accuracy of the scheme. The promise of the approach is demonstrated by its superior root-mean-square-error performance relative to leading methods in filtering the Lorenz ‘96 and Kuramoto-Sivashinsky models.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"547 ","pages":"Article 114550"},"PeriodicalIF":3.8,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145733945","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}
Pub Date : 2025-12-04DOI: 10.1016/j.jcp.2025.114559
Xiaofei Guan , Lijian Jiang , Yajun Wang , Zihao Yang
This paper introduces a novel localized subspace iteration (LSI) method for constructing generalized finite element basis functions, designed to address multiscale problems on complex domains without scale separation. The proposed method synergistically combines operator localization with subspace iteration applied to local spectral problems. Localization is achieved by employing local homogeneous Dirichlet boundary conditions in conjunction with partition-of-unity functions. We subsequently develop two computationally efficient implementations: the localized standard subspace iteration (LSSI) and the localized krylov subspace iteration (LKSI), founded on standard and Krylov subspaces, respectively. Furthermore, from a unifying theoretical perspective, we demonstrate that several established multiscale methods can be reinterpreted as specific instances of subspace iteration for approximating the eigenspaces of these local spectral problems. A rigorous convergence analysis is provided to substantiate the method’s theoretical foundations. Finally, numerical experiments confirm the robustness and high efficiency of our method, showcasing its superior capability in handling challenging scenarios such as long-channel configurations in fractured media.
{"title":"Localized subspace iteration methods for multiscale problems","authors":"Xiaofei Guan , Lijian Jiang , Yajun Wang , Zihao Yang","doi":"10.1016/j.jcp.2025.114559","DOIUrl":"10.1016/j.jcp.2025.114559","url":null,"abstract":"<div><div>This paper introduces a novel localized subspace iteration (LSI) method for constructing generalized finite element basis functions, designed to address multiscale problems on complex domains without scale separation. The proposed method synergistically combines operator localization with subspace iteration applied to local spectral problems. Localization is achieved by employing local homogeneous Dirichlet boundary conditions in conjunction with partition-of-unity functions. We subsequently develop two computationally efficient implementations: the localized standard subspace iteration (LSSI) and the localized krylov subspace iteration (LKSI), founded on standard and Krylov subspaces, respectively. Furthermore, from a unifying theoretical perspective, we demonstrate that several established multiscale methods can be reinterpreted as specific instances of subspace iteration for approximating the eigenspaces of these local spectral problems. A rigorous convergence analysis is provided to substantiate the method’s theoretical foundations. Finally, numerical experiments confirm the robustness and high efficiency of our method, showcasing its superior capability in handling challenging scenarios such as long-channel configurations in fractured media.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"547 ","pages":"Article 114559"},"PeriodicalIF":3.8,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145733948","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}
Pub Date : 2025-12-02DOI: 10.1016/j.jcp.2025.114562
Jinpeng Xiang , Wenbo Cao , Shufang Song , Weiwei Zhang
For PDE-constrained optimization, direct adjoint looping (DAL) solves the state and adjoint equations separately until convergence for per update of the design variables, providing accurate gradient and robust optimization. One-shot method simultaneously solves the state equation, adjoint equation, and design equation in a fully coupled system, requiring just O(1) forward PDE solves and significantly reducing simulation cost. However, one-shot systems often exhibit high condition numbers, which can lead to slow convergence or numerical divergence. This study develops a robust one-shot optimization framework based on adjoint surrogate model, where the surrogate model approximates the adjoint variables and is embedded into the coupled optimization process. Numerical experiments on three PDE-constrained benchmarks, including parameter identification and aerodynamic shape optimization, demonstrate that the present method achieves over an order-of-magnitude speedup compared with DAL. This study highlights the effects of using adjoint-system surrogates on the efficiency and robustness of one-shot optimization, providing a general and practical pathway for accelerating PDE-constrained design problems.
{"title":"A robust one-shot method based on adjoint surrogate model for PDE-constrained optimization","authors":"Jinpeng Xiang , Wenbo Cao , Shufang Song , Weiwei Zhang","doi":"10.1016/j.jcp.2025.114562","DOIUrl":"10.1016/j.jcp.2025.114562","url":null,"abstract":"<div><div>For PDE-constrained optimization, direct adjoint looping (DAL) solves the state and adjoint equations separately until convergence for per update of the design variables, providing accurate gradient and robust optimization. One-shot method simultaneously solves the state equation, adjoint equation, and design equation in a fully coupled system, requiring just O(1) forward PDE solves and significantly reducing simulation cost. However, one-shot systems often exhibit high condition numbers, which can lead to slow convergence or numerical divergence. This study develops a robust one-shot optimization framework based on adjoint surrogate model, where the surrogate model approximates the adjoint variables and is embedded into the coupled optimization process. Numerical experiments on three PDE-constrained benchmarks, including parameter identification and aerodynamic shape optimization, demonstrate that the present method achieves over an order-of-magnitude speedup compared with DAL. This study highlights the effects of using adjoint-system surrogates on the efficiency and robustness of one-shot optimization, providing a general and practical pathway for accelerating PDE-constrained design problems.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"547 ","pages":"Article 114562"},"PeriodicalIF":3.8,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145734011","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}
This paper presents a novel inverse Lax-Wendroff (ILW) boundary treatment for finite difference Hermite weighted essentially non-oscillatory (HWENO) schemes to solve hyperbolic conservation laws on arbitrary geometries. The complex geometric domain is divided by a uniform Cartesian grid, resulting in challenges in boundary treatment. The proposed ILW boundary treatment could provide high order approximations of both solution values and spatial derivatives at ghost points outside the computational domain. Distinct from existing ILW approaches, our boundary treatment constructs the extrapolation through optimization via a least squares formulation, coupled with the spatial derivatives at the boundary obtained via the ILW procedure. Theoretical analysis indicates that compared with other ILW methods, our proposed one would require fewer terms obtained via the ILW procedure on the boundary and thus reduce computational complexity while preserving accuracy and stability. The effectiveness and robustness of the method are validated through numerical experiments.
{"title":"Inverse Lax-Wendroff boundary treatment for solving conservation laws with finite difference HWENO methods","authors":"Guangyao Zhu , Yan Jiang , Zhuang Zhao , Mengping Zhang","doi":"10.1016/j.jcp.2025.114552","DOIUrl":"10.1016/j.jcp.2025.114552","url":null,"abstract":"<div><div>This paper presents a novel inverse Lax-Wendroff (ILW) boundary treatment for finite difference Hermite weighted essentially non-oscillatory (HWENO) schemes to solve hyperbolic conservation laws on arbitrary geometries. The complex geometric domain is divided by a uniform Cartesian grid, resulting in challenges in boundary treatment. The proposed ILW boundary treatment could provide high order approximations of both solution values and spatial derivatives at ghost points outside the computational domain. Distinct from existing ILW approaches, our boundary treatment constructs the extrapolation through optimization via a least squares formulation, coupled with the spatial derivatives at the boundary obtained via the ILW procedure. Theoretical analysis indicates that compared with other ILW methods, our proposed one would require fewer terms obtained via the ILW procedure on the boundary and thus reduce computational complexity while preserving accuracy and stability. The effectiveness and robustness of the method are validated through numerical experiments.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"547 ","pages":"Article 114552"},"PeriodicalIF":3.8,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145733949","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}
Pub Date : 2025-11-30DOI: 10.1016/j.jcp.2025.114555
William Doherty , Timothy N. Phillips , Markus Uhlmann , Zhihua Xie
We proposed a novel diffused interface approach for the interface normal and curvature calculation in the conservative level set method framework for both Newtonian and non-Newtonian multiphase flows. The standard benchmark of reversible vortex problem is used to test the interface capturing method for both standard and conservative level set method. In addition, the new approach is validated to accurately simulate oscillating droplet, bubble rising in a viscoelastic fluid, and droplet impact in a deep pool, in which a good agreement is obtained with analytical solutions and experimental measurements.
{"title":"Interface normal and curvature calculation for the conservative level set method","authors":"William Doherty , Timothy N. Phillips , Markus Uhlmann , Zhihua Xie","doi":"10.1016/j.jcp.2025.114555","DOIUrl":"10.1016/j.jcp.2025.114555","url":null,"abstract":"<div><div>We proposed a novel diffused interface approach for the interface normal and curvature calculation in the conservative level set method framework for both Newtonian and non-Newtonian multiphase flows. The standard benchmark of reversible vortex problem is used to test the interface capturing method for both standard and conservative level set method. In addition, the new approach is validated to accurately simulate oscillating droplet, bubble rising in a viscoelastic fluid, and droplet impact in a deep pool, in which a good agreement is obtained with analytical solutions and experimental measurements.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"547 ","pages":"Article 114555"},"PeriodicalIF":3.8,"publicationDate":"2025-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145733946","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}
Pub Date : 2025-11-29DOI: 10.1016/j.jcp.2025.114549
Owen Melia , Daniel Fortunato , Jeremy Hoskins , Rebecca Willett
We provide a flexible, open-source framework for hardware acceleration, namely massively-parallel execution on general-purpose graphics processing units (GPUs), applied to the hierarchical Poincaré–Steklov (HPS) family of algorithms for building fast direct solvers for linear elliptic partial differential equations. To take full advantage of the power of hardware acceleration, we propose two variants of HPS algorithms to improve performance on two- and three-dimensional problems. In the two-dimensional setting, we introduce a novel recomputation strategy that minimizes costly data transfers to and from the GPU; in three dimensions, we modify and extend the adaptive discretization technique of Geldermans and Gillman [1] to greatly reduce peak memory usage. We provide an open-source implementation of these methods written in JAX, a high-level accelerated linear algebra package, which allows for the first integration of a high-order fast direct solver with automatic differentiation tools. We conclude with extensive numerical examples showing our methods are fast and accurate on two- and three-dimensional problems.
{"title":"Hardware acceleration for HPS algorithms in two and three dimensions","authors":"Owen Melia , Daniel Fortunato , Jeremy Hoskins , Rebecca Willett","doi":"10.1016/j.jcp.2025.114549","DOIUrl":"10.1016/j.jcp.2025.114549","url":null,"abstract":"<div><div>We provide a flexible, open-source framework for hardware acceleration, namely massively-parallel execution on general-purpose graphics processing units (GPUs), applied to the hierarchical Poincaré–Steklov (HPS) family of algorithms for building fast direct solvers for linear elliptic partial differential equations. To take full advantage of the power of hardware acceleration, we propose two variants of HPS algorithms to improve performance on two- and three-dimensional problems. In the two-dimensional setting, we introduce a novel recomputation strategy that minimizes costly data transfers to and from the GPU; in three dimensions, we modify and extend the adaptive discretization technique of Geldermans and Gillman [1] to greatly reduce peak memory usage. We provide an open-source implementation of these methods written in JAX, a high-level accelerated linear algebra package, which allows for the first integration of a high-order fast direct solver with automatic differentiation tools. We conclude with extensive numerical examples showing our methods are fast and accurate on two- and three-dimensional problems.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"547 ","pages":"Article 114549"},"PeriodicalIF":3.8,"publicationDate":"2025-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145733894","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}
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