Pub Date : 2025-11-22DOI: 10.1016/j.jcp.2025.114539
Micol Bassanini , Simone Deparis , Paolo Ricci
In wave propagation problems, finite difference methods implemented on staggered grids are commonly used to avoid checkerboard patterns and to improve accuracy in the approximation of short-wavelength components of the solutions. In this study, we develop a mimetic finite difference (MFD) method on staggered grids for transport operators with divergence-free advective field that is proven to be energy-preserving in wave problems. This method mimics some characteristics of the summation-by-parts (SBP) operators framework, in particular it preserves the divergence theorem at the discrete level. Its design is intended to be versatile and applicable to wave problems characterized by a divergence-free velocity. As an application, we consider the electrostatic shear Alfvén waves (SAWs), appearing in the modeling of plasmas. These waves are solved in a magnetic field configuration recalling that of a tokamak device. The study of the generalized eigenvalue problem associated with the SAWs shows the energy conservation of the discretization scheme, demonstrating the stability of the numerical solution.
{"title":"Mimetic finite difference schemes for transport operators with divergence-free advective field and applications to plasma physics","authors":"Micol Bassanini , Simone Deparis , Paolo Ricci","doi":"10.1016/j.jcp.2025.114539","DOIUrl":"10.1016/j.jcp.2025.114539","url":null,"abstract":"<div><div>In wave propagation problems, finite difference methods implemented on staggered grids are commonly used to avoid checkerboard patterns and to improve accuracy in the approximation of short-wavelength components of the solutions. In this study, we develop a mimetic finite difference (MFD) method on staggered grids for transport operators with divergence-free advective field that is proven to be energy-preserving in wave problems. This method mimics some characteristics of the summation-by-parts (SBP) operators framework, in particular it preserves the divergence theorem at the discrete level. Its design is intended to be versatile and applicable to wave problems characterized by a divergence-free velocity. As an application, we consider the electrostatic shear Alfvén waves (SAWs), appearing in the modeling of plasmas. These waves are solved in a magnetic field configuration recalling that of a tokamak device. The study of the generalized eigenvalue problem associated with the SAWs shows the energy conservation of the discretization scheme, demonstrating the stability of the numerical solution.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"547 ","pages":"Article 114539"},"PeriodicalIF":3.8,"publicationDate":"2025-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145682857","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 : 2025-11-22DOI: 10.1016/j.jcp.2025.114540
Jiachun Zheng , Yunqing Huang , Nianyu Yi
In this work, we develop interface-gated physics-informed neural networks (IG-PINNs) to solve elliptic interface equations. In IG-PINNs, we use a fully connected neural network to capture the smooth behavior across the entire domain. In each subdomain separated by the interface, an interface-gated network is utilized to provide corrections at the interface. In the architectural design of the interface-gated network, we introduce a gating mechanism and a level-set function derived from the interface. This design enables the interface-gated network to effectively handle discontinuous jumps across the interface. Some numerical experiments have confirmed the effectiveness of the IG-PINNs, demonstrating higher accuracy compared with PINNs, interface PINNs (I-PINNs) and multi-domain PINNs (M-PINNs).
{"title":"IG-PINNs: Interface-gated physics-informed neural networks for solving elliptic interface problems","authors":"Jiachun Zheng , Yunqing Huang , Nianyu Yi","doi":"10.1016/j.jcp.2025.114540","DOIUrl":"10.1016/j.jcp.2025.114540","url":null,"abstract":"<div><div>In this work, we develop interface-gated physics-informed neural networks (IG-PINNs) to solve elliptic interface equations. In IG-PINNs, we use a fully connected neural network to capture the smooth behavior across the entire domain. In each subdomain separated by the interface, an interface-gated network is utilized to provide corrections at the interface. In the architectural design of the interface-gated network, we introduce a gating mechanism and a level-set function derived from the interface. This design enables the interface-gated network to effectively handle discontinuous jumps across the interface. Some numerical experiments have confirmed the effectiveness of the IG-PINNs, demonstrating higher accuracy compared with PINNs, interface PINNs (I-PINNs) and multi-domain PINNs (M-PINNs).</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"547 ","pages":"Article 114540"},"PeriodicalIF":3.8,"publicationDate":"2025-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145617583","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 : 2025-11-22DOI: 10.1016/j.jcp.2025.114538
Gerardo E. Oleaga, Daniel Ortega-Lozano, Valeri A. Makarov
Exploring environments with static and moving obstacles is a fundamental problem with numerous applications in physics and engineering. The Fast Marching Method (FMM) offers a computationally efficient numerical solution to the Eikonal equation, which describes a wavefront propagating through a medium. The FMM is effective in media with static obstacles, but, as we show, it fails in the presence of moving ones. We introduce a novel, robust method for wave exploration of environments of arbitrary dimension and complexity, and prove its convergence numerically. The method accurately handles both dynamic and static obstacles while preserving the computational efficiency of the FMM, ensuring a fast and reliable global search for collision-free trajectories. The algorithm can also serve as an interception strategy for catching a moving target among many obstacles.
{"title":"A robust method for fast exploration of environments with moving obstacles","authors":"Gerardo E. Oleaga, Daniel Ortega-Lozano, Valeri A. Makarov","doi":"10.1016/j.jcp.2025.114538","DOIUrl":"10.1016/j.jcp.2025.114538","url":null,"abstract":"<div><div>Exploring environments with static and moving obstacles is a fundamental problem with numerous applications in physics and engineering. The Fast Marching Method (FMM) offers a computationally efficient numerical solution to the Eikonal equation, which describes a wavefront propagating through a medium. The FMM is effective in media with static obstacles, but, as we show, it fails in the presence of moving ones. We introduce a novel, robust method for wave exploration of environments of arbitrary dimension and complexity, and prove its convergence numerically. The method accurately handles both dynamic and static obstacles while preserving the computational efficiency of the FMM, ensuring a fast and reliable global search for collision-free trajectories. The algorithm can also serve as an interception strategy for catching a moving target among many obstacles.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"547 ","pages":"Article 114538"},"PeriodicalIF":3.8,"publicationDate":"2025-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145616998","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 : 2025-11-20DOI: 10.1016/j.jcp.2025.114522
Gaurav Kumar, Aditya G. Nair
This work introduces a novel adaptive mesh refinement (AMR) method that utilizes dominant balance analysis (DBA) for efficient and accurate grid adaptation in computational fluid dynamics (CFD) simulations. The proposed method leverages a Gaussian mixture model (GMM) to classify grid cells into active and passive regions based on the dominant physical interactions within the equation space. By modeling truncation error probabilistically from discretized terms, the method identifies regions of high interaction where numerical accuracy is most sensitive to resolution. Unlike traditional AMR strategies, this approach does not rely on heuristic-based sensors or user-defined thresholds, providing a fully automated and problem-independent framework for AMR. Applied to the incompressible Navier-Stokes equations for steady and unsteady flow past a cylinder, the DBA-based AMR method achieves comparable accuracy to high-resolution grids while reducing computational costs by up to 70 %. The validation highlights the method’s effectiveness in capturing complex flow features while minimizing grid cells, directing computational resources toward regions with the most critical dynamics. This modular and scalable strategy is adaptable to a wide range of applications, presenting a promising tool for efficient high-fidelity simulations in CFD and other multiphysics domains.
{"title":"Dominant balance-based adaptive mesh refinement for incompressible fluid flows","authors":"Gaurav Kumar, Aditya G. Nair","doi":"10.1016/j.jcp.2025.114522","DOIUrl":"10.1016/j.jcp.2025.114522","url":null,"abstract":"<div><div>This work introduces a novel adaptive mesh refinement (AMR) method that utilizes dominant balance analysis (DBA) for efficient and accurate grid adaptation in computational fluid dynamics (CFD) simulations. The proposed method leverages a Gaussian mixture model (GMM) to classify grid cells into active and passive regions based on the dominant physical interactions within the equation space. By modeling truncation error probabilistically from discretized terms, the method identifies regions of high interaction where numerical accuracy is most sensitive to resolution. Unlike traditional AMR strategies, this approach does not rely on heuristic-based sensors or user-defined thresholds, providing a fully automated and problem-independent framework for AMR. Applied to the incompressible Navier-Stokes equations for steady and unsteady flow past a cylinder, the DBA-based AMR method achieves comparable accuracy to high-resolution grids while reducing computational costs by up to 70 %. The validation highlights the method’s effectiveness in capturing complex flow features while minimizing grid cells, directing computational resources toward regions with the most critical dynamics. This modular and scalable strategy is adaptable to a wide range of applications, presenting a promising tool for efficient high-fidelity simulations in CFD and other multiphysics domains.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"547 ","pages":"Article 114522"},"PeriodicalIF":3.8,"publicationDate":"2025-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145600613","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 : 2025-11-19DOI: 10.1016/j.jcp.2025.114481
Gilbert Strang
Peter Lax was a wonderful mathematician and a very generous guide to his students and friends.My first step started with the Lax Equivalence Theorem (see below—I reported on it to the Henrici seminar at UCLA). The theorem tells us why and how to test the stability of difference equations—Peter followed von Neumann in applying the test to all complex exponentials . This paper applies that test to highly accurate approximations of a model wave equation. We need to prove stability |Σakeikθ| ≤ 1 for various complex polynomials of high degree. A long ago paper (1962) found a productive approach to necessary conditions on the ak, and this short note carries the analysis to necessary and sufficient conditions.
{"title":"High Order Lax-Wendroff Methods for Hyperbolic Systems","authors":"Gilbert Strang","doi":"10.1016/j.jcp.2025.114481","DOIUrl":"10.1016/j.jcp.2025.114481","url":null,"abstract":"<div><div>Peter Lax was a wonderful mathematician and a very generous guide to his students and friends.My first step started with the Lax Equivalence Theorem (see below—I reported on it to the Henrici seminar at UCLA). The theorem tells us why and how to test the stability of difference equations—Peter followed von Neumann in applying the test to all complex exponentials <span><math><mrow><mi>u</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><msup><mi>e</mi><mrow><mi>i</mi><mi>θ</mi><mi>x</mi></mrow></msup></mrow></math></span>. This paper applies that test to highly accurate approximations of a model wave equation. We need to prove stability |Σ<em>a<sub>k</sub>e<sup>ikθ</sup></em>| ≤ 1 for various complex polynomials of high degree. A long ago paper (1962) found a productive approach to necessary conditions on the <em>a<sub>k</sub></em>, and this short note carries the analysis to necessary and sufficient conditions.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"547 ","pages":"Article 114481"},"PeriodicalIF":3.8,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145682802","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 : 2025-11-19DOI: 10.1016/j.jcp.2025.114523
William A. Sands, Jing-Mei Qiu, Daniel Hayes, Nanyi Zheng
In this paper, we propose a novel adaptive-rank method for simulating multi-scale BGK equations which is based on a greedy sampling technique. The method adaptively identifies important rows and columns of the solution matrix, and reduces computational complexity by updating only the selected rows and columns through a local solver. Once updated, the solution at selected rows and columns is used together with an adaptive cross approximation to reconstruct the entire solution matrix. The approach extends the semi-Lagrangian adaptive-rank approach, introduced in our previous work for the Vlasov-Poisson system [1] in several ways. Unlike the step-and-truncate low-rank integrators discussed in [2], the greedy sampling technique considered in this paper avoids the need for explicit low-rank decompositions of nonlinear terms, such as the local Maxwellian in the BGK collision operator. We enforce mass, momentum, and energy conservation by introducing a new locally macroscopic conservative correction, which implicitly couples the kinetic solution to the solution of the corresponding macroscopic system. Using asymptotic analysis, we show that the macroscopic correction preserves the asymptotic properties intrinsic to the full-grid scheme and that the proposed method in the low-rank setting possesses a conditionally asymptotic-preserving property. Another unique advantage of our approach is the use of a local semi-Lagrangian solver, which permits large time steps compared to Eulerian schemes. This flexibility is retained in the macroscopic solver by employing high-order stiffly-accurate diagonally implicit Runge-Kutta methods. The resulting nonlinear macroscopic systems are solved efficiently using a Jacobian-free Newton-Krylov method, which eliminates the need for preconditioning at modest CFL numbers. Each iteration of the nonlinear macroscopic solver provides a self-consistent correction to a provisional low-rank kinetic solution, which is then used as a dynamic closure for the macroscopic system. Numerical results demonstrate the efficacy of the proposed method in capturing shocks and discontinuous solution structures. We also highlight its performance in a challenging mixed-regime problem, where the Knudsen number spans multiple orders of magnitude.
{"title":"An adaptive-rank approach with greedy sampling for multi-scale BGK equations","authors":"William A. Sands, Jing-Mei Qiu, Daniel Hayes, Nanyi Zheng","doi":"10.1016/j.jcp.2025.114523","DOIUrl":"10.1016/j.jcp.2025.114523","url":null,"abstract":"<div><div>In this paper, we propose a novel adaptive-rank method for simulating multi-scale BGK equations which is based on a greedy sampling technique. The method adaptively identifies important rows and columns of the solution matrix, and reduces computational complexity by updating only the selected rows and columns through a local solver. Once updated, the solution at selected rows and columns is used together with an adaptive cross approximation to reconstruct the entire solution matrix. The approach extends the semi-Lagrangian adaptive-rank approach, introduced in our previous work for the Vlasov-Poisson system [1] in several ways. Unlike the step-and-truncate low-rank integrators discussed in [2], the greedy sampling technique considered in this paper avoids the need for explicit low-rank decompositions of nonlinear terms, such as the local Maxwellian in the BGK collision operator. We enforce mass, momentum, and energy conservation by introducing a new locally macroscopic conservative correction, which implicitly couples the kinetic solution to the solution of the corresponding macroscopic system. Using asymptotic analysis, we show that the macroscopic correction preserves the asymptotic properties intrinsic to the full-grid scheme and that the proposed method in the low-rank setting possesses a conditionally asymptotic-preserving property. Another unique advantage of our approach is the use of a local semi-Lagrangian solver, which permits large time steps compared to Eulerian schemes. This flexibility is retained in the macroscopic solver by employing high-order stiffly-accurate diagonally implicit Runge-Kutta methods. The resulting nonlinear macroscopic systems are solved efficiently using a Jacobian-free Newton-Krylov method, which eliminates the need for preconditioning at modest CFL numbers. Each iteration of the nonlinear macroscopic solver provides a self-consistent correction to a provisional low-rank kinetic solution, which is then used as a dynamic closure for the macroscopic system. Numerical results demonstrate the efficacy of the proposed method in capturing shocks and discontinuous solution structures. We also highlight its performance in a challenging mixed-regime problem, where the Knudsen number spans multiple orders of magnitude.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"547 ","pages":"Article 114523"},"PeriodicalIF":3.8,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145600612","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 : 2025-11-19DOI: 10.1016/j.jcp.2025.114537
Zecheng Zhang , Christian Moya , Lu Lu , Guang Lin , Hayden Schaeffer
We propose a novel fine-tuning method to achieve multi-operator learning through training a distributed neural operator with diverse function data and then zero-shot fine-tuning the neural network using physics-informed losses for downstream tasks. Operator learning effectively approximates solution operators for PDEs and various PDE-related problems, yet it often struggles to generalize to new tasks. To address this, we investigate fine-tuning a pretrained model, while carefully selecting an initialization that enables rapid adaptation to new tasks with minimal data. Our approach combines distributed learning to integrate data from various operators in pre-training, while physics-informed methods enable zero-shot fine-tuning, minimizing the reliance on downstream data. We investigate standard fine-tuning and Low-Rank Adaptation fine-tuning, applying both to train complex nonlinear target operators that are difficult to learn only using random initialization. Through comprehensive numerical examples, we demonstrate the advantages of our approach, showcasing significant improvements in accuracy. Our findings provide a robust framework for advancing multi-operator learning and highlight the potential of transfer learning techniques in this domain.
{"title":"DeepONet as a multi-Operator extrapolation model: Distributed pretraining with physics-Informed fine-Tuning","authors":"Zecheng Zhang , Christian Moya , Lu Lu , Guang Lin , Hayden Schaeffer","doi":"10.1016/j.jcp.2025.114537","DOIUrl":"10.1016/j.jcp.2025.114537","url":null,"abstract":"<div><div>We propose a novel fine-tuning method to achieve multi-operator learning through training a distributed neural operator with diverse function data and then zero-shot fine-tuning the neural network using physics-informed losses for downstream tasks. Operator learning effectively approximates solution operators for PDEs and various PDE-related problems, yet it often struggles to generalize to new tasks. To address this, we investigate fine-tuning a pretrained model, while carefully selecting an initialization that enables rapid adaptation to new tasks with minimal data. Our approach combines distributed learning to integrate data from various operators in pre-training, while physics-informed methods enable zero-shot fine-tuning, minimizing the reliance on downstream data. We investigate standard fine-tuning and Low-Rank Adaptation fine-tuning, applying both to train complex nonlinear target operators that are difficult to learn only using random initialization. Through comprehensive numerical examples, we demonstrate the advantages of our approach, showcasing significant improvements in accuracy. Our findings provide a robust framework for advancing multi-operator learning and highlight the potential of transfer learning techniques in this domain.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"547 ","pages":"Article 114537"},"PeriodicalIF":3.8,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145617584","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 : 2025-11-19DOI: 10.1016/j.jcp.2025.114511
Zhiqiang Zeng , Hao Wang , Tiegang Liu , Changsheng Yu
In this paper, we propose a path-conservative finite volume scheme to address the non-conservative nature of governing equations for hypo-elastic plastic solids. By combining the Hooke’s law-preserving path with the Riemann solver, a novel class of piecewise paths is proposed. Furthermore, we process the model changes during elastic-plastic transitions by incorporating deviatoric stress iteration, establishing transition formulas, and formulating the elastic-plastic interface fluxes. Our method has been applied to both one-dimensional and two-dimensional elastic-plastic solid models. Numerical tests have demonstrated its effectiveness.
{"title":"Path-conservative finite volume scheme with Hooke’s law-preserving paths for non-conservative hyperbolic system of hypo-elastic plastic solid","authors":"Zhiqiang Zeng , Hao Wang , Tiegang Liu , Changsheng Yu","doi":"10.1016/j.jcp.2025.114511","DOIUrl":"10.1016/j.jcp.2025.114511","url":null,"abstract":"<div><div>In this paper, we propose a path-conservative finite volume scheme to address the non-conservative nature of governing equations for hypo-elastic plastic solids. By combining the Hooke’s law-preserving path with the Riemann solver, a novel class of piecewise paths is proposed. Furthermore, we process the model changes during elastic-plastic transitions by incorporating deviatoric stress iteration, establishing transition formulas, and formulating the elastic-plastic interface fluxes. Our method has been applied to both one-dimensional and two-dimensional elastic-plastic solid models. Numerical tests have demonstrated its effectiveness.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"546 ","pages":"Article 114511"},"PeriodicalIF":3.8,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145621493","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 : 2025-11-19DOI: 10.1016/j.jcp.2025.114521
Rémi Abgrall , Walter Boscheri , Yongle Liu
In this paper, we explore the use of the Virtual Element Method (VEM) concepts to solve scalar and system hyperbolic problems on general polygonal grids. The new schemes stem from the Active Flux approach [1], which combines the usage of point values at the element boundaries with an additional degree of freedom representing the average of the solution within each control volume. Along the lines of the family of residual distribution schemes introduced in [2, 3] that integrate the Active Flux technique, we devise novel third order accurate methods that rely on the VEM technology to discretize gradients of the numerical solution by means of a polynomial-free approximation, by adopting a virtual basis that is locally defined for each element. The obtained discretization is globally continuous, and for nonlinear problems it needs a stabilization which is provided by a monolithic convex limiting strategy extended from [4]. This is applied to both point and average values of the discrete solution. We show applications to scalar problems, as well as to the acoustics and Euler equations in two dimension. The accuracy and the robustness of the proposed schemes are assessed against a suite of benchmarks involving smooth solutions, shock waves and other discontinuities.
{"title":"Virtual finite element and hyperbolic problems: The PAMPA algorithm","authors":"Rémi Abgrall , Walter Boscheri , Yongle Liu","doi":"10.1016/j.jcp.2025.114521","DOIUrl":"10.1016/j.jcp.2025.114521","url":null,"abstract":"<div><div>In this paper, we explore the use of the Virtual Element Method (VEM) concepts to solve scalar and system hyperbolic problems on general polygonal grids. The new schemes stem from the Active Flux approach [1], which combines the usage of point values at the element boundaries with an additional degree of freedom representing the average of the solution within each control volume. Along the lines of the family of residual distribution schemes introduced in [2, 3] that integrate the Active Flux technique, we devise novel third order accurate methods that rely on the VEM technology to discretize gradients of the numerical solution by means of a polynomial-free approximation, by adopting a virtual basis that is locally defined for each element. The obtained discretization is globally continuous, and for nonlinear problems it needs a stabilization which is provided by a monolithic convex limiting strategy extended from [4]. This is applied to both point and average values of the discrete solution. We show applications to scalar problems, as well as to the acoustics and Euler equations in two dimension. The accuracy and the robustness of the proposed schemes are assessed against a suite of benchmarks involving smooth solutions, shock waves and other discontinuities.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"546 ","pages":"Article 114521"},"PeriodicalIF":3.8,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145621492","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 : 2025-11-14DOI: 10.1016/j.jcp.2025.114520
Xiuguang Zhou, Liyan Wang
Electrocardiographic imaging (ECGI) faces fundamental challenges in non-invasive cardiac source reconstruction, primarily stemming from the ill-posed nature of the inverse problem and theoretical limitations on solution uniqueness for distributed sources. In this study, a rigorous theoretical framework guaranteeing solution uniqueness is established for the inverse reconstruction of monopole-dipole composite sources based on boundary potential measurements. To address the coupled complexities, a two-stage algorithmic framework is proposed, decoupling the ill-posed Cauchy problem from the non-convexity of source parameter estimation. Stage I: Cardiac surface Cauchy potentials are recovered from body surface potential measurements via an iterative optimization scheme, utilizing finite element discretization and adjoint-field formulation. Stage II: Inverse source recovery is resolved through the theoretical establishment of solution uniqueness under constrained source models and the development of a momentum-accelerated stochastic gradient descent algorithm (SGD-MT) to enhance parameter estimation robustness. A series of comprehensive numerical experiments have been conducted to assess the framework’s reconstruction accuracy and computational efficiency. The experimental results have confirmed the viability of the framework for non-invasive cardiac source imaging.
{"title":"A two-stage inverse electrocardiographic imaging approach for combined source reconstruction","authors":"Xiuguang Zhou, Liyan Wang","doi":"10.1016/j.jcp.2025.114520","DOIUrl":"10.1016/j.jcp.2025.114520","url":null,"abstract":"<div><div>Electrocardiographic imaging (ECGI) faces fundamental challenges in non-invasive cardiac source reconstruction, primarily stemming from the ill-posed nature of the inverse problem and theoretical limitations on solution uniqueness for distributed sources. In this study, a rigorous theoretical framework guaranteeing solution uniqueness is established for the inverse reconstruction of monopole-dipole composite sources based on boundary potential measurements. To address the coupled complexities, a two-stage algorithmic framework is proposed, decoupling the ill-posed Cauchy problem from the non-convexity of source parameter estimation. Stage I: Cardiac surface Cauchy potentials are recovered from body surface potential measurements via an iterative optimization scheme, utilizing finite element discretization and adjoint-field formulation. Stage II: Inverse source recovery is resolved through the theoretical establishment of solution uniqueness under constrained source models and the development of a momentum-accelerated stochastic gradient descent algorithm (SGD-MT) to enhance parameter estimation robustness. A series of comprehensive numerical experiments have been conducted to assess the framework’s reconstruction accuracy and computational efficiency. The experimental results have confirmed the viability of the framework for non-invasive cardiac source imaging.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"546 ","pages":"Article 114520"},"PeriodicalIF":3.8,"publicationDate":"2025-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145621489","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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