Pub Date : 2026-05-01Epub Date: 2026-01-26DOI: 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.
{"title":"Analysis and elimination of numerical pressure dependency in coupled Stokes-Darcy problem","authors":"Jiachuan Zhang","doi":"10.1016/j.jcp.2026.114710","DOIUrl":"10.1016/j.jcp.2026.114710","url":null,"abstract":"<div><div>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 <em>a priori</em> 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.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"552 ","pages":"Article 114710"},"PeriodicalIF":3.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146075595","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 : 2026-05-01Epub Date: 2026-01-14DOI: 10.1016/j.jcp.2026.114682
Stefan Henneking , Sreeram Venkat , Omar Ghattas
We present a goal-oriented framework for constructing digital twins with the following properties: (1) they employ discretizations of high-fidelity partial differential equation (PDE) models governed by autonomous dynamical systems, leading to large-scale forward problems; (2) they solve a linear inverse problem to assimilate observational data to infer uncertain model components followed by a forward prediction of the evolving dynamics; and (3) the entire end-to-end, data-to-inference-to-prediction computation is carried out without approximation and in real time through a Bayesian framework that rigorously accounts for uncertainties. Several challenges must be overcome to realize this framework, including the large scale of the forward problem, the high dimensionality of the parameter space, and for a class of problems including those we target, the slow decay of the singular values of the parameter-to-observable map. Here we introduce a methodology to overcome these challenges by exploiting the autonomous structure of the forward model to decompose the solution of the inverse problem into a one-time-only offline phase in which the PDE model is solved a limited number of times (equal to the number of sensors), and an online phase that maps well onto GPUs and computes the parameter inference and prediction of quantities of interest in real time, given observational data. Our ultimate goal is to apply this framework to construct digital twins for subduction zones, including Cascadia, to provide early warning for tsunamis generated by megathrust earthquakes. To this end, we demonstrate how our methodology can be used to employ seafloor pressure observations, along with the coupled acoustic–gravity wave equations, to infer the earthquake-induced spatiotemporal seafloor motion (discretized with parameters) and forward predict the tsunami propagation. We present results of an end-to-end inference, prediction, and uncertainty quantification for a representative test problem with inversion parameters for which goal-oriented Bayesian inference is accomplished exactly and in real time, that is, in a matter of seconds.
{"title":"Goal-oriented real-time Bayesian inference for linear autonomous dynamical systems with application to digital twins for tsunami early warning","authors":"Stefan Henneking , Sreeram Venkat , Omar Ghattas","doi":"10.1016/j.jcp.2026.114682","DOIUrl":"10.1016/j.jcp.2026.114682","url":null,"abstract":"<div><div>We present a goal-oriented framework for constructing digital twins with the following properties: (1) they employ discretizations of high-fidelity partial differential equation (PDE) models governed by autonomous dynamical systems, leading to large-scale forward problems; (2) they solve a linear inverse problem to assimilate observational data to infer uncertain model components followed by a forward prediction of the evolving dynamics; and (3) the entire end-to-end, data-to-inference-to-prediction computation is carried out without approximation and in real time through a Bayesian framework that rigorously accounts for uncertainties. Several challenges must be overcome to realize this framework, including the large scale of the forward problem, the high dimensionality of the parameter space, and for a class of problems including those we target, the slow decay of the singular values of the parameter-to-observable map. Here we introduce a methodology to overcome these challenges by exploiting the autonomous structure of the forward model to decompose the solution of the inverse problem into a one-time-only offline phase in which the PDE model is solved a limited number of times (equal to the number of sensors), and an online phase that maps well onto GPUs and computes the parameter inference and prediction of quantities of interest in real time, given observational data. Our ultimate goal is to apply this framework to construct digital twins for subduction zones, including Cascadia, to provide early warning for tsunamis generated by megathrust earthquakes. To this end, we demonstrate how our methodology can be used to employ seafloor pressure observations, along with the coupled acoustic–gravity wave equations, to infer the earthquake-induced spatiotemporal seafloor motion (discretized with <span><math><mrow><mi>O</mi><mo>(</mo><msup><mn>10</mn><mn>9</mn></msup><mo>)</mo></mrow></math></span> parameters) and forward predict the tsunami propagation. We present results of an end-to-end inference, prediction, and uncertainty quantification for a representative test problem with <span><math><mrow><mi>O</mi><mo>(</mo><msup><mn>10</mn><mn>8</mn></msup><mo>)</mo></mrow></math></span> inversion parameters for which goal-oriented Bayesian inference is accomplished exactly and in real time, that is, in a matter of seconds.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"552 ","pages":"Article 114682"},"PeriodicalIF":3.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025848","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}
High-dimensional, complex, and dynamic environments pose significant challenges in solving mean field games (MFGs). To address these challenges, we propose an online interactive physics-informed diffusion-adversarial network (IPIDAN), which offers enhanced interpretability and flexibility by leveraging a novel agent strategy generator based on diffusion models. This generator utilizes a noise process to improve its ability to escape local optima, while a stepwise optimization process during the denoising phase generates refined agent strategies, thereby enhancing the quality and diversity of the generated results. The discriminator perceives the distribution and strategies of agents in MFGs by extracting the physical information exchange from agent interactions. By using variational techniques, the typical MFG problem is transformed into a static optimization problem, which is then efficiently approximated using a generative adversarial framework through adversarial training. IPIDAN, with its diffusion generation model architecture, provides the network with greater tunability and significantly enhances its ability to model randomness in high-dimensional strategy spaces. Furthermore, by establishing a connection between the diffusion process and the agents’ motion dynamics, the network achieves improved interpretability and robustness. Numerical experiments and comparisons with experimental results validate the effectiveness of the novel agent strategy generator based on diffusion models, particularly demonstrating its superior performance through quadrotor obstacle avoidance experiments conducted in various complex scenarios.
{"title":"An online interactive physics-informed diffusion-adversarial network for solving mean field games","authors":"Longqiang Xu , Weishi Yin , Pinchao Meng , Zhengxuan Shen , Hongyu Liu","doi":"10.1016/j.jcp.2026.114700","DOIUrl":"10.1016/j.jcp.2026.114700","url":null,"abstract":"<div><div>High-dimensional, complex, and dynamic environments pose significant challenges in solving mean field games (MFGs). To address these challenges, we propose an online interactive physics-informed diffusion-adversarial network (IPIDAN), which offers enhanced interpretability and flexibility by leveraging a novel agent strategy generator based on diffusion models. This generator utilizes a noise process to improve its ability to escape local optima, while a stepwise optimization process during the denoising phase generates refined agent strategies, thereby enhancing the quality and diversity of the generated results. The discriminator perceives the distribution and strategies of agents in MFGs by extracting the physical information exchange from agent interactions. By using variational techniques, the typical MFG problem is transformed into a static optimization problem, which is then efficiently approximated using a generative adversarial framework through adversarial training. IPIDAN, with its diffusion generation model architecture, provides the network with greater tunability and significantly enhances its ability to model randomness in high-dimensional strategy spaces. Furthermore, by establishing a connection between the diffusion process and the agents’ motion dynamics, the network achieves improved interpretability and robustness. Numerical experiments and comparisons with experimental results validate the effectiveness of the novel agent strategy generator based on diffusion models, particularly demonstrating its superior performance through quadrotor obstacle avoidance experiments conducted in various complex scenarios.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"552 ","pages":"Article 114700"},"PeriodicalIF":3.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025849","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 : 2026-05-01Epub Date: 2026-01-15DOI: 10.1016/j.jcp.2026.114691
Clément Lasuen
In this paper, we propose a finite volume scheme for the grey and multi-group radiative equations. We present it in one space dimension but it can be easily generalized to the two dimensional case using the ideas from Lasuen [1]. This scheme is designed as an upwind scheme where the velocity is modified so as to recover the correct diffusion limit. The resulting scheme is asymptotic preserving, positive under a classical CFL condition and conservative. We also add a reconstruction procedure so as to make it second order consistent. Besides, its computational cost is similar to an explicit scheme.
{"title":"A positive and asymptotic preserving scheme for the multi-group radiative equations","authors":"Clément Lasuen","doi":"10.1016/j.jcp.2026.114691","DOIUrl":"10.1016/j.jcp.2026.114691","url":null,"abstract":"<div><div>In this paper, we propose a finite volume scheme for the grey and multi-group radiative equations. We present it in one space dimension but it can be easily generalized to the two dimensional case using the ideas from Lasuen [1]. This scheme is designed as an upwind scheme where the velocity is modified so as to recover the correct diffusion limit. The resulting scheme is <em>asymptotic preserving</em>, positive under a classical <em>CFL</em> condition and conservative. We also add a reconstruction procedure so as to make it second order consistent. Besides, its computational cost is similar to an explicit scheme.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"552 ","pages":"Article 114691"},"PeriodicalIF":3.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025859","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 : 2026-04-15Epub Date: 2026-01-15DOI: 10.1016/j.jcp.2026.114669
Nuo Lei , Juan Cheng , Chi-Wang Shu
This paper presents a novel two-dimensional intersection-based remapping method for isoparametric curvilinear meshes within the indirect arbitrary Lagrangian-Eulerian (ALE) framework, addressing the challenges of transferring physical quantities between high-order curved-edge meshes. Our method leverages the Weiler-Atherton clipping algorithm to compute intersections between curved-edge quadrangles, enabling robust handling of arbitrary order isoparametric curves. By integrating multi-resolution weighted essentially non-oscillatory (WENO) reconstruction, we achieve high-order accuracy while suppressing numerical oscillations near discontinuities. A positivity-preserving limiter is further applied to ensure physical quantities such as density remain non-negative without compromising conservation or accuracy. Notably, the computational cost of handling higher-order curved meshes, such as cubic or even higher-degree parametric curves, does not significantly increase compared to second-order curved meshes. This ensures that our method remains efficient and scalable, making it applicable to arbitrary two-dimensional high-order isoparametric curvilinear cells without compromising performance. Numerical experiments demonstrate that the proposed method achieves high-order accuracy, strict conservation (with errors approaching machine precision), essential non-oscillation and positivity-preserving. The proposed approach is currently restricted to two-dimensional meshes, and an extension to fully three-dimensional curved polyhedral mesh is beyond the scope of the present work.
{"title":"A high-order, conservative and positivity-preserving intersection-based remapping method between meshes with isoparametric curvilinear cells","authors":"Nuo Lei , Juan Cheng , Chi-Wang Shu","doi":"10.1016/j.jcp.2026.114669","DOIUrl":"10.1016/j.jcp.2026.114669","url":null,"abstract":"<div><div>This paper presents a novel two-dimensional intersection-based remapping method for isoparametric curvilinear meshes within the indirect arbitrary Lagrangian-Eulerian (ALE) framework, addressing the challenges of transferring physical quantities between high-order curved-edge meshes. Our method leverages the Weiler-Atherton clipping algorithm to compute intersections between curved-edge quadrangles, enabling robust handling of arbitrary order isoparametric curves. By integrating multi-resolution weighted essentially non-oscillatory (WENO) reconstruction, we achieve high-order accuracy while suppressing numerical oscillations near discontinuities. A positivity-preserving limiter is further applied to ensure physical quantities such as density remain non-negative without compromising conservation or accuracy. Notably, the computational cost of handling higher-order curved meshes, such as cubic or even higher-degree parametric curves, does not significantly increase compared to second-order curved meshes. This ensures that our method remains efficient and scalable, making it applicable to arbitrary two-dimensional high-order isoparametric curvilinear cells without compromising performance. Numerical experiments demonstrate that the proposed method achieves high-order accuracy, strict conservation (with errors approaching machine precision), essential non-oscillation and positivity-preserving. The proposed approach is currently restricted to two-dimensional meshes, and an extension to fully three-dimensional curved polyhedral mesh is beyond the scope of the present work.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114669"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146035678","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 : 2026-04-15Epub Date: 2026-01-11DOI: 10.1016/j.jcp.2026.114671
Zhixuan Li , Qinglin Tang , Hanquan Wang , Yong Zhang
We perform a dimension reduction for spin-1 dipolar Bose-Einstein condensate (BEC), which is described by the mean-field Gross-Pitaevskii equations (GPEs) coupled with dipole-dipole interaction (DDI), under strongly anisotropic external confining potentials. The original three dimensions (3D) problem is then reduced to quasi-2D and quasi-1D models for pancake- and cigar-shaped trapping potentials respectively. To compute the ground state, we propose an efficient and accurate algorithm by incorporating the kernel truncation method (KTM) for the dipolar potential evaluation into the projected gradient flow (PGF) method. The long-range dipolar potential is computed efficiently and accurately by KTM with optimal zero-padding factor, and the resulted PGF-KTM algorithm achieves spectral accuracy in the ground states. We compute the ground states in different space dimensions, and confirm the convergence and rates of dimension reduction from 3D to quasi-2D and from 3D to quasi-1D. Extensive numerical results of ground states for BECs with ferromagnetic/antiferromagnetic interaction and various external potentials in 1D/2D/3D are reported.
{"title":"On ground states of spin-1 dipolar Bose-Einstein condensate: Dimension reduction and numerical computation","authors":"Zhixuan Li , Qinglin Tang , Hanquan Wang , Yong Zhang","doi":"10.1016/j.jcp.2026.114671","DOIUrl":"10.1016/j.jcp.2026.114671","url":null,"abstract":"<div><div>We perform a dimension reduction for spin-1 dipolar Bose-Einstein condensate (BEC), which is described by the mean-field Gross-Pitaevskii equations (GPEs) coupled with dipole-dipole interaction (DDI), under strongly anisotropic external confining potentials. The original three dimensions (3D) problem is then reduced to quasi-2D and quasi-1D models for pancake- and cigar-shaped trapping potentials respectively. To compute the ground state, we propose an efficient and accurate algorithm by incorporating the kernel truncation method (KTM) for the dipolar potential evaluation into the projected gradient flow (PGF) method. The long-range dipolar potential is computed efficiently and accurately by KTM with optimal zero-padding factor, and the resulted PGF-KTM algorithm achieves spectral accuracy in the ground states. We compute the ground states in different space dimensions, and confirm the convergence and rates of dimension reduction from 3D to quasi-2D and from 3D to quasi-1D. Extensive numerical results of ground states for BECs with ferromagnetic/antiferromagnetic interaction and various external potentials in 1D/2D/3D are reported.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114671"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145975683","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 : 2026-04-15Epub Date: 2026-01-13DOI: 10.1016/j.jcp.2026.114670
Kun Huang , Irene M. Gamba , Chi-Wang Shu
Particle-wave interaction is of fundamental interest in plasma physics, especially in the study of runaway electrons in magnetic confinement fusion. Analogous to the concept of photons and phonons, wave packets in plasma can also be treated as quasi-particles, called plasmons. To model the “mixture” of electrons and plasmons in plasma, a set of “collisional” kinetic equations has been derived, based on weak turbulence limit and the Wentzel-Kramers-Brillouin (WKB) approximation.
There are two main challenges in solving the electron-plasmon kinetic system numerically. Firstly, non-uniform plasma density and magnetic field results in high dimensionality and the presence of multiple time scales. Secondly, a physically reliable numerical solution requires a structure-preserving scheme that enforces the conservation of mass, momentum, and energy.
In this paper, we propose a structure-preserving multiscale solver for particle-wave interaction in non-uniform magnetized plasmas. The solver combines a conservative local discontinuous Galerkin (LDG) scheme for the interaction part with a trajectory averaging method for the plasmon Hamiltonian flow part. Numerical examples for a non-uniform magnetized plasma in an infinitely long symmetric cylinder are presented. It is verified that the LDG scheme rigorously preserves all the conservation laws, and the trajectory averaging method significantly reduces the computational cost.
{"title":"A structure-preserving multiscale solver for particle-wave interaction in non-uniform magnetized plasmas","authors":"Kun Huang , Irene M. Gamba , Chi-Wang Shu","doi":"10.1016/j.jcp.2026.114670","DOIUrl":"10.1016/j.jcp.2026.114670","url":null,"abstract":"<div><div>Particle-wave interaction is of fundamental interest in plasma physics, especially in the study of runaway electrons in magnetic confinement fusion. Analogous to the concept of photons and phonons, wave packets in plasma can also be treated as quasi-particles, called plasmons. To model the “mixture” of electrons and plasmons in plasma, a set of “collisional” kinetic equations has been derived, based on weak turbulence limit and the Wentzel-Kramers-Brillouin (WKB) approximation.</div><div>There are two main challenges in solving the electron-plasmon kinetic system numerically. Firstly, non-uniform plasma density and magnetic field results in high dimensionality and the presence of multiple time scales. Secondly, a physically reliable numerical solution requires a structure-preserving scheme that enforces the conservation of mass, momentum, and energy.</div><div>In this paper, we propose a structure-preserving multiscale solver for particle-wave interaction in non-uniform magnetized plasmas. The solver combines a conservative local discontinuous Galerkin (LDG) scheme for the interaction part with a trajectory averaging method for the plasmon Hamiltonian flow part. Numerical examples for a non-uniform magnetized plasma in an infinitely long symmetric cylinder are presented. It is verified that the LDG scheme rigorously preserves all the conservation laws, and the trajectory averaging method significantly reduces the computational cost.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114670"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976094","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 : 2026-04-15Epub Date: 2026-01-14DOI: 10.1016/j.jcp.2026.114672
Youjun Deng, Lingzheng Kong, Gongsheng Tong
Multi-layered structures have attracted increasing attention due to their potential applications in imaging and cloaking. Such structures, which include GPT-vanishing and SC-vanishing configurations, are known to exhibit significant non-uniqueness in inverse problems under low-frequency or slowly oscillating incident fields. Unique recovery in these settings typically requires high-order incident waves, resulting in severe ill-posedness and instability. Motivated by these insights and the hybridization behavior of plasmon modes across interfaces in multi-layered media, we develop a mathematical framework for plasmon hybridization theory in multi-layered structures of general shape based on perturbation theory. Our analysis yields a spectral expansion of the shape sensitivity functional, providing a foundation for highly sensitive shape reconstruction. Numerical simulations are presented to corroborate the theoretical findings and show new plasmon hybridization phenomena.
{"title":"Theory and computation of plasmon hybridization modes for multi-layered complex media","authors":"Youjun Deng, Lingzheng Kong, Gongsheng Tong","doi":"10.1016/j.jcp.2026.114672","DOIUrl":"10.1016/j.jcp.2026.114672","url":null,"abstract":"<div><div>Multi-layered structures have attracted increasing attention due to their potential applications in imaging and cloaking. Such structures, which include GPT-vanishing and SC-vanishing configurations, are known to exhibit significant non-uniqueness in inverse problems under low-frequency or slowly oscillating incident fields. Unique recovery in these settings typically requires high-order incident waves, resulting in severe ill-posedness and instability. Motivated by these insights and the hybridization behavior of plasmon modes across interfaces in multi-layered media, we develop a mathematical framework for plasmon hybridization theory in multi-layered structures of general shape based on perturbation theory. Our analysis yields a spectral expansion of the shape sensitivity functional, providing a foundation for highly sensitive shape reconstruction. Numerical simulations are presented to corroborate the theoretical findings and show new plasmon hybridization phenomena.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114672"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976095","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 : 2026-04-15Epub Date: 2026-01-14DOI: 10.1016/j.jcp.2026.114692
Benoit Nennig , Martin Ghienne , Emmanuel Perrey-Debain
A numerical algorithm is proposed to deal with parametric eigenvalue problems involving non-Hermitian matrices and is exploited to find location of defective eigenvalues in the parameter space of non-Hermitian parametric eigenvalue problems. These non-Hermitian degeneracies also called exceptional points (EP) have raised considerable attention in the scientific community as these can have a great impact in a variety of physical problems. The method first requires the computation of high order derivatives of a few selected eigenvalues with respect to each parameter involved. The second step is to recombine these quantities to form new coefficients associated with a partial characteristic polynomial (PCP). By construction, these coefficients are regular functions in a large domain of the parameter space which means that the PCP allows one to recover the selected eigenvalues as well as the localization of high order EPs by simply using standard root-finding algorithms.
The versatility of the proposed approach is tested on several applications, from mass-spring systems to guided acoustic waves with absorbing walls and room acoustics. The scalability of the method to large sparse matrices arising from conventional discretization techniques such as the finite element method is demonstrated. The proposed approach can be extended to a large number of applications where EPs play an important role in quantum mechanics, optics and photonics or in mechanical engineering.
{"title":"Fast recovery of parametric eigenvalues depending on several parameters and location of high order exceptional points","authors":"Benoit Nennig , Martin Ghienne , Emmanuel Perrey-Debain","doi":"10.1016/j.jcp.2026.114692","DOIUrl":"10.1016/j.jcp.2026.114692","url":null,"abstract":"<div><div>A numerical algorithm is proposed to deal with parametric eigenvalue problems involving non-Hermitian matrices and is exploited to find location of defective eigenvalues in the parameter space of non-Hermitian parametric eigenvalue problems. These non-Hermitian degeneracies also called exceptional points (EP) have raised considerable attention in the scientific community as these can have a great impact in a variety of physical problems. The method first requires the computation of high order derivatives of a few selected eigenvalues with respect to each parameter involved. The second step is to recombine these quantities to form new coefficients associated with a partial characteristic polynomial (PCP). By construction, these coefficients are regular functions in a large domain of the parameter space which means that the PCP allows one to recover the selected eigenvalues as well as the localization of high order EPs by simply using standard root-finding algorithms.</div><div>The versatility of the proposed approach is tested on several applications, from mass-spring systems to guided acoustic waves with absorbing walls and room acoustics. The scalability of the method to large sparse matrices arising from conventional discretization techniques such as the finite element method is demonstrated. The proposed approach can be extended to a large number of applications where EPs play an important role in quantum mechanics, optics and photonics or in mechanical engineering.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114692"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146035640","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}
We propose a novel dual physics-informed neural network for topology optimization (DPNN-TO), which merges physics-informed neural networks (PINNs) with the traditional SIMP-based topology optimization (TO) algorithm. This approach leverages two interlinked neural networks–a displacement network and an implicit density network-connected through an energy-minimization-based loss function derived from the variational principles of the governing equations. By embedding deep learning within the physical constraints of the problem, DPNN-TO eliminates the need for large-scale data and analytical sensitivity analysis, addressing key limitations of traditional methods. The framework efficiently minimizes compliance through energy-based objectives while enforcing volume fraction constraints, producing high-resolution designs for both 2D and 3D optimization problems. Extensive numerical validation demonstrates that DPNN-TO outperforms conventional methods, solving complex structural optimization scenarios with greater flexibility and computational efficiency, while addressing challenges such as multiple load cases and three-dimensional problems without compromising accuracy.
{"title":"A dual physics-informed neural network for topology optimization","authors":"Ajendra Singh , Souvik Chakraborty , Rajib Chowdhury","doi":"10.1016/j.jcp.2026.114666","DOIUrl":"10.1016/j.jcp.2026.114666","url":null,"abstract":"<div><div>We propose a novel dual physics-informed neural network for topology optimization (DPNN-TO), which merges physics-informed neural networks (PINNs) with the traditional SIMP-based topology optimization (TO) algorithm. This approach leverages two interlinked neural networks–a displacement network and an implicit density network-connected through an energy-minimization-based loss function derived from the variational principles of the governing equations. By embedding deep learning within the physical constraints of the problem, DPNN-TO eliminates the need for large-scale data and analytical sensitivity analysis, addressing key limitations of traditional methods. The framework efficiently minimizes compliance through energy-based objectives while enforcing volume fraction constraints, producing high-resolution designs for both 2D and 3D optimization problems. Extensive numerical validation demonstrates that DPNN-TO outperforms conventional methods, solving complex structural optimization scenarios with greater flexibility and computational efficiency, while addressing challenges such as multiple load cases and three-dimensional problems without compromising accuracy.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114666"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145975679","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号