Journal of Computational Physics最新文献

{"title":"A multiscale hybrid Maxwellian-Monte-Carlo Coulomb collision algorithm for particle simulations","authors":"G. Chen,&nbsp;A.J. Stanier,&nbsp;L. Chacón,&nbsp;S.E. Anderson,&nbsp;B. Philip","doi":"10.1016/j.jcp.2025.113771","DOIUrl":"10.1016/j.jcp.2025.113771","url":null,"abstract":"<div><div>Coulomb collisions in particle simulations for weakly coupled plasmas are modeled by the Landau-Fokker-Planck equation, which is typically solved by Monte-Carlo (MC) methods. One of the main disadvantages of MC is the timestep accuracy constraint <figure><img></figure>Δt ≪ 1 to resolve the collision frequency <figure><img></figure>. The constraint becomes extremely stringent for self-collisions in the presence of high-charge state species and for inter-species collisions with large mass disparities (such as present in Inertial Confinement Fusion hohlraums), rendering long-time-scale simulations prohibitively expensive or impractical. To overcome these difficulties, we explore a hybrid Maxwellian-MC (HMMC) model for particle simulations. Specifically, we devise a collisional algorithm that describes weakly collisional species with particles, and highly collisional species and fluid components with Maxwellians. We employ the Lemons method for particle-Maxwellian collisions, enhanced with a more careful treatment of low-relative-speed particles, and a five-moment model for Maxwellian-Maxwellian collisions. Particle-particle binary collisions are dealt with classic Takizuka-Abe MC, which we extend to accommodate arbitrary particle weights to deal with large density disparities without compromising conservation properties. HMMC is strictly conservative and significantly outperforms standard MC methods in situations with large mass disparities among species or large charge states, demonstrating orders of magnitude improvement in computational efficiency. We will substantiate the accuracy and performance of the proposed method with several examples of varying complexity, including both zero-dimensional relaxation and one-dimensional transport problems, the latter using a hybrid kinetic-ion/fluid-electron model.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"526 ","pages":"Article 113771"},"PeriodicalIF":3.8,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178217","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}

{"title":"Estimating QSVT angles for matrix inversion with large condition numbers","authors":"I. Novikau,&nbsp;I. Joseph","doi":"10.1016/j.jcp.2025.113767","DOIUrl":"10.1016/j.jcp.2025.113767","url":null,"abstract":"<div><div>Quantum Singular Value Transformation (QSVT) is a state-of-the-art, near-optimal quantum algorithm that can be used for matrix inversion. The QSVT circuit is parameterized by a sequence of angles that must be pre-calculated classically, with the number of angles increasing as the matrix condition number grows. Computing QSVT angles for ill-conditioned problems is a numerically challenging task. We propose a numerical technique for estimating QSVT angles for large condition numbers. This technique allows one to avoid expensive numerical computations of QSVT angles and to emulate QSVT circuits for solving ill-conditioned problems.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"525 ","pages":"Article 113767"},"PeriodicalIF":3.8,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143175036","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}

{"title":"p-Multigrid high-order discontinuous Galerkin solver for three-dimensional compressible turbulent flows","authors":"D. Bulgarini,&nbsp;A. Ghidoni,&nbsp;E. Mantecca,&nbsp;G. Noventa","doi":"10.1016/j.jcp.2025.113766","DOIUrl":"10.1016/j.jcp.2025.113766","url":null,"abstract":"<div><div>The study of turbulent flows through steady-state simulations based on the Reynolds-averaged Navier-Stokes equations and turbulence models can be considered the workhorse in different scientific and industrial applications. Among the different numerical approaches, discontinuous Galerkin methods demonstrated to be perfectly suited for high-order accurate numerical solutions on structured or arbitrary unstructured and non-conforming meshes, and high-performance computing with massively parallel processing. However, their computational cost increases rapidly when the solution is discretized with higher-order polynomial approximations. For this reason, many research efforts have been devoted to overcome this drawback. Literature shows many applications of <em>p</em>-multigrid algorithms for the solution of Euler and Navier-Stokes equations, while few works report the solution of the Reynolds-averaged Navier-Stokes equations with <em>p</em>-multigrid algorithms. In fact, different authors highlighted a lack of performance for the stiffness associated with the discretized RANS equations, and for highly stretched meshes, typically used for an accurate resolution of turbulent boundary layers. This work presents the implementation of an improved <em>p</em>-multigrid algorithm based on the nonlinear full approximation scheme in a discontinuous Galerkin solver for the solution of the three-dimensional and compressible Reynolds-Average Navier-Stokes equations. The performance of the algorithm with different smoothers is compared with the implicit (single-order) time integration on many test cases with different flow conditions, domains, and meshes, showing an average reduction of the computing time around 75% with respect to single-order implicit solvers.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"525 ","pages":"Article 113766"},"PeriodicalIF":3.8,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143175034","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}

{"title":"On a two-phase incompressible diffuse interface fluid model with curvature-dependent mobility","authors":"Junxiang Yang ,&nbsp;Junseok Kim","doi":"10.1016/j.jcp.2025.113764","DOIUrl":"10.1016/j.jcp.2025.113764","url":null,"abstract":"<div><div>A mass-conserved diffuse interface two-phase fluid model is developed to capture more fluid details without introducing a large number of meshes. The original Cahn–Hilliard (CH) model satisfies the energy dissipation law by minimizing the total length of the interface. Although the total mass is conserved, the original CH dynamics will lead to the local mass loss of small fluids. The traditional approaches for fixing the local mass loss are to increase the number of mesh grids and to utilize the adaptive mesh refinement technique. However, these approaches either require significant computational time or increase the difficulty in numerical implementation. To reduce the local mass loss with the same computational resources, we propose a curvature-dependent mobility. In the regions with large curvature, this mobility minimizes the shrinking dynamics of the interface in the diffuse interface. In regions with small curvature, this mobility only minimizes the interfacial dynamics on the fluid interface. Since the new mobility is always nonnegative, the proposed model still satisfies the total mass conservation and energy dissipation property. Compared with the original CH model, the present model has better capability for local mass conservation. For two-phase fluid flow problems where the density and viscosity ratios are equal, we develop a linear, second-order accurate, and energy-stable time-marching scheme. The leap-frog-type method is adopted to discretize the proposed CH model in time and the simplified auxiliary variable method with correction is used to discretize the incompressible Navier–Stokes equations in time. We name this new scheme the leap-frog-auxiliary-variable (LFAV) method. For an arbitrary time step, we analytically prove the time-discretized energy stability. In each time step, we only need to separately solve several parabolic equations for the velocities, a Poisson equation for pressure, and a parabolic equation with variable coefficients for the phase-field variable. Several numerical experiments have been performed to validate the accuracy, stability, and capability of interface capturing of the developed model and method. The proposed model is further extended to simulate a dam break in three-dimensional space. The numerical results show that this new model has good potential in capturing large fluid deformation and small splashing liquids.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"525 ","pages":"Article 113764"},"PeriodicalIF":3.8,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143175032","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}

{"title":"Efficient h-adaptive isogeometric discontinuous Galerkin solver for turbulent flows","authors":"D. Bulgarini,&nbsp;A. Ghidoni,&nbsp;G. Noventa,&nbsp;S. Rebay","doi":"10.1016/j.jcp.2025.113763","DOIUrl":"10.1016/j.jcp.2025.113763","url":null,"abstract":"<div><div>The numerical simulation of turbulent flows is still a significant challenge for the complex interplay of scales and nonlinear dynamics that characterize these phenomena. This work presents a method for the accurate simulation of turbulent compressible flows, while preserving the accuracy of the geometric representation provided by the CAD. The proposed method combines high-order CAD-consistent meshes with adaptive refinement, enabling the use of the exact CAD geometry without approximation, as in the isogeometric analysis framework. Key elements include the use of the discontinuous Galerkin method for solving the compressible Reynolds-Averaged Navier-Stokes equations, and the integration of the NURBS representation for enhanced geometric accuracy. Local mesh refinement based on NURBS properties allows for dynamic adaptation that can capture specific flow phenomena. The accuracy of this methodology is assessed through different test cases, demonstrating the robustness and the computational efficiency for different flow regimes, from inviscid to turbulent subsonic and transonic flows.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"526 ","pages":"Article 113763"},"PeriodicalIF":3.8,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178718","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}

{"title":"A front-tracking immersed-boundary framework for simulating Lagrangian melting problems","authors":"Kevin Zhong ,&nbsp;Christopher J. Howland ,&nbsp;Detlef Lohse ,&nbsp;Roberto Verzicco","doi":"10.1016/j.jcp.2025.113762","DOIUrl":"10.1016/j.jcp.2025.113762","url":null,"abstract":"<div><div>In so-called Lagrangian melting problems, a solid immersed in a fluid medium is free to rotate and translate in tandem with its phase-change from solid to liquid. Such configurations may be classified as a fluid-solid interaction (FSI) problem coupled to phase-change. Our present work proposes a numerical method capable of simulating these Lagrangian melting problems and adopts a front-tracking immersed-boundary (IB) method. We use the moving least squares IB framework, a well-established method for simulating a diverse range of FSI problems <span><span>[1]</span></span>, <span><span>[2]</span></span> and extend this framework to accommodate melting by additionally imposing the Stefan condition at the interface. In the spirit of canonical front-tracking methods, the immersed solid is represented by a discrete triangulated mesh which is separate from the Eulerian mesh in which the governing flow equations are solved. A known requirement for these methods is the need for comparable Eulerian and Lagrangian grid spacings to stabilise interpolation and spreading operations between the two grids. For a melting object, this requirement is inevitably violated unless interventional remeshing is introduced. Our work therefore presents a novel dynamic remeshing procedure to overcome this. The remeshing is based on a gradual coarsening of the triangulated Lagrangian mesh and amounts to a negligible computational burden per timestep owing to the incremental and local nature of its operations, making it a scalable approach. Moreover, the coarsening is coupled to a volume-conserving smoothing procedure detailed by Kuprat et al. <span><span>[3]</span></span>, ensuring a zero net volume change in the remeshing step to machine precision. This added feature makes our present method highly specialised to the study of melting problems, where precise measurements of the melting solid's volume is often the primary predictive quantity of interest.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"525 ","pages":"Article 113762"},"PeriodicalIF":3.8,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143175037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Characterization of the forcing and sub-filter scale terms in the volume-filtering immersed boundary method","authors":"Himanshu Dave ,&nbsp;Marcus Herrmann ,&nbsp;Peter Brady ,&nbsp;M. Houssem Kasbaoui","doi":"10.1016/j.jcp.2025.113765","DOIUrl":"10.1016/j.jcp.2025.113765","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We present a characterization of the forcing and sub-filter scale terms produced in the volume-filtering immersed boundary (VF-IB) method by Dave et al. &lt;span&gt;&lt;span&gt;[5]&lt;/span&gt;&lt;/span&gt;. The process of volume-filtering produces bodyforces in the form of surface integrals to describe the boundary conditions at the interface. Furthermore, the approach also produces unclosed terms called &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;sfs&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. The level of contribution from &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;sfs&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; on the numerical solution depends on the filter width &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. In order to understand these terms better we take a 2 dimensional, varying coefficient hyperbolic equation shown by Brady and Livescu &lt;span&gt;&lt;span&gt;[3]&lt;/span&gt;&lt;/span&gt;. This case is chosen for two reasons. First, the case involves 2 distinct regions separated by an interface, making it an ideal case for the VF-IB method. Second, an existing analytical solution allows us to properly investigate the contribution from &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;sfs&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; for varying &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. The filter width controls how well resolved the interface is. The smaller the filter width, the more resolved the interface will be. A thorough numerical analysis of the method is presented, as well as the effect of &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;sfs&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; on the numerical solution. In order to perform a direct comparison, the numerical solution is compared to the filtered analytical solution. Through this we highlight three important points. First, we present a methodical approach to volume filtering a hyperbolic PDE. Second, we show that the VF-IB method exhibits second order convergence with respect to decreasing &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; (i.e. making the interface sharper). Finally, we show that &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;sfs&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; scales with &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt;. Large filter widths would require a modeling approach to sufficiently resolve &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;sfs&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. However for finer filter widths that have a sufficiently sharp interface, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;sfs&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; can be ignored without any significant reduction in the accuracy of solution. We show that through the inclusion of these unclosed terms, the VF-IB method can bridge the gap between fully modeled and fully resolved methods by providing accurate results when the filter width is of the same ord","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"525 ","pages":"Article 113765"},"PeriodicalIF":3.8,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143175035","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}

{"title":"Projected Langevin Monte Carlo algorithms in non-convex and super-linear setting","authors":"Chenxu Pang ,&nbsp;Xiaojie Wang ,&nbsp;Yue Wu","doi":"10.1016/j.jcp.2025.113754","DOIUrl":"10.1016/j.jcp.2025.113754","url":null,"abstract":"&lt;div&gt;&lt;div&gt;It is of significant interest in many applications to sample from a high-dimensional target distribution &lt;em&gt;π&lt;/em&gt; with the density &lt;span&gt;&lt;math&gt;&lt;mi&gt;π&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mtext&gt;d&lt;/mtext&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∝&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mtext&gt;d&lt;/mtext&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, based on the temporal discretization of the Langevin stochastic differential equations (SDEs). In this paper, we propose an explicit projected Langevin Monte Carlo (PLMC) algorithm with non-convex potential &lt;em&gt;U&lt;/em&gt; and super-linear gradient of &lt;em&gt;U&lt;/em&gt; and investigate the non-asymptotic analysis of its sampling error in total variation distance. Equipped with time-independent regularity estimates for the associated Kolmogorov equation, we derive the non-asymptotic bounds on the total variation distance between the target distribution of the Langevin SDEs and the law induced by the PLMC scheme with order &lt;span&gt;&lt;math&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;max&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;ln&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;em&gt;d&lt;/em&gt; is the dimension of the target distribution and &lt;span&gt;&lt;math&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; characterizes the growth of the gradient of &lt;em&gt;U&lt;/em&gt;. In addition, if the gradient of &lt;em&gt;U&lt;/em&gt; is globally Lipschitz continuous, an improved convergence order of &lt;span&gt;&lt;math&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; for the classical Langevin Monte Carlo (LMC) scheme is derived with a refinement of the proof based on Malliavin calculus techniques. To achieve a given precision &lt;em&gt;ϵ&lt;/em&gt;, the smallest number of iterations of the PLMC algorithm is proved to be of order &lt;span&gt;&lt;math&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;max&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;ln&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;ln&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. In particular, the classical Langevin Monte Carlo (LMC) scheme with the non-convex potential &lt;em&gt;U&lt;/em&gt; and the globally Lipschitz gradient of &lt;em&gt;U&lt;/em&gt; can be guaranteed by order &lt;span&gt;&lt;math&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;ln&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. Numerical experim","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"526 ","pages":"Article 113754"},"PeriodicalIF":3.8,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178173","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}

{"title":"Regularized reduced order Lippmann-Schwinger-Lanczos method for inverse scattering problems in the frequency domain","authors":"J. Baker ,&nbsp;E. Cherkaev ,&nbsp;V. Druskin ,&nbsp;S. Moskow ,&nbsp;M. Zaslavsky","doi":"10.1016/j.jcp.2025.113725","DOIUrl":"10.1016/j.jcp.2025.113725","url":null,"abstract":"<div><div>Inverse scattering is broadly applicable in quantum mechanics, remote sensing, geophysical, and medical imaging. This paper presents a robust direct non-iterative reduced order model (ROM) method for solving inverse scattering problems based on an efficient approximation of the resolvent operator, resulting in the regularized Lippmann-Schwinger-Lanczos (LSL) algorithm. We show that the efficiency of the method relies upon the weak dependence of the orthogonalized basis on the unknown potential in the Schrödinger equation by demonstrating that the Lanczos orthogonalization is equivalent to performing Gram-Schmidt on the ROM time snapshots. We then develop the LSL algorithm in the frequency domain with two levels of regularization. The proposed bi-level regularization of the algorithm represents a significant advancement in computational stability, enabling its application to real data sets that are larger than used previously with LSL and inherently contain errors. We show that the same procedure can be extended beyond the Schrödinger formulation to the diffusive Helmholtz equation, e.g., to imaging the conductivity using diffusive electromagnetic fields in conductive media with localized positive conductivity perturbations. Numerical experiments for diffusive Helmholtz and Schrödinger problems show that the proposed bi-level regularization scheme significantly improves the performance of the LSL algorithm, allowing for accurate reconstructions with noisy data and large data sets.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"525 ","pages":"Article 113725"},"PeriodicalIF":3.8,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143175030","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}

{"title":"GSIS-ALE for moving boundary problems in rarefied gas flows","authors":"Jianan Zeng,&nbsp;Yanbing Zhang,&nbsp;Lei Wu","doi":"10.1016/j.jcp.2025.113761","DOIUrl":"10.1016/j.jcp.2025.113761","url":null,"abstract":"<div><div>Multiscale rarefied gas flows with moving boundaries pose significant challenges to the numerical simulation, where the primary difficulties involve robustly managing the mesh movement and ensuring computational efficiency across all flow regimes. Build upon recent advancements of the general synthetic iterative scheme (GSIS), this paper presents an efficient solver to simulate the large displacement of rigid-body in rarefied gas flows. The newly developed solver utilizes a dual time step method to solve the mesoscopic kinetic and macroscopic synthetic equations alternately, in an arbitrary Lagrangian-Eulerian framework. Additionally, the overset mesh is used and the six degree-of-freedom rigid body dynamics equation is integrated to track the motion of solids. Four moving boundary problems encompassing a wide range of flow velocities and gas rarefaction are simulated, including the periodic pitching of airfoil, particle motion in lid-driven cavity flow, two-body separation in supersonic flow, and three-dimensional lunar landing, demonstrating the accuracy and efficiency of the GSIS in handling multi-scale moving boundary problems within an overset framework.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"525 ","pages":"Article 113761"},"PeriodicalIF":3.8,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143175029","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}