Journal of Computational Physics最新文献

{"title":"Data-enabled reduction of the time complexity of iterative solvers","authors":"Yuanwei Bin ,&nbsp;Xiang I.A. Yang ,&nbsp;Samuel J. Grauer ,&nbsp;Robert F. Kunz","doi":"10.1016/j.jcp.2025.113859","DOIUrl":"10.1016/j.jcp.2025.113859","url":null,"abstract":"<div><div>In the field of scientific computing, complex matrices arise from Laplace, Burgers, Kuramoto-Sivashinsky, and Allen-Cahn equations that are not necessarily symmetric positive definite. Computational fluid dynamics, in particular, often deals with pressure Poisson equation. For iterative solvers, time complexity is one of the most critical properties, if not the most critical. Its notation is <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mi>α</mi></mrow></msup><mo>)</mo></math></span> with <em>N</em> denoting the size of the discretized system and <em>α</em> the scaling exponent. This property indicates how an iterative method's performance scales with the size of the discretized system. Due to the large size of systems in today's scientific computing, methods with lower time complexity are almost always preferred over those with higher time complexity, regardless of the prefactor. This emphasis on time complexity reveals a significant gap in the literature: although the integration of data-enabled methodologies in scientific computing has led to the developments of convergence accelerators and the observation of a speedup of O(10) or so, the reported reductions in cost predominantly concern the prefactor rather than the time complexity. This paper aims to explore reduction in time complexity. The accelerator developed in this paper involves projecting the intermediate solution, which is otherwise only used to assess the residual in the baseline iterative method, onto a low-dimensional Hilbert subspace and directly solving the discretized system there. The solver alternates between the baseline iterative method and the accelerator. Our scaling analysis, which is usually not possible for data-based methods, shows a <span><math><mi>O</mi><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></math></span> reduction in the time complexity for <span><math><msubsup><mrow><mi>N</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>d</mi></mrow></msubsup></math></span>-sized problems in <em>d</em>-dimensional space. Here, <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> is the number of grids in each dimension, and the system size is <span><math><mi>N</mi><mo>=</mo><msubsup><mrow><mi>N</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>d</mi></mrow></msubsup></math></span>. Consolidated by tests up to 10⁹ degrees of freedom, the present method is shown to offer increasingly more acceleration as the problem size increases, up to 200 times speedup for systems of size 10⁹. Moreover, we demonstrate that the accelerator remains effective for highly nonlinear equations and unstructured grids, yielding similar speedup as for Poisson equation.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"529 ","pages":"Article 113859"},"PeriodicalIF":3.8,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519002","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 bound- and positivity-preserving path-conservative discontinuous Galerkin method for compressible two-medium flows","authors":"Haiyun Wang ,&nbsp;Hongqiang Zhu ,&nbsp;Zhen Gao","doi":"10.1016/j.jcp.2025.113867","DOIUrl":"10.1016/j.jcp.2025.113867","url":null,"abstract":"<div><div>This work presents a high-order path-conservative Runge-Kutta discontinuous Galerkin method to simulate compressible two-medium flows by solving a <em>γ</em>-based model with the stiffened equation of state. The main contributions are as follows. Firstly, the path-conservative discontinuous Galerkin method is used to solve the <em>γ</em>-based model and is able to preserve uniform velocity and pressure fields around an isolated material interface. Secondly, a conservative-variables-based affine-invariant weighted essentially non-oscillatory limiter is employed to suppress nonlinear instability in the vicinity of discontinuities. Furthermore, an adaptive local Lax-Friedrichs numerical flux is adopted to improve the numerical resolutions. Last but not least, a bound- and positivity-preserving limiting strategy with strict theoretical analysis is developed for the stiffened equation of state to avoid the occurrence of inadmissible solutions while improving the robustness of the simulations. The <em>h</em>-adaptive Cartesian mesh is used for the numerical experiments to verify the validity of proposed method, and the numerical results of various one- and two-dimensional benchmark test cases demonstrate that the proposed method can efficiently and accurately handle complex two-phase flow problems involving pronounced interface deformations and large pressure ratios up to 10⁵.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"529 ","pages":"Article 113867"},"PeriodicalIF":3.8,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474713","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 finite volume mesh-tying method for computing flows in rotor-stator configurations","authors":"Kian Karimian,&nbsp;Fabian Sewerin","doi":"10.1016/j.jcp.2025.113863","DOIUrl":"10.1016/j.jcp.2025.113863","url":null,"abstract":"<div><div>A finite volume mesh-tying method for the accurate, time-implicit calculation of flows in rotor-stator configurations is presented. We specifically reconsider the problem of coupling two moving domains with patched, but possibly non-conforming meshes at the common interface in a mass and momentum conserving manner. Here, the interfacial mass fluxes and tractions are considered as Lagrange multipliers that adjust instantaneously in such a way that the flow field remains continuous across the interface. For simplicity and computational efficiency, both the Lagrange multipliers and the corresponding continuity constraints for the velocity and pressure are collocated at a finite number of points along the mesh-tying interface. Concomitantly, an iterative augmentation scheme is invoked to eliminate the multipliers from the semi-discrete system of equations and shown to converge even for small values of the associated penalty parameter, thus preventing any deterioration in conditioning. If an iterative linear system solver is employed, then the augmentation is tantamount to the execution of additional solver iterations. Furthermore, our mesh-tying formulation maintains the sparsity of the system matrix and can be incorporated into existing block-structured flow solvers with a minimal implementational effort. For cylindrical grids with azimuthally equisized cells and matching axial grid lines, the mesh-tying approach is demonstrated to preserve the accuracy order of the spatial discretization scheme regardless of the degree of mesh disparity and to maintain long-term temporal accuracy. Finally, we employ the mesh-tying method to calculate unsteady flows in two- and three-dimensional baffled stirred tanks.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113863"},"PeriodicalIF":3.8,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686395","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":"A class of high-order physics-preserving schemes for thermodynamically consistent model of incompressible and immiscible two-phase flow in porous media","authors":"Xiaoli Li ,&nbsp;Yujing Yan ,&nbsp;Huangxin Chen","doi":"10.1016/j.jcp.2025.113864","DOIUrl":"10.1016/j.jcp.2025.113864","url":null,"abstract":"<div><div>In this paper, we construct several high-order and physics-preserving numerical schemes for thermodynamically consistent model of incompressible and immiscible two-phase flow in porous media based on the modified generalized scalar auxiliary variable (mGSAV) approach with new relaxation and the Lagrange multiplier (LM) method with the well-known Karush-Kuhn-Tucker (KKT) conditions. We construct high-order implicit-explicit BDF-<em>k</em> schemes with first to fifth orders for the system with homogeneous injection/production rate and boundary condition. Due to the fact that high-order BDF-<em>k</em> schemes with <span><math><mi>k</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn></math></span> are difficult to preserve mass conservation for both phases for the system with inhomogeneous injection/production rate and boundary condition, the first- and second-order schemes are proposed based on the backward Euler and Crank-Nicolson discretizations for the mass conservation constraint equation. The constructed schemes only need to solve one linear system and a nonlinear algebraic equation with negligible computational cost at each time step. We also prove that the proposed schemes are energy stable, mass-conservative and bounds-preserving for each phase without any restrictions of time step size. Finally, various interesting numerical examples are presented to verify the accuracy and efficiency of the proposed schemes.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"529 ","pages":"Article 113864"},"PeriodicalIF":3.8,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143453714","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":"Novel and general discontinuity-removing PINNs for elliptic interface problems","authors":"Haolong Fan ,&nbsp;Zhijun Tan","doi":"10.1016/j.jcp.2025.113861","DOIUrl":"10.1016/j.jcp.2025.113861","url":null,"abstract":"<div><div>This paper proposes a novel and general framework of the discontinuity-removing physics-informed neural networks (DR-PINNs) for addressing elliptic interface problems. In the DR-PINNs, the solution is split into a smooth component and a non-smooth component, each represented by a separate network surrogate that can be trained either independently or together. The decoupling strategy involves training the two components sequentially. The first network handles the non-smooth part and pre-learns partial or full jumps to assist the second network in learning the complementary PDE conditions. Three decoupling strategies of handling interface problems are built by removing some jumps and incorporating cusp-capturing techniques. On the other hand, the decoupled approaches rely heavily on the cusp-enforced level-set function and are less efficient due to the need for two separate training stages. To overcome these limitations, a novel DR-PINN coupled approach is proposed in this work, where both components learn complementary conditions simultaneously in an integrated single network, eliminating the need for cusp-enforced level-set functions. Furthermore, the stability and accuracy of training are enhanced by an innovative architecture of the lightweight feedforward neural network (FNN) and a powerful geodesic acceleration Levenberg-Marquardt (gd-LM) optimizer. Several numerical experiments illustrate the effectiveness and great potential of the proposed method, with accuracy outperforming most deep neural network approaches and achieving the state-of-the-art results.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"529 ","pages":"Article 113861"},"PeriodicalIF":3.8,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143478733","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":"Multicontinuum homogenization in perforated domains","authors":"Wei Xie ,&nbsp;Yalchin Efendiev ,&nbsp;Yunqing Huang ,&nbsp;Wing Tat Leung ,&nbsp;Yin Yang","doi":"10.1016/j.jcp.2025.113845","DOIUrl":"10.1016/j.jcp.2025.113845","url":null,"abstract":"<div><div>In this paper, we develop a general framework for multicontinuum homogenization in perforated domains. The simulations of problems in perforated domains are expensive and, in many applications, coarse-grid macroscopic models are developed. Many previous approaches include homogenization, multiscale finite element methods, and so on. In our paper, we propose multicontinuum homogenization method for problems in perforated domains. We distinguish different spatial regions in perforations based on their sizes. For example, very thin perforations are considered as one continuum, while larger perforations are considered as another continuum. By differentiating perforations in this way, we are able to predict flows in each of them more accurately. Cell problems are formulated for each continuum using appropriate constraints for the solution averages and their gradients. These cell problem solutions are used in a multiscale expansion and in deriving novel macroscopic systems for multicontinuum homogenization. Our proposed approaches are designed for problems without scale separation. We present numerical results for two continuum problems and demonstrate the accuracy of the proposed methods.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"530 ","pages":"Article 113845"},"PeriodicalIF":3.8,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552162","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 fast neural hybrid Newton solver adapted to implicit methods for nonlinear dynamics","authors":"Tianyu Jin ,&nbsp;Georg Maierhofer ,&nbsp;Katharina Schratz ,&nbsp;Yang Xiang","doi":"10.1016/j.jcp.2025.113869","DOIUrl":"10.1016/j.jcp.2025.113869","url":null,"abstract":"<div><div>The use of implicit time-stepping schemes for the numerical approximation of solutions to stiff nonlinear time-evolution equations brings well-known advantages including, typically, better stability behaviour and corresponding support of larger time steps, and better structure preservation properties. However, this comes at the price of having to solve a nonlinear equation at every time step of the numerical scheme. In this work, we propose a novel deep learning based hybrid Newton's method to accelerate this solution of the nonlinear time step system for stiff time-evolution nonlinear equations. We propose a targeted learning strategy which facilitates robust unsupervised learning in an offline phase and provides a highly efficient initialisation for the Newton iteration leading to consistent acceleration of Newton's method. A quantifiable rate of improvement in Newton's method achieved by improved initialisation is provided and we analyse the upper bound of the generalisation error of our unsupervised learning strategy. These theoretical results are supported by extensive numerical results, demonstrating the efficiency of our proposed neural hybrid solver both in one- and two-dimensional cases.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"529 ","pages":"Article 113869"},"PeriodicalIF":3.8,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474714","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":"Wave propagation modeling using machine learning-based finite difference scheme","authors":"Duofa Ji ,&nbsp;Chenxi Li ,&nbsp;Changhai Zhai","doi":"10.1016/j.jcp.2025.113870","DOIUrl":"10.1016/j.jcp.2025.113870","url":null,"abstract":"<div><div>The staggered-grid finite-difference (SGFD) method is essential in wave forward modeling, waveform inversion, and seismic imaging. However, the numerical dispersion that can lead to reduced accuracy in simulations may arise from either coarse spatial discretization or a suboptimal SGFD scheme. Given the high computational cost associated with finer spatial steps, employing the optimal SGFD scheme offers a feasible and effective approach for dispersion suppression. However, the commonly used SGFD schemes are limited by a narrow maximum wavenumber range, reducing their dispersion suppression efficacy. To address this issue, a machine learning-based SGFD scheme is presented in this study. A composite objective function that combines the sum of the absolute error and the maximum absolute error is proposed, aiming to broaden the maximum wavenumber range while minimizing the cumulative error. A physics-consistent neural network is constructed by specifying weights, biases, activation functions, layer connections, and loss function, enabling the back-propagation of the proposed objective function within the machine learning framework to yield globally optimal SGFD coefficients.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"529 ","pages":"Article 113870"},"PeriodicalIF":3.8,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143471641","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":"An improved SPH method for compressible flows with high density ratios","authors":"Wenbo Fan ,&nbsp;Delong Xiao ,&nbsp;Jun Liu","doi":"10.1016/j.jcp.2025.113868","DOIUrl":"10.1016/j.jcp.2025.113868","url":null,"abstract":"<div><div>An improved Smoothed Particle Hydrodynamics (SPH) method is proposed for supersonic compressible flows with high density ratios. Based on the Reproducing Kernel Particle Method (RKPM), the interaction forces are adjusted by incorporating a pressure correction factor that accounts for the sound speed in the momentum and thermal energy equations. The modification enhances the accuracy and stability of the SPH method when calculating supersonic compressible flows with high density ratios while ensuring conservation. Numerical results demonstrate the capability of the improved SPH method to accurately capture shock waves and rarefaction waves in benchmark problems. Furthermore, compared with the RKPM, the improved SPH method exhibits reduced uncertainty at contact discontinuities in one dimensional strong shock problems with high density ratios. The method also mitigates unphysical oscillations in physical quantities and imposes lower requirements on the time step. Additionally, when simulating two dimensional compressible flow problems with high density ratios, it can effectively suppress tensile and compressive instabilities.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"529 ","pages":"Article 113868"},"PeriodicalIF":3.8,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143464539","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":"Local conservation of energy in fully implicit PIC algorithms","authors":"L. Chacón,&nbsp;G. Chen","doi":"10.1016/j.jcp.2025.113862","DOIUrl":"10.1016/j.jcp.2025.113862","url":null,"abstract":"<div><div>We consider the issue of strict, fully discrete <em>local</em> energy conservation for a whole class of fully implicit local-charge- and global-energy-conserving particle-in-cell (PIC) algorithms. Earlier studies demonstrated these algorithms feature strict global energy conservation. However, whether a local energy conservation theorem exists (in which the local energy update is governed by a flux balance equation at every mesh cell) for these schemes is unclear. In this study, we show that a local energy conservation theorem indeed exists. We begin our analysis with the 1D electrostatic PIC model without orbit-averaging, and then generalize our conclusions to account for orbit averaging, multiple dimensions, and electromagnetic models (Darwin). In all cases, a temporally, spatially, and particle-discrete local energy conservation theorem is shown to exist, proving that these formulations (as originally proposed in the literature), in addition to being locally charge conserving and globally energy conserving, are strictly locally energy conserving as well. In contrast to earlier proofs of local conservation in the literature <span><span>[1]</span></span>, which only considered continuum time, our result is valid for the fully implicit time-discrete version of all models considered, including important features such as orbit averaging. We demonstrate the local-energy-conservation property numerically with a paradigmatic numerical example.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"529 ","pages":"Article 113862"},"PeriodicalIF":3.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143452951","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}