Journal of Scientific Computing最新文献

Stochastic Conformal Integrators for Linearly Damped Stochastic Poisson Systems. 线性阻尼随机泊松系统的随机共形积分器。

IF 3.3 2区数学

Journal of Scientific Computing Pub Date : 2026-01-01 Epub Date: 2025-12-02 DOI: 10.1007/s10915-025-03097-4

Charles-Edouard Bréhier, David Cohen, Yoshio Komori

引用次数: 0

Multiharmonic Algorithms for Contrast-Enhanced Ultrasound. 对比增强超声的多谐波算法。

IF 3.3 2区数学

Journal of Scientific Computing Pub Date : 2026-01-01 Epub Date: 2026-03-24 DOI: 10.1007/s10915-026-03247-2

Vanja Nikolić, Teresa Rauscher

{"title":"Multiharmonic Algorithms for Contrast-Enhanced Ultrasound.","authors":"Vanja Nikolić, Teresa Rauscher","doi":"10.1007/s10915-026-03247-2","DOIUrl":"10.1007/s10915-026-03247-2","url":null,"abstract":"Harmonic generation plays a crucial role in contrast-enhanced ultrasound, both for imaging and therapeutic applications. However, accurately capturing these nonlinear effects is computationally demanding when using traditional time-domain approaches. To address this issue, we develop algorithms based on a time discretization that uses a multiharmonic Ansatz applied to a model that couples the Westervelt equation for acoustic pressure with a volume-based approximation of the Rayleigh-Plesset equation for the dynamics of microbubble contrast agents. We first rigorously establish the existence of time-periodic solutions for this Westervelt-ODE system. We then derive a multiharmonic representation of the system under time-periodic excitation and develop iterative algorithms that rely on the successive computation of higher harmonics assuming either real-valued or complex-valued solution fields. In the real-valued setting, we characterize the approximation error in terms of the number of harmonics and a contribution arising from the fixed-point iteration. Finally, we investigate these algorithms numerically and illustrate how the number of harmonics and the presence of microbubbles influence the propagation of acoustic waves.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"107 2","pages":"41"},"PeriodicalIF":3.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13013266/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147522321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Robust Finite Element Method for Linearized Magnetohydrodynamics on General Domains. 一般区域线性化磁流体力学的鲁棒有限元方法。

IF 3.3 2区数学

Journal of Scientific Computing Pub Date : 2026-01-01 Epub Date: 2026-04-11 DOI: 10.1007/s10915-026-03291-y

L Beirão da Veiga, C Lovadina, M Trezzi

引用次数: 0

Inf-sup stable space-time Local Discontinuous Galerkin method for the heat equation. 热方程的稳定时空局部不连续伽辽金方法。

IF 3.3 2区数学

Journal of Scientific Computing Pub Date : 2026-01-01 Epub Date: 2025-12-05 DOI: 10.1007/s10915-025-03121-7

Sergio Gómez, Chiara Perinati, Paul Stocker

引用次数: 0

Inf-Sup Stable Space-Time Discretization of the Wave Equation Based on a First-Order-In-Time Variational Formulation. 基于一阶时变分公式的波动方程的中稳定时空离散化。

IF 3.3 2区数学

Journal of Scientific Computing Pub Date : 2026-01-01 Epub Date: 2026-05-04 DOI: 10.1007/s10915-026-03293-w

Matteo Ferrari, Ilaria Perugia, Enrico Zampa

引用次数: 0

Fast Numerical Solvers for Parameter Identification Problems in Mathematical Biology. 数学生物学参数辨识问题的快速数值求解。

IF 3.3 2区数学

Journal of Scientific Computing Pub Date : 2026-01-01 Epub Date: 2026-03-16 DOI: 10.1007/s10915-025-03170-y

Karolína Benková, John W Pearson, Mariya Ptashnyk

引用次数: 0

Matrix-Free Inexact Preconditioning Techniques for Isogeometric Tensor-Product Discretizations. 等几何张量积离散化的无矩阵不精确预处理技术。

IF 3.3 2区数学

Journal of Scientific Computing Pub Date : 2026-01-01 Epub Date: 2026-04-27 DOI: 10.1007/s10915-026-03253-4

Michał Ł Mika, René R Hiemstra, Dominik Schillinger

{"title":"Matrix-Free Inexact Preconditioning Techniques for Isogeometric Tensor-Product Discretizations.","authors":"Michał Ł Mika, René R Hiemstra, Dominik Schillinger","doi":"10.1007/s10915-026-03253-4","DOIUrl":"https://doi.org/10.1007/s10915-026-03253-4","url":null,"abstract":"We propose a matrix-free inexact preconditioning strategy for elliptic partial differential equations discretized by the isogeometric Galerkin method on tensor-product spline spaces. We base our preconditioner on an approximation of the discrete linear operator by a sum of Kronecker product matrices. The action of its inverse on a vector of coefficients is approximated by an inner preconditioned conjugate gradient solve. The forward problem is solved by the inexact preconditioned conjugate gradient method. The complexity of the Kronecker matrix-vector products in the inner iteration is lower than the complexity of the matrix-vector products in the forward problem, leading to a reduced number of iterations and significant performance gains. We show the robustness, efficiency and effectiveness of our approach in test problems involving the Poisson equation and linear elasticity, and illustrate the performance gain with respect to preconditioning techniques based on fast diagonalization. The proposed method is implemented in our open-source Julia framework for spline based discretization methods.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"107 3","pages":"81"},"PeriodicalIF":3.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13121230/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147787376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations. 自动微分是训练神经网络求解微分方程的关键。

IF 3.3 2区数学

Journal of Scientific Computing Pub Date : 2025-08-01 Epub Date: 2025-06-24 DOI: 10.1007/s10915-025-02965-3

Chuqi Chen, Yahong Yang, Yang Xiang, Wenrui Hao

{"title":"Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations.","authors":"Chuqi Chen, Yahong Yang, Yang Xiang, Wenrui Hao","doi":"10.1007/s10915-025-02965-3","DOIUrl":"10.1007/s10915-025-02965-3","url":null,"abstract":"Neural network-based approaches have recently shown significant promise in solving partial differential equations (PDEs) in science and engineering, especially in scenarios featuring complex domains or incorporation of empirical data. One advantage of the neural network methods for PDEs lies in its automatic differentiation (AD), which necessitates only the sample points themselves, unlike traditional finite difference (FD) approximations that require nearby local points to compute derivatives. In this paper, we quantitatively demonstrate the advantage of AD in training neural networks. The concept of truncated entropy is introduced to characterize the training property. Specifically, through comprehensive experimental and theoretical analyses conducted on random feature models and two-layer neural networks, we discover that the defined truncated entropy serves as a reliable metric for quantifying the residual loss of random feature models and the training speed of neural networks for both AD and FD methods. Our experimental and theoretical analyses demonstrate that, from a training perspective, AD outperforms FD in solving PDEs.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"104 2","pages":""},"PeriodicalIF":3.3,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12407148/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145001825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Homotopy Relaxation Training Algorithms for Infinite-Width Two-Layer ReLU Neural Networks. 无限宽双层ReLU神经网络的同伦松弛训练算法。

IF 2.8 2区数学

Journal of Scientific Computing Pub Date : 2025-02-01 Epub Date: 2025-01-03 DOI: 10.1007/s10915-024-02761-5

Yahong Yang, Qipin Chen, Wenrui Hao

引用次数: 0

Mimetic Metrics for the DGSEM. DGSEM的模拟度量。

IF 3.3 2区数学

Journal of Scientific Computing Pub Date : 2025-01-01 Epub Date: 2025-10-14 DOI: 10.1007/s10915-025-03082-x

Daniel Bach, Andrés Rueda-Ramírez, David A Kopriva, Gregor J Gassner

引用次数: 0