SIAM Journal on Numerical Analysis最新文献_第5页

Stability and Convergence of Multi-Product Expansion Splitting Methods with Negative Weights for Semilinear Parabolic Equations 半线性抛物方程负权多积展开分裂方法的稳定性与收敛性

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-06-23 DOI: 10.1137/25m1792475

Xianglong Duan, Chaoyu Quan, Jiang Yang, Zijing Zhu

引用次数: 0

Efficient Numerical Reconstruction of Wave Equation Sources via Droplet-Induced Asymptotics 用液滴诱导渐近法对波动方程源进行有效数值重建

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-06-23 DOI: 10.1137/25m1794899

Shutong Hou, Mourad Sini, Haibing Wang

{"title":"Efficient Numerical Reconstruction of Wave Equation Sources via Droplet-Induced Asymptotics","authors":"Shutong Hou, Mourad Sini, Haibing Wang","doi":"10.1137/25m1794899","DOIUrl":"https://doi.org/10.1137/25m1794899","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 3, Page 1018-1042, June 2026. Abstract. In this paper, we develop and numerically implement a novel approach for solving the inverse source problem of the acoustic wave equation in three dimensions. By injecting a small high-contrast droplet into the medium, we exploit the resulting wave field perturbation measured at a single external point over time. The method enables stable source reconstructions where conventional approaches fail due to ill-posedness, with potential applications in medical imaging and nondestructive testing. Key contributions include: (1) Implementation of a theoretically justified asymptotic expansion, from [], using the eigensystem of the Newtonian operator, with error analysis for the spectral truncation. (2) Novel numerical schemes for solving the time-domain Lippmann–Schwinger equation and reconstructing the source via Riesz basis expansions and mollification-based numerical differentiations. (3) Reconstruction requiring only single-point measurements, overcoming traditional spatial data limitations. (4) 3D numerical experiments demonstrating accurate source recovery under noise (SNR of the order [math]), with error analysis for the droplet size (of the order [math]) and the number of spectral modes [math].","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"35 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148305352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Approximation of Viscous Transport and Conservative Equations with One Sided Lipschitz Velocity Fields 单侧Lipschitz速度场的粘性输运和保守方程的近似

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-06-23 DOI: 10.1137/25m1760350

Fabio Camilli, Adriano Festa, Luciano Marzufero

引用次数: 0

Convergence Analysis of Lie and Strang Splitting for Operator-Valued Differential Riccati Equations 算子值微分Riccati方程Lie和strange分裂的收敛性分析

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-06-23 DOI: 10.1137/25m1754406

Eskil Hansen, Tony Stillfjord, Teodor Åberg

{"title":"Convergence Analysis of Lie and Strang Splitting for Operator-Valued Differential Riccati Equations","authors":"Eskil Hansen, Tony Stillfjord, Teodor Åberg","doi":"10.1137/25m1754406","DOIUrl":"https://doi.org/10.1137/25m1754406","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 3, Page 957-988, June 2026. Abstract. Differential Riccati equations (DREs) are semilinear matrix- or operator-valued differential equations with quadratic nonlinearities. They arise in many different areas, and are particularly important in optimal control of linear quadratic regulators, where they provide the optimal feedback control laws. In the context of control of partial differential equations, these Riccati equations are operator-valued. To approximate their solutions, both spatial and temporal discretizations are needed. While the former have been well analyzed in the literature, there are very few rigorous convergence analyses of time stepping methods applied to DREs, particularly in the infinite-dimensional, operator-valued setting. In view of this, we analyze two numerical time-stepping schemes, the Lie and Strang splitting methods, in such a setting. The analysis relies on the assumption that the uncontrolled system is parabolic and that either the initial condition is sufficiently smooth, or the nonlinearity in the DRE is sufficiently smoothing. These assumptions are mild, in the sense that they are not enough to even guarantee continuity in the operator norm of the exact solution to the DRE. However, they imply certain regularity in a pointwise sense, which can be leveraged to prove convergence in the operator norm with the classical orders. The results are illustrated by four numerical experiments, where convergence with the expected order is correlated with the relevant assumptions being fulfilled. The experiments also demonstrate that matrix-valued DREs which arise as spatial discretizations of operator-valued DREs behave similarly, unless the discretization is coarse.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"31 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148299490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Convergence of ParaOpt for General Runge–Kutta Time Discretizations 一般龙格-库塔时间离散的ParaOpt收敛性

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-06-22 DOI: 10.1137/25m1747099

Felix Kwok, Julien Salomon, Djahou N. Tognon

引用次数: 0

Uniform Semiclassical Observable Error Bound of Trotter–Suzuki Splitting: A Simple Algebraic Proof Trotter-Suzuki分裂的一致半经典可观测误差界：一个简单的代数证明

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-06-19 DOI: 10.1137/25m1777098

Di Fang, Conrad Qu

{"title":"Uniform Semiclassical Observable Error Bound of Trotter–Suzuki Splitting: A Simple Algebraic Proof","authors":"Di Fang, Conrad Qu","doi":"10.1137/25m1777098","DOIUrl":"https://doi.org/10.1137/25m1777098","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 3, Page 876-899, June 2026. Abstract. Efficient simulation of the semiclassical Schrödinger equation has garnered significant attention in the numerical analysis community. While controlling the error in the unitary evolution or the wavefunction typically requires the time step size to shrink as the semiclassical parameter [math] decreases, it has been observed–and proved for first- and second-order Trotterization schemes–that the error in certain classes of observables admits a time step size independent of [math]. In this work, we explicitly characterize this class of observables and present a new, simple algebraic proof of uniform-in-[math] error bounds for arbitrarily high-order Trotterization schemes. Our proof relies solely on the algebraic structure of the underlying operators in both the continuous and discrete settings. Unlike previous analyses, it avoids Egorov-type theorems and bypasses heavy semiclassical machinery. To the best of our knowledge, this is the first proof of uniform-in-[math] observable error bounds for Trotterization in the semiclassical regime that relies only on algebraic structure, without invoking the semiclassical limit.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"14 1","pages":"876-899"},"PeriodicalIF":2.9,"publicationDate":"2026-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148288317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Hybridizable Discontinuous Galerkin Method for the Miscible Displacement Problem under Minimal Regularity 最小正则性下混相位移问题的可杂交不连续Galerkin方法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-06-19 DOI: 10.1137/25m1759239

Keegan L. A. Kirk, Beatrice Riviere

引用次数: 0

A Semi-Lagrangian Scheme on Embedded Manifolds Using Generalized Local Polynomial Reproductions 基于广义局部多项式再现的嵌入式流形半拉格朗日格式

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-06-10 DOI: 10.1137/25m1788476

Thomas Hangelbroek, Christian Rieger, Grady B. Wright

{"title":"A Semi-Lagrangian Scheme on Embedded Manifolds Using Generalized Local Polynomial Reproductions","authors":"Thomas Hangelbroek, Christian Rieger, Grady B. Wright","doi":"10.1137/25m1788476","DOIUrl":"https://doi.org/10.1137/25m1788476","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 3, Page 853-875, June 2026. Abstract. We analyze rates of uniform convergence for a class of high-order semi-Lagrangian schemes for first-order, time-dependent partial differential equations on embedded submanifolds of [math] (including advection equations on surfaces) by extending the error analysis of Falcone and Ferretti [SIAM J. Numer. Anal., 35 (1998), pp. 909–940]. A central requirement in our analysis is a remapping operator that achieves both high approximation orders and strong stability, a combination that is challenging to obtain and of independent interest. For this task, we propose a novel mesh-free remapping operator based on [math] minimizing generalized polynomial reproduction, which uses only point values and requires no additional geometric information from the manifold (such as access to tangent spaces or curvature). Our framework also rigorously addresses the numerical solution of ordinary differential equations on manifolds via projection methods. We include numerical experiments that support the theoretical results and also suggest some new directions for future research.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"161 1","pages":"853-875"},"PeriodicalIF":2.9,"publicationDate":"2026-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148288350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Low-Order Finite Element Complex with Application to a Fourth-Order Elliptic Singular Perturbation Problem 低阶有限元复形在四阶椭圆奇异摄动问题中的应用

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-06-08 DOI: 10.1137/25m1772320

Xuewei Cui, Xuehai Huang

{"title":"Low-Order Finite Element Complex with Application to a Fourth-Order Elliptic Singular Perturbation Problem","authors":"Xuewei Cui, Xuehai Huang","doi":"10.1137/25m1772320","DOIUrl":"https://doi.org/10.1137/25m1772320","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 3, Page 828-852, June 2026. Abstract. A low-order nonconforming finite element discretization of a smooth de Rham complex starting from the [math] space in three dimensions is proposed, involving an [math]-nonconforming finite element space, a new tangentially continuous [math]-nonconforming vector-valued finite element space, the lowest-order Raviart–Thomas space, and piecewise constant functions. While nonconforming for the smooth complex, the discretization conforms to the classical de Rham complex. It is applied to develop a decoupled mixed finite element method for a fourth-order elliptic singular perturbation problem, focusing on the discretization of a generalized singularly perturbed Stokes-type equation. In contrast to Nitsche’s method, which requires additional stabilization to handle boundary layers, the nodal interpolation operator for the lowest-order Nédélec element of the second kind is introduced into the discrete bilinear forms. This modification yields a decoupled mixed method that achieves optimal convergence rates uniformly with respect to the perturbation parameter, even in the presence of strong boundary layers, without requiring any additional stabilization.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"1 1","pages":"828-852"},"PeriodicalIF":2.9,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148288346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Quasi-Optimal Time-Space Discretizations for a Class of Nonlinear Parabolic PDEs 一类非线性抛物型偏微分方程的拟最优时空离散化

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-06-05 DOI: 10.1137/25m1797156

Nina Beranek, Robin Smeets, Rob Stevenson

引用次数: 0