Advances in Computational Mathematics最新文献

Sectional Kolmogorov N-widths for parameter-dependent function spaces: a general framework with application to parametrized Friedrichs’ systems 参数相关函数空间的分段Kolmogorov n -宽度：一个应用于参数化friedrich系统的一般框架

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-10-19 DOI: 10.1007/s10444-026-10375-8

Christian Engwer, Mario Ohlberger, Lukas Renelt

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引用次数: 0

Local multilevel preconditioned Jacobi-Davidson method for elliptic eigenvalue problems on adaptive meshes 自适应网格上椭圆特征值问题的局部多水平预条件Jacobi-Davidson方法

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-10-12 DOI: 10.1007/s10444-026-10373-w

Jianing Guo, Qigang Liang, Xuejun Xu

引用次数: 0

Operator inference aware quadratic manifolds with isotropic reduced coordinates for nonintrusive model reduction 非侵入式模型约简中具有各向同性简化坐标的算子推理感知二次流形

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-10-05 DOI: 10.1007/s10444-026-10367-8

Paul Schwerdtner, Prakash Mohan, Julie Bessac, Marc T. Henry de Frahan, Benjamin Peherstorfer

引用次数: 0

Image noise removal via Nash game theory involving non-local and fractional operators 图像噪声去除通过纳什博弈论涉及非局部和分数算子

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-10-01 DOI: 10.1007/s10444-026-10371-y

Requia Addouch, Noureddine Moussaid, Omar Gouasnouane, Anouar Ben-loghfyry

引用次数: 0

HDG methods for the semilinear elliptic optimal control problem: a priori and a posteriori error estimates 半线性椭圆型最优控制问题的HDG方法：先验和后验误差估计

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-10-01 DOI: 10.1007/s10444-026-10370-z

Huangxin Chen, Haitao Leng

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引用次数: 0

Eigenvalue bounds of a block three-by-three nonsymmetric positive semi-definite matrix 块三乘三非对称正半定矩阵的特征值界

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-10-01 DOI: 10.1007/s10444-026-10368-7

Sheng-Zhong Song, Zheng-Da Huang

引用次数: 0

Atlas-based meshless finite differences for elliptic partial differential equations on manifolds represented as point clouds 以点云表示的流形上椭圆型偏微分方程的无网格差分

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-10-01 DOI: 10.1007/s10444-026-10369-6

Yichen Su, Ka Chun Cheung, Leevan Ling

{"title":"Atlas-based meshless finite differences for elliptic partial differential equations on manifolds represented as point clouds","authors":"Yichen Su, Ka Chun Cheung, Leevan Ling","doi":"10.1007/s10444-026-10369-6","DOIUrl":"10.1007/s10444-026-10369-6","url":null,"abstract":"<div><p>We present a systematic investigation of atlas-based radial basis function finite difference (RBFFD) methods for solving elliptic partial differential equations on smooth, compact surfaces represented as point clouds. This approach organizes point cloud data according to coordinate charts and computes differentiation weights collectively within each chart, contrasting with traditional RBFFD methods that construct independent stencils at each point. While the theoretical convergence framework has been established, practical implementation strategies and convergence behavior under different refinement regimes remain unexplored. We address these gaps by formalizing implementation strategies for both intrinsic and extrinsic formulations, including practical algorithms for atlas construction and local parameterization from point cloud data. We conduct convergence studies under two refinement scenarios: simultaneous refinement validates theoretical convergence rates, while the fixed-atlas regime reveals accuracy saturation due to geometric discretization error. We compare different local parameterization approaches and investigate weighted variants to improve method performance. Numerical experiments on various complex surfaces demonstrate that atlas-based RBFFD methods accurately solve elliptic problems without requiring explicit surface parameterizations or mesh connectivity.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-026-10369-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149090373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Trefftz Discontinuous Galerkin methods for scattering by periodic structures 周期结构散射的Trefftz不连续伽辽金方法

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-09-30 DOI: 10.1007/s10444-026-10372-x

Armando Maria Monforte, Andrea Moiola

引用次数: 0

Higher-order approximation rates for ReLU CNNs in Korobov spaces Korobov空间中ReLU cnn的高阶近似率

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-09-24 DOI: 10.1007/s10444-026-10348-x

Yuwen Li, Guozhi Zhang

引用次数: 0

G-invariant representations using coorbits: bi-Lipschitz properties 使用共轨道的g不变表示：bi-Lipschitz性质