Advances in Computational Mathematics最新文献_第8页

Ellipsoidal density-equalizing map for genus-0 closed surfaces 属0封闭曲面的椭球密度均衡图

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2026-04-17 DOI: 10.1007/s10444-026-10304-9

Zhiyuan Lyu, Lok Ming Lui, Gary P. T. Choi

{"title":"Ellipsoidal density-equalizing map for genus-0 closed surfaces","authors":"Zhiyuan Lyu, Lok Ming Lui, Gary P. T. Choi","doi":"10.1007/s10444-026-10304-9","DOIUrl":"10.1007/s10444-026-10304-9","url":null,"abstract":"<div><p>Surface parameterization is a fundamental task in geometry processing and plays an important role in many science and engineering applications. In recent years, the density-equalizing map, a shape deformation technique based on the physical principle of density diffusion, has been utilized for the parameterization of simply connected and multiply connected open surfaces. More recently, a spherical density-equalizing mapping method has been developed for the parameterization of genus-0 closed surfaces. However, for genus-0 closed surfaces with extreme geometry, using a spherical domain for the parameterization may induce large geometric distortion. In this work, we develop a novel method for computing density-equalizing maps of genus-0 closed surfaces onto an ellipsoidal domain. This allows us to achieve ellipsoidal area-preserving parameterizations and ellipsoidal parameterizations with controlled area change. We further propose an energy minimization approach that combines density-equalizing maps and quasi-conformal maps, which allows us to produce ellipsoidal density-equalizing quasi-conformal maps for achieving a balance between density equalization and quasi-conformality. Using our proposed methods, we can significantly improve the performance of surface remeshing for genus-0 closed surfaces. Experimental results on a large variety of genus-0 closed surfaces are presented to demonstrate the effectiveness of our proposed methods.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-026-10304-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147686675","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

Deep orthogonal decomposition: a continuously adaptive neural network approach to model order reduction of parametrized partial differential equations 深度正交分解：一种连续自适应神经网络方法来模拟参数化偏微分方程的降阶

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2026-04-17 DOI: 10.1007/s10444-026-10295-7

Nicola Rares Franco, Andrea Manzoni, Paolo Zunino, Jan S. Hesthaven

{"title":"Deep orthogonal decomposition: a continuously adaptive neural network approach to model order reduction of parametrized partial differential equations","authors":"Nicola Rares Franco, Andrea Manzoni, Paolo Zunino, Jan S. Hesthaven","doi":"10.1007/s10444-026-10295-7","DOIUrl":"10.1007/s10444-026-10295-7","url":null,"abstract":"<div><p>We develop a novel deep learning technique, termed deep orthogonal decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter-dependent partial differential equations. The approach involves constructing a deep neural network model that approximates the solution manifold using a continuously adaptive local basis. In contrast to global methods, such as proper orthogonal decomposition (POD), this adaptivity allows the DOD to mitigate the Kolmogorov barrier when dealing with space-interacting parameters, making the approach applicable to a wide spectrum of parametric problems. Leveraging this idea, we use the DOD to construct an adaptive alternative to the so-called POD-NN method, here termed DOD-NN. The approach is fully data-driven and non-intrusive but, at the same time, allows for a tight control on error propagation and remains highly interpretable thanks to the rich structure present in the latent space. For this reason, the proposed approach stands out as a valuable alternative to other nonlinear model order reduction techniques, such as those based on deep autoencoders. The methodology is discussed both theoretically and practically, evaluating its performances on problems involving nonlinear PDEs, parametrized geometries, and high-dimensional parameter spaces. Finally, we conclude with a brief discussion on potential applications of the DOD beyond DOD-NN, featuring, for instance, the integration of our approach within intrusive reduced order models such as the reduced basis method.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-026-10295-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147686690","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

Convergence analysis of time-filtered backward differentiation methods up to fourth-order for the molecular beam epitaxial model without slope selection 无坡度选择的分子束外延模型四阶时间滤波后向微分法的收敛性分析

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2026-04-08 DOI: 10.1007/s10444-026-10302-x

Jiexin Wang, Hong-lin Liao

引用次数: 0

On randomized explicit block Kaczmarz method for solving large linear systems 求解大型线性系统的随机显式分块Kaczmarz方法

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2026-04-06 DOI: 10.1007/s10444-026-10301-y

Cun-Qiang Miao, Xue-Yuan Tan

{"title":"On randomized explicit block Kaczmarz method for solving large linear systems","authors":"Cun-Qiang Miao, Xue-Yuan Tan","doi":"10.1007/s10444-026-10301-y","DOIUrl":"10.1007/s10444-026-10301-y","url":null,"abstract":"<div><p>The randomized block Kaczmarz method (Linear Algebra Appl., 441: 199-221, 2014) proposed by Needell and Tropp is efficient for solving large consistent linear systems. However, each iteration of the randomized block Kaczmarz method carries a high cost, as it calls for the computation of a pseudoinverse, or equivalently, the solution of a least-squares problem. In this paper, we propose a randomized explicit block Kaczmarz method that avoids the direct computation of pseudoinverses by exploiting the structure of the block updates. This explicit formulation allows for a more flexible selection of the rows in the working block at each iteration, without relying on a predefined partition of the row indices. Based on a randomized block selection strategy, we further establish the convergence properties of the proposed method. It indicates that the randomized explicit block Kaczmarz method exhibits faster convergence compared to the multi-step standard randomized Kaczmarz method and the randomized block Kaczmarz method. Finally, numerical experiments are carried out to show great superiority and robustness over some state-of-the-art randomized block Kaczmarz methods.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 2","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147619931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Spatially semi-discretely uniformly exponential stability approximation for one-dimensional thermoelastic system 一维热弹性系统的空间半离散均匀指数稳定性近似

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2026-04-06 DOI: 10.1007/s10444-026-10298-4

Jiankang Liu, Bao-Zhu Guo

引用次数: 0

Analyzing the function (zuparrow uparrow !a) for fractional a 分析分数a的函数$$zuparrow uparrow !a$$

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2026-04-01 DOI: 10.1007/s10444-026-10300-z

William Paulsen

{"title":"Analyzing the function (zuparrow uparrow !a) for fractional a","authors":"William Paulsen","doi":"10.1007/s10444-026-10300-z","DOIUrl":"10.1007/s10444-026-10300-z","url":null,"abstract":"<div><p>In this paper, we will extend Knuth’s up arrow notation <span>(b uparrow uparrow n)</span>, which for integer <i>n</i> is <span>(b^{b^{cdot ^{cdot ^{b}}}})</span> with <i>n</i> <i>b</i>’s, to allow <i>n</i> to be a fraction, or even complex. We do this by first considering the unique complex tetration <span>(kappa _b(z))</span>, which satisfies the equations <span>(kappa _b(z+1) = b^{kappa _b(z)})</span> with <span>(kappa _b(0)=1)</span>, and then fix the value of <i>z</i> as we vary the base <i>b</i>. In particular, we will consider the “half-iterate,” which is the case with <span>(z=1/2)</span>, and analytically continue the function into the complex <i>b</i>-plane. To consider “third-iterates” and “fourth-iterates,” we also use 11 other values of <i>z</i>, namely 1/12, 1/6, 1/4, 1/3, 5/12, 7/12, 2/3, 3/4, 5/6, 11/12, and finally <span>(z=i)</span>. We make several discoveries by analyzing these functions. First of all, we discover that there is a branch cut at <span>(b=e^{1/e})</span>, and find that as we approach this point, the functions approach one of the known super-exponentials for the base <span>(e^{1/e})</span>. Also, we find that <span>(b=1)</span> is also a branch point, and discover what happens as the base approaches 1.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 2","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147586399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

GP-CMRH: an inner product free iterative method for block two-by-two nonsymmetric linear systems GP-CMRH：块二乘二非对称线性系统的内积自由迭代方法

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2026-04-01 DOI: 10.1007/s10444-026-10299-3

Kui Du, Jia-Jun Fan

引用次数: 0

Smoothed distance kernels for MMDs and applications in Wasserstein gradient flows MMDs的平滑距离核及其在Wasserstein梯度流中的应用

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2026-03-27 DOI: 10.1007/s10444-026-10289-5

Nicolaj Rux, Michael Quellmalz, Gabriele Steidl

{"title":"Smoothed distance kernels for MMDs and applications in Wasserstein gradient flows","authors":"Nicolaj Rux, Michael Quellmalz, Gabriele Steidl","doi":"10.1007/s10444-026-10289-5","DOIUrl":"10.1007/s10444-026-10289-5","url":null,"abstract":"<div><p>Negative distance kernels <span>(K(x,y) := - Vert x-yVert )</span> were used in the definition of maximum mean discrepancies (MMDs) in statistics and lead to favorable numerical results in various applications. In particular, so-called slicing techniques for handling high-dimensional kernel summations profit from the simple parameter-free structure of the distance kernel. However, due to its non-smoothness in <span>(x=y)</span>, most of the classical theoretical results, e.g., on Wasserstein gradient flows of the corresponding MMD functional, no longer hold true. In this paper, we propose a new kernel which keeps the favorable properties of the negative distance kernel as being conditionally positive definite of order one with a nearly linear increase towards infinity and a simple slicing structure, but is Lipschitz differentiable now. Our construction is based on a simple 1D smoothing procedure of the absolute value function followed by a Riemann–Liouville fractional integral transform. Numerical results demonstrate that the new kernel performs similarly well as the negative distance kernel in gradient descent methods, but now with theoretical guarantees.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 2","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-026-10289-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147536003","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

Constrained rational fitting for (mathcal {D})-stable model order reduction Constrained rational fitting for Ddocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$mathcal {D}$$end{document}-stable model order reduction

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2026-03-24 DOI: 10.1007/s10444-026-10297-5

Tommaso Bradde, Stefano Grivet-Talocia

{"title":"Constrained rational fitting for (mathcal {D})-stable model order reduction","authors":"Tommaso Bradde, Stefano Grivet-Talocia","doi":"10.1007/s10444-026-10297-5","DOIUrl":"10.1007/s10444-026-10297-5","url":null,"abstract":"<div><p>A classical problem in data-driven model order reduction (MOR) of linear time-invariant (LTI) systems is the preservation of structural properties of the underlying large-scale dynamics. When dealing with MOR based on transfer function measurements, one relevant problem is how to force the reduced-order model (ROM) to inherit the asymptotic stability of the reference system, i.e., to enforce the poles of the ROM transfer function to have strictly negative real part. In this work, we tackle the more general problem of placing such poles in arbitrary linear matrix inequality (LMI) regions of the complex plane, which include a rich class of convex sets symmetric with respect to the real axis. LTI systems with poles constrained to this kind of regions are called <span>(mathcal {D})</span>-stable. Combining well-established results from control theory and recent developments in asymptotically stable rational approximation algorithms, we show that the problem can be solved efficiently via standard convex optimization routines. Several numerical testbenches of engineering interest confirm the effectiveness of the proposed methodology in practical applications.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 2","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-026-10297-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147507849","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

Anderson acceleration of a Picard solver for the Oldroyd-B model of viscoelastic fluids 粘弹性流体Oldroyd-B模型Picard解算器的Anderson加速度

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2026-03-09 DOI: 10.1007/s10444-025-10270-8

Duygu Vargun, Igor O. Monteiro, Leo G. Rebholz

引用次数: 0