Advances in Computational Mathematics最新文献_第3页

A unified local projection-based stabilized virtual element method for the coupled Stokes-Darcy problem 斯托克斯-达西耦合问题的基于局部投影的统一稳定虚拟元素法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-10-21 DOI: 10.1007/s10444-024-10199-4

Sudheer Mishra, E. Natarajan

引用次数: 0

A pressure-residual augmented GLS stabilized method for a type of Stokes equations with nonstandard boundary conditions 具有非标准边界条件的斯托克斯方程类型的压力-滞后增强 GLS 稳定方法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-10-14 DOI: 10.1007/s10444-024-10204-w

Huoyuan Duan, Roger C. E. Tan, Duowei Zhu

{"title":"A pressure-residual augmented GLS stabilized method for a type of Stokes equations with nonstandard boundary conditions","authors":"Huoyuan Duan, Roger C. E. Tan, Duowei Zhu","doi":"10.1007/s10444-024-10204-w","DOIUrl":"10.1007/s10444-024-10204-w","url":null,"abstract":"<div>With local pressure-residual stabilizations as an augmentation to the classical Galerkin/least-squares (GLS) stabilized method, a new locally evaluated residual-based stabilized finite element method is proposed for a type of Stokes equations from the incompressible flows. We focus on the study of a type of nonstandard boundary conditions involving the mixed tangential velocity and pressure Dirichlet boundary conditions. Unexpectedly, in sharp contrast to the standard no-slip velocity Dirichlet boundary condition, neither the discrete LBB inf-sup stable elements nor the stabilized methods such as the classical GLS method could certainly ensure a convergent finite element solution, because the velocity solution could be very weak with its gradient not being square integrable. The main purpose of this paper is to study the error estimates of the new stabilized method for approximating the very weak velocity solution; with the local pressure-residual stabilizations, we can manage to prove the error estimates with a reasonable convergence order. Numerical results are provided to illustrate the performance and the theoretical results of the proposed method.</div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142431043","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

A stochastic perturbation analysis of the QR decomposition and its applications QR 分解的随机扰动分析及其应用

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-10-02 DOI: 10.1007/s10444-024-10198-5

Tianru Wang, Yimin Wei

引用次数: 0

An electrical engineering perspective on naturality in computational physics 从电气工程角度看计算物理学的自然性

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-10-01 DOI: 10.1007/s10444-024-10197-6

P. Robert Kotiuga, Valtteri Lahtinen

引用次数: 0

Maximal volume matrix cross approximation for image compression and least squares solution 用于图像压缩和最小二乘法求解的最大体积矩阵交叉近似法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-09-16 DOI: 10.1007/s10444-024-10196-7

Kenneth Allen, Ming-Jun Lai, Zhaiming Shen

引用次数: 0

Multilevel approximation of Gaussian random fields: Covariance compression, estimation, and spatial prediction 高斯随机场的多级近似：协方差压缩、估计和空间预测

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-09-14 DOI: 10.1007/s10444-024-10187-8

Helmut Harbrecht, Lukas Herrmann, Kristin Kirchner, Christoph Schwab

{"title":"Multilevel approximation of Gaussian random fields: Covariance compression, estimation, and spatial prediction","authors":"Helmut Harbrecht, Lukas Herrmann, Kristin Kirchner, Christoph Schwab","doi":"10.1007/s10444-024-10187-8","DOIUrl":"10.1007/s10444-024-10187-8","url":null,"abstract":"<div>The distribution of centered Gaussian random fields (GRFs) indexed by compacta such as smooth, bounded Euclidean domains or smooth, compact and orientable manifolds is determined by their covariance operators. We consider centered GRFs given as variational solutions to coloring operator equations driven by spatial white noise, with an elliptic self-adjoint pseudodifferential coloring operator from the Hörmander class. This includes the Matérn class of GRFs as a special case. Using biorthogonal multiresolution analyses on the manifold, we prove that the precision and covariance operators, respectively, may be identified with bi-infinite matrices and finite sections may be diagonally preconditioned rendering the condition number independent of the dimension p of this section. We prove that a tapering strategy by thresholding applied on finite sections of the bi-infinite precision and covariance matrices results in optimally numerically sparse approximations. That is, asymptotically only linearly many nonzero matrix entries are sufficient to approximate the original section of the bi-infinite covariance or precision matrix using this tapering strategy to arbitrary precision. The locations of these nonzero matrix entries can be determined a priori. The tapered covariance or precision matrices may also be optimally diagonally preconditioned. Analysis of the relative size of the entries of the tapered covariance matrices motivates novel, multilevel Monte Carlo (MLMC) oracles for covariance estimation, in sample complexity that scales log-linearly with respect to the number p of parameters. In addition, we propose and analyze novel compressive algorithms for simulating and kriging of GRFs. The complexity (work and memory vs. accuracy) of these three algorithms scales near-optimally in terms of the number of parameters p of the sample-wise approximation of the GRF in Sobolev scales.</div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-024-10187-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142231551","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

Improved a posteriori error bounds for reduced port-Hamiltonian systems 改进的还原端口-哈密尔顿系统后验误差边界

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-09-11 DOI: 10.1007/s10444-024-10195-8

Johannes Rettberg, Dominik Wittwar, Patrick Buchfink, Robin Herkert, Jörg Fehr, Bernard Haasdonk

引用次数: 0

Interpolating refinable functions and (n_s)-step interpolatory subdivision schemes 可细化函数内插和 $$n_s$$ 步内插细分方案

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-09-05 DOI: 10.1007/s10444-024-10192-x

Bin Han

{"title":"Interpolating refinable functions and (n_s)-step interpolatory subdivision schemes","authors":"Bin Han","doi":"10.1007/s10444-024-10192-x","DOIUrl":"10.1007/s10444-024-10192-x","url":null,"abstract":"<div>Standard interpolatory subdivision schemes and their underlying interpolating refinable functions are of interest in CAGD, numerical PDEs, and approximation theory. Generalizing these notions, we introduce and study (n_s)-step interpolatory (textsf{M})-subdivision schemes and their interpolating (textsf{M})-refinable functions with (n_sin mathbb {N}cup {infty }) and a dilation factor (textsf{M}in mathbb {N}backslash {1}). We completely characterize (mathscr {C}^m)-convergence and smoothness of (n_s)-step interpolatory subdivision schemes and their interpolating (textsf{M})-refinable functions in terms of their masks. Inspired by (n_s)-step interpolatory stationary subdivision schemes, we further introduce the notion of r-mask quasi-stationary subdivision schemes, and then we characterize their (mathscr {C}^m)-convergence and smoothness properties using only their masks. Moreover, combining (n_s)-step interpolatory subdivision schemes with r-mask quasi-stationary subdivision schemes, we can obtain (r n_s)-step interpolatory subdivision schemes. Examples and construction procedures of convergent (n_s)-step interpolatory (textsf{M})-subdivision schemes are provided to illustrate our results with dilation factors (textsf{M}=2,3,4). In addition, for the dyadic dilation (textsf{M}=2) and (r=2,3), using r masks with only two-ring stencils, we provide examples of (mathscr {C}^r)-convergent r-step interpolatory r-mask quasi-stationary dyadic subdivision schemes.</div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142138151","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

SVD-based algorithms for tensor wheel decomposition 基于 SVD 的张量轮分解算法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-09-05 DOI: 10.1007/s10444-024-10194-9

Mengyu Wang, Honghua Cui, Hanyu Li

引用次数: 0

Eigenvalue analysis and applications of the Legendre dual-Petrov-Galerkin methods for initial value problems 初值问题的特征值分析和 Legendre 双-Petrov-Galerkin 方法的应用

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-09-02 DOI: 10.1007/s10444-024-10190-z

Desong Kong, Jie Shen, Li-Lian Wang, Shuhuang Xiang

{"title":"Eigenvalue analysis and applications of the Legendre dual-Petrov-Galerkin methods for initial value problems","authors":"Desong Kong, Jie Shen, Li-Lian Wang, Shuhuang Xiang","doi":"10.1007/s10444-024-10190-z","DOIUrl":"10.1007/s10444-024-10190-z","url":null,"abstract":"<div>In this paper, we show that the eigenvalues and eigenvectors of the spectral discretisation matrices resulting from the Legendre dual-Petrov-Galerkin (LDPG) method for the mth-order initial value problem (IVP): (u^{(m)}(t)=sigma u(t),, tin (-1,1)) with constant (sigma not =0) and usual initial conditions at t(=-1,) are associated with the generalised Bessel polynomials (GBPs). In particular, we derive analytical formulae for the eigenvalues and eigenvectors in the cases m(=1,2). As a by-product, we are able to answer some open questions related to the collocation method at Legendre points (extensively studied in the 1980s) for the first-order IVP, by reformulating it into a Petrov-Galerkin formulation. Our results have direct bearing on the CFL conditions of time-stepping schemes with spectral or spectral-element discretisation in space. Moreover, we present two stable algorithms for computing zeros of the GBPs and develop a general space-time method for evolutionary PDEs. We provide ample numerical results to demonstrate the high accuracy and robustness of the space-time methods for some interesting examples of linear and nonlinear wave problems.</div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142123679","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