Advances in Computational Mathematics最新文献_第8页

A sparse spectral method for fractional differential equations in one-spatial dimension 单空间维分数微分方程的稀疏谱方法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-10 DOI: 10.1007/s10444-024-10164-1

Ioannis P. A. Papadopoulos, Sheehan Olver

{"title":"A sparse spectral method for fractional differential equations in one-spatial dimension","authors":"Ioannis P. A. Papadopoulos, Sheehan Olver","doi":"10.1007/s10444-024-10164-1","DOIUrl":"10.1007/s10444-024-10164-1","url":null,"abstract":"<div>We develop a sparse spectral method for a class of fractional differential equations, posed on (mathbb {R}), in one dimension. These equations may include sqrt-Laplacian, Hilbert, derivative, and identity terms. The numerical method utilizes a basis consisting of weighted Chebyshev polynomials of the second kind in conjunction with their Hilbert transforms. The former functions are supported on ([-1,1]) whereas the latter have global support. The global approximation space may contain different affine transformations of the basis, mapping ([-1,1]) to other intervals. Remarkably, not only are the induced linear systems sparse, but the operator decouples across the different affine transformations. Hence, the solve reduces to solving K independent sparse linear systems of size (mathcal {O}(n)times mathcal {O}(n)), with (mathcal {O}(n)) nonzero entries, where K is the number of different intervals and n is the highest polynomial degree contained in the sum space. This results in an (mathcal {O}(n)) complexity solve. Applications to fractional heat and wave equations are considered.</div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-024-10164-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141566341","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

Topological phase estimation method for reparameterized periodic functions 重新参数化周期函数的拓扑相位估算方法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-08 DOI: 10.1007/s10444-024-10157-0

Thomas Bonis, Frédéric Chazal, Bertrand Michel, Wojciech Reise

引用次数: 0

An adaptive finite element DtN method for the acoustic-elastic interaction problem 声弹相互作用问题的自适应有限元 DtN 方法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-08 DOI: 10.1007/s10444-024-10160-5

Lei Lin, Junliang Lv, Shuxin Li

引用次数: 0

Estimates for coefficients in Jacobi series for functions with limited regularity by fractional calculus 用分数微积分估算有限正则函数的雅可比数列系数

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-08 DOI: 10.1007/s10444-024-10159-y

Guidong Liu, Wenjie Liu, Beiping Duan

引用次数: 0

An adaptive time-stepping Fourier pseudo-spectral method for the Zakharov-Rubenchik equation 扎哈罗夫-鲁本奇克方程的自适应时间步进傅立叶伪谱方法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-03 DOI: 10.1007/s10444-024-10155-2

Bingquan Ji, Xuanxuan Zhou

{"title":"An adaptive time-stepping Fourier pseudo-spectral method for the Zakharov-Rubenchik equation","authors":"Bingquan Ji, Xuanxuan Zhou","doi":"10.1007/s10444-024-10155-2","DOIUrl":"10.1007/s10444-024-10155-2","url":null,"abstract":"<div>An adaptive time-stepping scheme is developed for the Zakharov-Rubenchik system to resolve the multiple time scales accurately and to improve the computational efficiency during long-time simulations. The Crank-Nicolson formula and the Fourier pseudo-spectral method are respectively utilized for the temporal and spatial approximations. The proposed numerical method is proved to preserve the mass and energy conservative laws in the discrete levels exactly so that the magnetic field, the density of mass, and the fluid speed are stable on a general class of nonuniform time meshes. With the aid of the priori estimates derived from the discrete invariance and the newly proved discrete Gronwall inequality on variable time grids, sharp convergence analysis of the fully discrete scheme is established rigorously. Error estimate shows that the suggested adaptive time-stepping method can attain the second-order accuracy in time and the spectral accuracy in space. Extensive numerical experiments coupled with an adaptive time-stepping algorithm are presented to show the effectiveness of our numerical method in capturing the multiple time scale evolution for various velocity cases during the interactions of solitons.</div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-024-10155-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141495975","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

Further analysis of multilevel Stein variational gradient descent with an application to the Bayesian inference of glacier ice models 多层次斯泰因变分梯度下降法的进一步分析及其在冰川冰模型贝叶斯推断中的应用

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-03 DOI: 10.1007/s10444-024-10153-4

Terrence Alsup, Tucker Hartland, Benjamin Peherstorfer, Noemi Petra

引用次数: 0

On an accurate numerical integration for the triangular and tetrahedral spectral finite elements 论三角形和四面体谱有限元的精确数值积分

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-03 DOI: 10.1007/s10444-024-10173-0

Ziqing Xie, Shangyou Zhang

引用次数: 0

Convergence of projected subgradient method with sparse or low-rank constraints 具有稀疏或低阶约束条件的投影子梯度法的收敛性

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-02 DOI: 10.1007/s10444-024-10163-2

Hang Xu, Song Li, Junhong Lin

引用次数: 0

Extrapolated regularization of nearly singular integrals on surfaces 曲面上近奇异积分的外推正则化

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-01 DOI: 10.1007/s10444-024-10161-4

J. Thomas Beale, Svetlana Tlupova

{"title":"Extrapolated regularization of nearly singular integrals on surfaces","authors":"J. Thomas Beale, Svetlana Tlupova","doi":"10.1007/s10444-024-10161-4","DOIUrl":"10.1007/s10444-024-10161-4","url":null,"abstract":"<div>We present a method for computing nearly singular integrals that occur when single or double layer surface integrals, for harmonic potentials or Stokes flow, are evaluated at points nearby. Such values could be needed in solving an integral equation when one surface is close to another or to obtain values at grid points. We replace the singular kernel with a regularized version having a length parameter (delta ) in order to control discretization error. Analysis near the singularity leads to an expression for the error due to regularization which has terms with unknown coefficients multiplying known quantities. By computing the integral with three choices of (delta ), we can solve for an extrapolated value that has regularization error reduced to (O(delta ^5)), uniformly for target points on or near the surface. In examples with (delta /h) constant and moderate resolution, we observe total error about (O(h^5)) close to the surface. For convergence as (h rightarrow 0), we can choose (delta ) proportional to (h^q) with (q < 1) to ensure the discretization error is dominated by the regularization error. With (q = 4/5), we find errors about (O(h^4)). For harmonic potentials, we extend the approach to a version with (O(delta ^7)) regularization; it typically has smaller errors, but the order of accuracy is less predictable.</div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141489637","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

Stochastic modeling of stationary scalar Gaussian processes in continuous time from autocorrelation data 根据自相关数据建立连续时间内静止标量高斯过程的随机模型

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-06-24 DOI: 10.1007/s10444-024-10150-7

Martin Hanke

{"title":"Stochastic modeling of stationary scalar Gaussian processes in continuous time from autocorrelation data","authors":"Martin Hanke","doi":"10.1007/s10444-024-10150-7","DOIUrl":"10.1007/s10444-024-10150-7","url":null,"abstract":"<div>We consider the problem of constructing a vector-valued linear Markov process in continuous time, such that its first coordinate is in good agreement with given samples of the scalar autocorrelation function of an otherwise unknown stationary Gaussian process. This problem has intimate connections to the computation of a passive reduced model of a deterministic time-invariant linear system from given output data in the time domain. We construct the stochastic model in two steps. First, we employ the AAA algorithm to determine a rational function which interpolates the z-transform of the discrete data on the unit circle and use this function to assign the poles of the transfer function of the reduced model. Second, we choose the associated residues as the minimizers of a linear inequality constrained least squares problem which ensures the positivity of the transfer function’s real part for large frequencies. We apply this method to compute extended Markov models for stochastic processes obtained from generalized Langevin dynamics in statistical physics. Numerical examples demonstrate that the algorithm succeeds in determining passive reduced models and that the associated Markov processes provide an excellent match of the given data.</div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-024-10150-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141444892","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