Numerische Mathematik最新文献_第3页

Compression of boundary integral operators discretized by anisotropic wavelet bases 压缩用各向异性小波基离散的边界积分算子

IF 2.1 2区数学

Numerische Mathematik Pub Date : 2024-05-20 DOI: 10.1007/s00211-024-01403-0

H. Harbrecht, Remo von Rickenbach

引用次数: 0

Multiresolution kernel matrix algebra 多分辨率核矩阵代数

IF 2.1 2区数学

Numerische Mathematik Pub Date : 2024-05-09 DOI: 10.1007/s00211-024-01409-8

H. Harbrecht, M. Multerer, O. Schenk, Ch. Schwab

{"title":"Multiresolution kernel matrix algebra","authors":"H. Harbrecht, M. Multerer, O. Schenk, Ch. Schwab","doi":"10.1007/s00211-024-01409-8","DOIUrl":"https://doi.org/10.1007/s00211-024-01409-8","url":null,"abstract":"We propose a sparse algebra for samplet compressed kernel matrices to enable efficient scattered data analysis. We show that the compression of kernel matrices by means of samplets produces optimally sparse matrices in a certain S-format. The compression can be performed in cost and memory that scale essentially linearly with the number of data points for kernels of finite differentiability. The same holds true for the addition and multiplication of S-formatted matrices. We prove that the inverse of a kernel matrix, given that it exists, is compressible in the S-format as well. The use of selected inversion allows to directly compute the entries in the corresponding sparsity pattern. Moreover, S-formatted matrix operations enable the efficient, approximate computation of more complicated matrix functions such as ({varvec{A}}^alpha ) or (exp ({varvec{A}})) of a matrix ({varvec{A}}). The matrix algebra is justified mathematically by pseudo differential calculus. As an application, we consider Gaussian process learning algorithms for implicit surfaces. Numerical results are presented to illustrate and quantify our findings.","PeriodicalId":49733,"journal":{"name":"Numerische Mathematik","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140931362","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

Interior estimates for the virtual element method 虚拟元素法的内部估计

IF 2.1 2区数学

Numerische Mathematik Pub Date : 2024-05-09 DOI: 10.1007/s00211-024-01408-9

Silvia Bertoluzza, Micol Pennacchio, Daniele Prada

引用次数: 0

Adaptive hybrid high-order method for guaranteed lower eigenvalue bounds 保证特征值下限的自适应混合高阶方法

IF 2.1 2区数学

Numerische Mathematik Pub Date : 2024-05-06 DOI: 10.1007/s00211-024-01407-w

Carsten Carstensen, Benedikt Gräßle, Ngoc Tien Tran

{"title":"Adaptive hybrid high-order method for guaranteed lower eigenvalue bounds","authors":"Carsten Carstensen, Benedikt Gräßle, Ngoc Tien Tran","doi":"10.1007/s00211-024-01407-w","DOIUrl":"https://doi.org/10.1007/s00211-024-01407-w","url":null,"abstract":"The higher-order guaranteed lower eigenvalue bounds of the Laplacian in the recent work by Carstensen et al. (Numer Math 149(2):273–304, 2021) require a parameter (C_{text {st},1}) that is found not robust as the polynomial degree p increases. This is related to the (H^1) stability bound of the (L^{2}) projection onto polynomials of degree at most p and its growth (C_{textrm{st, 1}}propto (p+1)^{1/2}) as (p rightarrow infty ). A similar estimate for the Galerkin projection holds with a p-robust constant (C_{text {st},2}) and (C_{text {st},2} le 2) for right-isosceles triangles. This paper utilizes the new inequality with the constant (C_{text {st},2}) to design a modified hybrid high-order eigensolver that directly computes guaranteed lower eigenvalue bounds under the idealized hypothesis of exact solve of the generalized algebraic eigenvalue problem and a mild explicit condition on the maximal mesh-size in the simplicial mesh. A key advance is a p-robust parameter selection. The analysis of the new method with a different fine-tuned volume stabilization allows for a priori quasi-best approximation and improved (L^{2}) error estimates as well as a stabilization-free reliable and efficient a posteriori error control. The associated adaptive mesh-refining algorithm performs superior in computer benchmarks with striking numerical evidence for optimal higher empirical convergence rates.","PeriodicalId":49733,"journal":{"name":"Numerische Mathematik","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882670","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

Physics-preserving enriched Galerkin method for a fully-coupled thermo-poroelasticity model 针对全耦合热-弹塑性模型的物理保留富集伽勒金方法

IF 2.1 2区数学

Numerische Mathematik Pub Date : 2024-05-03 DOI: 10.1007/s00211-024-01406-x

Son-Young Yi, Sanghyun Lee

引用次数: 0

High-order bounds-satisfying approximation of partial differential equations via finite element variational inequalities 通过有限元变分不等式实现偏微分方程的高阶边界满足逼近

IF 2.1 2区数学

Numerische Mathematik Pub Date : 2024-04-30 DOI: 10.1007/s00211-024-01405-y

Robert C. Kirby, Daniel Shapero

{"title":"High-order bounds-satisfying approximation of partial differential equations via finite element variational inequalities","authors":"Robert C. Kirby, Daniel Shapero","doi":"10.1007/s00211-024-01405-y","DOIUrl":"https://doi.org/10.1007/s00211-024-01405-y","url":null,"abstract":"Solutions to many important partial differential equations satisfy bounds constraints, but approximations computed by finite element or finite difference methods typically fail to respect the same conditions. Chang and Nakshatrala (Comput Methods Appl Mech Eng 320:287–334, 2017) enforce such bounds in finite element methods through the solution of variational inequalities rather than linear variational problems. Here, we provide a theoretical justification for this method, including higher-order discretizations. We prove an abstract best approximation result for the linear variational inequality and estimates showing that bounds-constrained polynomials provide comparable approximation power to standard spaces. For any unconstrained approximation to a function, there exists a constrained approximation which is comparable in the (W^{1,p}) norm. In practice, one cannot efficiently represent and manipulate the entire family of bounds-constrained polynomials, but applying bounds constraints to the coefficients of a polynomial in the Bernstein basis guarantees those constraints on the polynomial. Although our theoretical results do not guaruntee high accuracy for this subset of bounds-constrained polynomials, numerical results indicate optimal orders of accuracy for smooth solutions and sharp resolution of features in convection–diffusion problems, all subject to bounds constraints.","PeriodicalId":49733,"journal":{"name":"Numerische Mathematik","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140838974","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

Trefftz discontinuous Galerkin discretization for the Stokes problem 斯托克斯问题的 Trefftz 非连续伽勒金离散法

IF 2.1 2区数学

Numerische Mathematik Pub Date : 2024-04-10 DOI: 10.1007/s00211-024-01404-z

Philip L. Lederer, Christoph Lehrenfeld, Paul Stocker

引用次数: 0

An iterative method for the solution of Laplace-like equations in high and very high space dimensions 高维和超高维空间拉普拉斯方程的迭代求解方法

IF 2.1 2区数学

Numerische Mathematik Pub Date : 2024-04-01 DOI: 10.1007/s00211-024-01401-2

{"title":"An iterative method for the solution of Laplace-like equations in high and very high space dimensions","authors":"","doi":"10.1007/s00211-024-01401-2","DOIUrl":"https://doi.org/10.1007/s00211-024-01401-2","url":null,"abstract":"<h3>Abstract</h3> This paper deals with the equation (-varDelta u+mu u=f) on high-dimensional spaces ({mathbb {R}}^m) , where the right-hand side (f(x)=F(Tx)) is composed of a separable function F with an integrable Fourier transform on a space of a dimension (n>m) and a linear mapping given by a matrix T of full rank and (mu ge 0) is a constant. For example, the right-hand side can explicitly depend on differences (x_i-x_j) of components of x. Following our publication (Yserentant in Numer Math 146:219–238, 2020), we show that the solution of this equation can be expanded into sums of functions of the same structure and develop in this framework an equally simple and fast iterative method for its computation. The method is based on the observation that in almost all cases and for large problem classes the expression (Vert T^tyVert ^2) deviates on the unit sphere (Vert yVert =1) the less from its mean value the higher the dimension m is, a concentration of measure effect. The higher the dimension m, the faster the iteration converges.","PeriodicalId":49733,"journal":{"name":"Numerische Mathematik","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140593521","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

Locality of the windowed local density of states 加窗局部态密度的位置性

IF 2.1 2区数学

Numerische Mathematik Pub Date : 2024-03-27 DOI: 10.1007/s00211-024-01400-3

Terry A. Loring, Jianfeng Lu, Alexander B. Watson

引用次数: 0

On the number of terms in the COS method for European option pricing 关于欧式期权定价 COS 方法中的条款数

IF 2.1 2区数学

Numerische Mathematik Pub Date : 2024-03-25 DOI: 10.1007/s00211-024-01402-1

Gero Junike

引用次数: 0