Numerische Mathematik最新文献_第3页

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":"22 1","pages":""},"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":"5 1","pages":""},"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

A structure-preserving parametric finite element method for geometric flows with anisotropic surface energy 具有各向异性表面能的几何流动的结构保持参数有限元方法

IF 2.1 2区数学

Numerische Mathematik Pub Date : 2024-03-11 DOI: 10.1007/s00211-024-01398-8

Weizhu Bao, Yifei Li

{"title":"A structure-preserving parametric finite element method for geometric flows with anisotropic surface energy","authors":"Weizhu Bao, Yifei Li","doi":"10.1007/s00211-024-01398-8","DOIUrl":"https://doi.org/10.1007/s00211-024-01398-8","url":null,"abstract":"We propose and analyze a structure-preserving parametric finite element method (SP-PFEM) for the evolution of a closed curve under different geometric flows with arbitrary anisotropic surface energy density (gamma (varvec{n})), where (varvec{n}in mathbb {S}^1) represents the outward unit normal vector. We begin with the anisotropic surface diffusion which possesses two well-known geometric structures—area conservation and energy dissipation—during the evolution of the closed curve. By introducing a novel surface energy matrix (varvec{G}_k(varvec{n})) depending on (gamma (varvec{n})) and the Cahn-Hoffman (varvec{xi })-vector as well as a nonnegative stabilizing function (k(varvec{n})), we obtain a new conservative geometric partial differential equation and its corresponding variational formulation for the anisotropic surface diffusion. Based on the new weak formulation, we propose a full discretization by adopting the parametric finite element method for spatial discretization and a semi-implicit temporal discretization with a proper and clever approximation for the outward normal vector. Under a mild and natural condition on (gamma (varvec{n})), we can prove that the proposed full discretization is structure-preserving, i.e. it preserves the area conservation and energy dissipation at the discretized level, and thus it is unconditionally energy stable. The proposed SP-PFEM is then extended to simulate the evolution of a close curve under other anisotropic geometric flows including anisotropic curvature flow and area-conserved anisotropic curvature flow. Extensive numerical results are reported to demonstrate the efficiency and unconditional energy stability as well as good mesh quality (and thus no need to re-mesh during the evolution) of the proposed SP-PFEM for simulating anisotropic geometric flows.","PeriodicalId":49733,"journal":{"name":"Numerische Mathematik","volume":"33 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140097371","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

Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration 利用准蒙特卡洛积分实现具有熵风险度量的不确定性下抛物线 PDE 受限最优控制

IF 2.1 2区数学

Numerische Mathematik Pub Date : 2024-03-11 DOI: 10.1007/s00211-024-01397-9

Philipp A. Guth, Vesa Kaarnioja, Frances Y. Kuo, Claudia Schillings, Ian H. Sloan

引用次数: 0

Wave scattering problems in exterior domains with the method of fundamental solutions 用基本解法解决外部域中的波散射问题

IF 2.1 2区数学

Numerische Mathematik Pub Date : 2024-02-28 DOI: 10.1007/s00211-024-01395-x

Carlos J. S. Alves, Pedro R. S. Antunes

引用次数: 0

A randomized operator splitting scheme inspired by stochastic optimization methods 受随机优化方法启发的随机算子分割方案