IMA Journal of Numerical Analysis最新文献

Computation of Miura surfaces with gradient Dirichlet boundary conditions 梯度Dirichlet边界条件下Miura曲面的计算

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-05-28 DOI: 10.1093/imanum/draf033

Frédéric Marazzato

引用次数: 0

An Lρ spaces-based mixed virtual element method for the steady ρ-type Brinkman–Forchheimer problem based on the velocity–stress–vorticity formulation 基于速度-应力-涡量公式的稳定ρ型Brinkman-Forchheimer问题的基于Lρ空间的混合虚元方法

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-05-16 DOI: 10.1093/imanum/draf029

Zeinab Gharibi, Mehdi Dehghan

{"title":"An Lρ spaces-based mixed virtual element method for the steady ρ-type Brinkman–Forchheimer problem based on the velocity–stress–vorticity formulation","authors":"Zeinab Gharibi, Mehdi Dehghan","doi":"10.1093/imanum/draf029","DOIUrl":"https://doi.org/10.1093/imanum/draf029","url":null,"abstract":"In this paper we devise and analyze a Banach-spaced mixed virtual element scheme for the steady motion of $rho $-type Brinkman–Forchheimer equation with strongly symmetric stress. Our approach introduces stress and vorticity as additional variables, enabling the elimination of pressure from the original unknowns, which can later be recovered using a postprocessing formula based solely on the stress. Consequently, a mixed variational formulation of the velocity and these new unknowns has been obtained within a Banach space framework. We then propose the $mathbb{H}({mathbf{div}}_varrho ;varOmega )$-conforming virtual element method, where $varrho $ is the conjugate of $rho $, to discretize this formulation and establish the existence and uniqueness of the discrete solution, along with stability bounds, using the Browder–Minty theorem without imposing any assumptions on the data. Furthermore, convergence analysis for all variables in their natural norms is conducted, demonstrating an optimal rate of convergence. Finally, several numerical experiments are presented to illustrate the efficiency and validity of the proposed method.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"14 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144066911","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

Numerical solution to the PML problem of the biharmonic wave scattering in periodic structures 周期结构中双谐波散射PML问题的数值解

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-05-16 DOI: 10.1093/imanum/draf025

Peijun Li, Xiaokai Yuan

引用次数: 0

Robust solutions of nonlinear least squares problems via min-max optimization 非线性最小二乘问题的最小最大优化鲁棒解

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-05-16 DOI: 10.1093/imanum/draf026

Xiaojun Chen, C T Kelley

引用次数: 0

A walk-on-sphere-motivated finite-difference method for the fractional Poisson equation on a bounded d-dimensional domain 有界d维域上分数阶泊松方程的球上行走驱动有限差分方法

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-05-16 DOI: 10.1093/imanum/draf031

Daxin Nie, Jing Sun, Weihua Deng

引用次数: 0

Convergence analysis of three semidiscrete numerical schemes for nonlocal geometric flows including perimeter terms 含周长项的非局部几何流动的三种半离散数值格式的收敛性分析

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-05-01 DOI: 10.1093/imanum/draf015

Wei Jiang, Chunmei Su, Ganghui Zhang

引用次数: 0

A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations 一种求解高维非线性后向随机微分方程的后向微分深度学习算法

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-04-28 DOI: 10.1093/imanum/draf022

Lorenc Kapllani, Long Teng

{"title":"A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations","authors":"Lorenc Kapllani, Long Teng","doi":"10.1093/imanum/draf022","DOIUrl":"https://doi.org/10.1093/imanum/draf022","url":null,"abstract":"In this work we propose a novel backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs), where the deep neural network (DNN) models are trained, not only on the inputs and labels, but also on the differentials of the corresponding labels. This is motivated by the fact that differential deep learning can provide an efficient approximation of the labels and their derivatives with respect to inputs. The BSDEs are reformulated as differential deep learning problems by using Malliavin calculus. The Malliavin derivatives of the BSDE solution themselves satisfy another BSDE, resulting thus in a system of BSDEs. Such formulation requires the estimation of the solution, its gradient and the Hessian matrix, represented by the triple of processes $left (Y, Z, varGamma right ).$ All the integrals within this system are discretized by using the Euler–Maruyama method. Subsequently, DNNs are employed to approximate the triple of these unknown processes. The DNN parameters are backwardly optimized at each time step by minimizing a differential learning type loss function, which is defined as a weighted sum of the dynamics of the discretized BSDE system, with the first term providing the dynamics of the process $Y$ and the other the process $Z$. An error analysis is carried out to show the convergence of the proposed algorithm. Various numerical experiments of up to $50$ dimensions are provided to demonstrate the high efficiency. Both theoretically and numerically, it is demonstrated that our proposed scheme is more efficient in terms of computation time or accuracy compared with other contemporary deep learning-based methodologies.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"39 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143884791","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

An asymptotic preserving scheme for the defocusing Davey–Stewartson II equation in the semiclassical limit 半经典极限下离焦Davey-Stewartson II方程的渐近保持格式

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-04-26 DOI: 10.1093/imanum/draf019

Dandan Wang, Hanquan Wang

引用次数: 0

Spatio-temporal Lie–Poisson discretization for incompressible magnetohydrodynamics on the sphere 球上不可压缩磁流体力学的时空Lie-Poisson离散化

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-04-26 DOI: 10.1093/imanum/draf024

Klas Modin, Michael Roop

引用次数: 0

On the approximation of singular functions by series of noninteger powers 关于用非整数幂级数逼近奇异函数

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2025-04-26 DOI: 10.1093/imanum/draf006

Mohan Zhao, Kirill Serkh

{"title":"On the approximation of singular functions by series of noninteger powers","authors":"Mohan Zhao, Kirill Serkh","doi":"10.1093/imanum/draf006","DOIUrl":"https://doi.org/10.1093/imanum/draf006","url":null,"abstract":"In this paper, we describe an algorithm for approximating functions of the form $f(x)=int _{a}^{b} x^{mu } sigma (mu ) , {text{d}} mu $ over $[0,1]$, where $sigma (mu )$ is some signed Radon measure, or, more generally, of the form $f(x) = {{langle sigma (mu ), x^mu rangle }}$, where $sigma (mu )$ is some distribution supported on $[a,b]$, with $0 &lt;a &lt; b&lt; infty $. One example from this class of functions is $x^{c} (log{x})^{m}=(-1)^{m} {{langle delta ^{(m)}(mu -c), x^mu rangle }}$, where $aleq c leq b$ and $m geq 0$ is an integer. Given the desired accuracy $varepsilon $ and the values of $a$ and $b$, our method determines a priori a collection of noninteger powers $t_{1}$, $t_{2}$, …, $t_{N}$, so that the functions are approximated by series of the form $f(x)approx sum _{j=1}^{N} c_{j} x^{t_{j}}$, and a set of collocation points $x_{1}$, $x_{2}$, …, $x_{N}$, such that the expansion coefficients can be found by collocating the function at these points. We prove that our method has a small uniform approximation error, which is proportional to $varepsilon $ multiplied by some small constants, and that the number of singular powers and collocation points grows as $N=O(log{frac{1}{varepsilon }})$. We demonstrate the performance of our algorithm with several numerical experiments.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"32 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878121","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