Results in Applied Mathematics最新文献_第6页

H(div)-conforming finite element tensors with constraints H(div)-conforming 有限元张量与约束条件

IF 1.4

Results in Applied Mathematics Pub Date : 2024-08-01 DOI: 10.1016/j.rinam.2024.100494

Long Chen , Xuehai Huang

{"title":"H(div)-conforming finite element tensors with constraints","authors":"Long Chen , Xuehai Huang","doi":"10.1016/j.rinam.2024.100494","DOIUrl":"10.1016/j.rinam.2024.100494","url":null,"abstract":"<div><p>A unified construction of <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mo>div</mo><mo>)</mo></mrow></mrow></math></span>-conforming finite element tensors, including vector element, symmetric matrix element, traceless matrix element, and, in general, tensors with linear constraints, is developed in this work. It is based on the geometric decomposition of Lagrange elements into bubble functions on each sub-simplex. Each tensor at a sub-simplex is further decomposed into tangential and normal components. The tangential component forms the bubble function space, while the normal component characterizes the trace. Some degrees of freedom can be redistributed to <span><math><mrow><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional faces. The developed finite element spaces are <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mo>div</mo><mo>)</mo></mrow></mrow></math></span>-conforming and satisfy the discrete inf-sup condition. Intrinsic bases of the constraint tensor space are also established.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"23 ","pages":"Article 100494"},"PeriodicalIF":1.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000645/pdfft?md5=8716e43d076745ec3408e0af1d9f2173&pid=1-s2.0-S2590037424000645-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142240774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Regular and exploratory resource extraction models considering sustainability 考虑可持续性的常规和探索性资源开采模式

IF 1.4

Results in Applied Mathematics Pub Date : 2024-08-01 DOI: 10.1016/j.rinam.2024.100484

Hidekazu Yoshioka

{"title":"Regular and exploratory resource extraction models considering sustainability","authors":"Hidekazu Yoshioka","doi":"10.1016/j.rinam.2024.100484","DOIUrl":"10.1016/j.rinam.2024.100484","url":null,"abstract":"<div><p>We formulate an optimal control problem of resource extraction, where a decision maker with sustainability concern dynamically controls the extraction rate. We assume harvesting to increase profit and incur a risk of resource depletion and aim to resolve sustainability concerns. The optimality equation of the control problem is the Hamilton–Jacobi–Bellman (HJB) equation with an unbounded Hamiltonian. A regularization technique to bound the Hamiltonian is proposed to prove the existence of a unique viscosity solution to both the modified and original HJB equations. We also investigate a relaxed control case, an exploratory control counterpart of our mathematical model, with the control variable belonging to a set of probability measures. Convergent, fully implicit finite difference methods to compute the viscosity solutions to the HJB equations are presented as well. These numerical methods exploit the characteristic direction of the Hamiltonians to avoid using any matrix inversions. Finally, a demonstrative application example of the proposed model to a fishery management problem is presented.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"23 ","pages":"Article 100484"},"PeriodicalIF":1.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000542/pdfft?md5=b0edaf2877c28d46961498b04a0a4236&pid=1-s2.0-S2590037424000542-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141950857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Piecewise nonlinear approximation for non-smooth functions 非光滑函数的分段非线性逼近

IF 1.4

Results in Applied Mathematics Pub Date : 2024-08-01 DOI: 10.1016/j.rinam.2024.100491

S. Akansha

{"title":"Piecewise nonlinear approximation for non-smooth functions","authors":"S. Akansha","doi":"10.1016/j.rinam.2024.100491","DOIUrl":"10.1016/j.rinam.2024.100491","url":null,"abstract":"<div><p>Piecewise affine or linear approximation has garnered significant attention as a technique for approximating piecewise-smooth functions. In this study, we propose a novel approach: piecewise non-linear approximation based on rational approximation, aimed at approximating non-smooth functions. We introduce a method termed piecewise Padé Chebyshev (PiPC) tailored for approximating univariate piecewise smooth functions. Our investigation focuses on assessing the effectiveness of PiPC in mitigating the Gibbs phenomenon during the approximation of piecewise smooth functions. Additionally, we provide error estimates and convergence results of PiPC for non-smooth functions. Notably, our technique excels in capturing singularities, if present, within the function with minimal Gibbs oscillations, without necessitating the explicit specification of singularity locations. To the best of our knowledge, prior research has not explored the use of piecewise non-linear approximation for approximating non-smooth functions. Finally, we validate the efficacy of our methods through numerical experiments, employing PiPC to reconstruct a non-trivial non-smooth function, thus demonstrating its capability to significantly alleviate the Gibbs phenomenon.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"23 ","pages":"Article 100491"},"PeriodicalIF":1.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S259003742400061X/pdfft?md5=8c7e63ace109567fe6eee77da6b27b4a&pid=1-s2.0-S259003742400061X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142075754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fixed point theorem for extended nonlinear quasi-contractions on b-metric spaces b-参数空间上扩展非线性准收缩的定点定理

IF 1.4

Results in Applied Mathematics Pub Date : 2024-08-01 DOI: 10.1016/j.rinam.2024.100497

Ivan D. Aranđelović , Sarah Aljohani , Zoran D. Mitrović , Vladimir V. Đokić , Nabil Mlaiki

引用次数: 0

A randomized neural network based Petrov–Galerkin method for approximating the solution of fractional order boundary value problems 基于随机神经网络的 Petrov-Galerkin 方法，用于近似求解分数阶边界值问题

IF 1.4

Results in Applied Mathematics Pub Date : 2024-08-01 DOI: 10.1016/j.rinam.2024.100493

John P. Roop

{"title":"A randomized neural network based Petrov–Galerkin method for approximating the solution of fractional order boundary value problems","authors":"John P. Roop","doi":"10.1016/j.rinam.2024.100493","DOIUrl":"10.1016/j.rinam.2024.100493","url":null,"abstract":"<div><p>This article presents the implementation of a randomized neural network (RNN) approach in approximating the solution of fractional order boundary value problems using a Petrov–Galerkin framework with Lagrange basis test functions. Traditional methods, like Physics Informed Neural Networks (PINNs), use standard deep learning techniques, which suffer from a computational bottleneck. In contrast, RNNs offer an alternative by employing a random structure with random coefficients, only solving for the output layer. We allow for the application of numerical analysis principles by using RNNs as trial functions and piecewise Lagrange polynomials as test functions. The article covers the construction and properties of the RNN basis, the definition and solution of fractional boundary value problems, and the implementation of the RNN Petrov–Galerkin method. We derive the stiffness matrix and solve it using least squares. Error analysis shows that the method meets the requirements of the Lax–Milgram lemma along with a Ceá inequality, ensuring optimal error estimates, depending on the regularity of the exact solution. Computational experiments demonstrate the method’s efficacy, including multiples cases with both regular and irregular solutions. The results highlight the utility of RNN-based Petrov–Galerkin methods in solving fractional differential equations with experimental convergence.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"23 ","pages":"Article 100493"},"PeriodicalIF":1.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000633/pdfft?md5=aeb3e87fe577f0dbe2c437bee7de39b5&pid=1-s2.0-S2590037424000633-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142136517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Sufficient conditions of blowup to a shallow water wave equation 浅水波方程爆炸的充分条件

IF 1.4

Results in Applied Mathematics Pub Date : 2024-08-01 DOI: 10.1016/j.rinam.2024.100487

Changtai Zhou , Jin Hong , Shaoyong Lai

引用次数: 0

L2 error estimates of unsymmetric RBF collocation for second order elliptic boundary value problems 二阶椭圆边界值问题的非对称 RBF 拼合的 L2 误差估计

IF 1.4

Results in Applied Mathematics Pub Date : 2024-08-01 DOI: 10.1016/j.rinam.2024.100495

Zhiyong Liu, Qiuyan Xu

引用次数: 0

Quadratic and cubic Lagrange finite elements for mixed Laplace eigenvalue problems on criss-cross meshes 十字网格上混合拉普拉斯特征值问题的二次和三次拉格朗日有限元

IF 1.4

Results in Applied Mathematics Pub Date : 2024-08-01 DOI: 10.1016/j.rinam.2024.100480

Kaibo Hu , Jiguang Sun , Qian Zhang

{"title":"Quadratic and cubic Lagrange finite elements for mixed Laplace eigenvalue problems on criss-cross meshes","authors":"Kaibo Hu , Jiguang Sun , Qian Zhang","doi":"10.1016/j.rinam.2024.100480","DOIUrl":"10.1016/j.rinam.2024.100480","url":null,"abstract":"<div><p>In Boffi et al. (2000), it was shown that the linear Lagrange element space on criss-cross meshes and its divergence exhibit spurious eigenvalues when applied in the mixed formulation of the Laplace eigenvalue problem, despite satisfying both the inf–sup condition and ellipticity on the discrete kernel. The lack of a Fortin interpolation is responsible for the spurious eigenvalues produced by the linear Lagrange space. In contrast, results in Boffi et al. (2022) confirm that quartic and higher-order Lagrange elements do not yield spurious eigenvalues on general meshes without nearly singular vertices, including criss-cross meshes as a special case. In this paper, we investigate quadratic and cubic Lagrange elements on criss-cross meshes. We prove the convergence of discrete eigenvalues by fitting the Lagrange elements on criss-cross meshes into a complex and constructing a Fortin interpolation. As a by-product, we construct bounded commuting projections for the finite element Stokes complex, which induces isomorphisms between cohomologies of the continuous and discrete complexes. We provide numerical examples to validate the theoretical results.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"23 ","pages":"Article 100480"},"PeriodicalIF":1.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000505/pdfft?md5=2c0021dd60f95baf31623b82ce7aa04b&pid=1-s2.0-S2590037424000505-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141962956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Global well-posedness and asymptotic behaviour for a reaction–diffusion system of competition type 竞争型反应扩散系统的全局良好性和渐近行为

IF 1.4

Results in Applied Mathematics Pub Date : 2024-08-01 DOI: 10.1016/j.rinam.2024.100486

Jeffrey Morgan , Samia Zermani

{"title":"Global well-posedness and asymptotic behaviour for a reaction–diffusion system of competition type","authors":"Jeffrey Morgan , Samia Zermani","doi":"10.1016/j.rinam.2024.100486","DOIUrl":"10.1016/j.rinam.2024.100486","url":null,"abstract":"<div><p>We analyse a reaction–diffusion system describing the growth of microbial species in a model of flocculation type that arises in biology. A generalized model is formulated on a one dimensional bounded domain with feed terms at one end of the interval. Existence of global classical positive solutions is proved under general growth assumptions, with polynomial flocculation and deflocculation rates that guarantee uniform sup norm bounds for all time t obtained by an <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>−</mo></mrow></math></span>energy functional estimate. We also show finite time blow up can occur when the yield coefficients are large enough. Also, using arguments relying on the spectral and fixed theory, we show persistence and existence of nonhomogeneous population steady-states. Finally, we present some numerical simulations to show the combined effects of motility coefficients and the flocculation–deflocculation rates on the coexistence of species.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"23 ","pages":"Article 100486"},"PeriodicalIF":1.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000566/pdfft?md5=5e220aeb5228af0297590ed4e0509892&pid=1-s2.0-S2590037424000566-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141963828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Itô-vector projection filter for exponential families 指数族的伊托向量投影滤波器

IF 1.4

Results in Applied Mathematics Pub Date : 2024-08-01 DOI: 10.1016/j.rinam.2024.100492

Muhammad Fuady Emzir

{"title":"Itô-vector projection filter for exponential families","authors":"Muhammad Fuady Emzir","doi":"10.1016/j.rinam.2024.100492","DOIUrl":"10.1016/j.rinam.2024.100492","url":null,"abstract":"<div><p>In this paper, we study the application of Itô-vector projection <span><span>[1]</span></span> to the optimal filtering problem. The algorithm projects one SDE to another, possibly lower dimensional, SDE by minimizing an Itô–Taylor expansion of the local projection error’s <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norm. We explicitly derive the projection filter equation for a general class of parametric densities, and then specifically apply it to exponential families. We demonstrate that for the case where the measurement drift function is in the span of the natural statistics, the Itô-vector projection filter (IVPF) coincides with the Stratonovich-projection filter (SPF) <span><span>[2]</span></span>. We then compare the performance of the IVPF against the SPF (with both being implemented using the Gaussian bijection proposed in <span><span>[3]</span></span> and the sparse Gauss–Patterson numerical integration) for two-dimensional optimal filtering problem to show the effectiveness of the proposed algorithm. We vary the measurement drift function to four different functions that are not in the span of natural statistics. Based on one hundred Monte Carlo simulations for each measurement drift, we found that their performances are comparable, with the IVPF potentially offering a slightly more robust performance. However, in our current numerical implementation, the SPF consistently outperforms the IVPF in terms of speed.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"23 ","pages":"Article 100492"},"PeriodicalIF":1.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000621/pdfft?md5=23e7e47144412c71556180da0f6cf1cd&pid=1-s2.0-S2590037424000621-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142136516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0