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Computational Methods in Applied Mathematics最新文献

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A Symmetric Interior Penalty Method for an Elliptic Distributed Optimal Control Problem with Pointwise State Constraints 带点态约束的椭圆型分布最优控制问题的对称内罚方法
IF 1.3 4区 数学
Computational Methods in Applied Mathematics Pub Date : 2023-02-15 DOI: 10.1515/cmam-2022-0148
S. C. Brenner, J. Gedicke, L. Sung
{"title":"A Symmetric Interior Penalty Method for an Elliptic Distributed Optimal Control Problem with Pointwise State Constraints","authors":"S. C. Brenner, J. Gedicke, L. Sung","doi":"10.1515/cmam-2022-0148","DOIUrl":"https://doi.org/10.1515/cmam-2022-0148","url":null,"abstract":"Abstract We construct a symmetric interior penalty method for an elliptic distributed optimal control problem with pointwise state constraints on general polygonal domains. The resulting discrete problems are quadratic programs with simple box constraints that can be solved efficiently by a primal-dual active set algorithm. Both theoretical analysis and corroborating numerical results are presented.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"23 1","pages":"565 - 589"},"PeriodicalIF":1.3,"publicationDate":"2023-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47032516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 2
Fractional Laplacian – Quadrature Rules for Singular Double Integrals in 3D 三维奇异二重积分的分数阶拉普拉斯-正交规则
4区 数学
Computational Methods in Applied Mathematics Pub Date : 2023-02-15 DOI: 10.1515/cmam-2022-0159
Bernd Feist, Mario Bebendorf
{"title":"Fractional Laplacian – Quadrature Rules for Singular Double Integrals in 3D","authors":"Bernd Feist, Mario Bebendorf","doi":"10.1515/cmam-2022-0159","DOIUrl":"https://doi.org/10.1515/cmam-2022-0159","url":null,"abstract":"Abstract In this article, quadrature rules for the efficient computation of the stiffness matrix for the fractional Laplacian in three dimensions are presented. These rules are based on the Duffy transformation, which is a common tool for singularity removal. Here, this transformation is adapted to the needs of the fractional Laplacian in three dimensions. The integrals resulting from this Duffy transformation are regular integrals over less-dimensional domains. We present bounds on the number of Gauss points to guarantee error estimates which are of the same order of magnitude as the finite element error. The methods presented in this article can easily be adapted to other singular double integrals in three dimensions with algebraic singularities.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"159 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135582564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Two-Level Error Estimation for the Integral Fractional Laplacian 积分分数阶拉普拉斯算子的两级误差估计
4区 数学
Computational Methods in Applied Mathematics Pub Date : 2023-02-14 DOI: 10.1515/cmam-2022-0195
Markus Faustmann, Ernst P. Stephan, David Wörgötter
{"title":"Two-Level Error Estimation for the Integral Fractional Laplacian","authors":"Markus Faustmann, Ernst P. Stephan, David Wörgötter","doi":"10.1515/cmam-2022-0195","DOIUrl":"https://doi.org/10.1515/cmam-2022-0195","url":null,"abstract":"Abstract For the singular integral definition of the fractional Laplacian, we consider an adaptive finite element method steered by two-level error indicators. For this algorithm, we show linear convergence in two and three space dimensions as well as convergence of the algorithm with optimal algebraic rates in 2D, when newest vertex bisection is employed for mesh refinement. A key step hereby is an equivalence of the nodal and Scott–Zhang interpolation operators in certain weighted <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>L</m:mi> <m:mn>2</m:mn> </m:msup> </m:math> L^{2} -norms.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135727304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Convergence of the Incremental Projection Method Using Conforming Approximations 保形近似增量投影法的收敛性
IF 1.3 4区 数学
Computational Methods in Applied Mathematics Pub Date : 2023-02-13 DOI: 10.48550/arXiv.2302.06240
R. Eymard, David Maltese
{"title":"Convergence of the Incremental Projection Method Using Conforming Approximations","authors":"R. Eymard, David Maltese","doi":"10.48550/arXiv.2302.06240","DOIUrl":"https://doi.org/10.48550/arXiv.2302.06240","url":null,"abstract":"Abstract We prove the convergence of an incremental projection numerical scheme for the time-dependent incompressible Navier–Stokes equations, without any regularity assumption on the weak solution. The velocity and the pressure are discretized in conforming spaces, whose compatibility is ensured by the existence of an interpolator for regular functions which preserves approximate divergence-free properties. Owing to a priori estimates, we get the existence and uniqueness of the discrete approximation. Compactness properties are then proved, relying on a Lions-like lemma for time translate estimates. It is then possible to show the convergence of the approximate solution to a weak solution of the problem. The construction of the interpolator is detailed in the case of the lowest degree Taylor–Hood finite element.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45629598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Simultaneous Inversion of the Space-Dependent Source Term and the Initial Value in a Time-Fractional Diffusion Equation 时间分数阶扩散方程中空间相关源项与初值的同时反演
IF 1.3 4区 数学
Computational Methods in Applied Mathematics Pub Date : 2023-02-08 DOI: 10.1515/cmam-2022-0058
Shuang Yu, Zewen Wang, Hongqi Yang
{"title":"Simultaneous Inversion of the Space-Dependent Source Term and the Initial Value in a Time-Fractional Diffusion Equation","authors":"Shuang Yu, Zewen Wang, Hongqi Yang","doi":"10.1515/cmam-2022-0058","DOIUrl":"https://doi.org/10.1515/cmam-2022-0058","url":null,"abstract":"Abstract The inverse problem for simultaneously identifying the space-dependent source term and the initial value in a time-fractional diffusion equation is studied in this paper. The simultaneous inversion is formulated into a system of two operator equations based on the Fourier method to the time-fractional diffusion equation. Under some suitable assumptions, the conditional stability of simultaneous inversion solutions is established, and the exponential Tikhonov regularization method is proposed to obtain the good approximations of simultaneous inversion solutions. Then the convergence estimations of inversion solutions are presented for a priori and a posteriori selections of regularization parameters. Finally, numerical experiments are conducted to illustrate effectiveness of the proposed method.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"23 1","pages":"767 - 782"},"PeriodicalIF":1.3,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45910681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A Novel Study Based on Shifted Jacobi Polynomials to Find the Numerical Solutions of Nonlinear Stochastic Differential Equations Driven by Fractional Brownian Motion 基于移位Jacobi多项式求分数阶布朗运动驱动非线性随机微分方程数值解的新研究
IF 1.3 4区 数学
Computational Methods in Applied Mathematics Pub Date : 2023-01-27 DOI: 10.1515/cmam-2022-0187
P. K. Singh, S. Saha Ray
{"title":"A Novel Study Based on Shifted Jacobi Polynomials to Find the Numerical Solutions of Nonlinear Stochastic Differential Equations Driven by Fractional Brownian Motion","authors":"P. K. Singh, S. Saha Ray","doi":"10.1515/cmam-2022-0187","DOIUrl":"https://doi.org/10.1515/cmam-2022-0187","url":null,"abstract":"Abstract The main objective of this article is to represent an efficient numerical approach based on shifted Jacobi polynomials to solve nonlinear stochastic differential equations driven by fractional Brownian motion. In this method, function approximation and operational matrices based on shifted Jacobi polynomials have been studied, which are further used with appropriate collocation points to reduce nonlinear stochastic differential equations driven by fractional Brownian motion into a system of algebraic equations. Newton’s method has been used to solve this nonlinear system of equations, and the desired approximate solution is achieved. Moreover, the error and convergence analysis of the presented method are also established in detail. Additionally, the applicability of the proposed method is demonstrated by solving some numerical examples.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"23 1","pages":"715 - 728"},"PeriodicalIF":1.3,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46681375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 3
Well-Posedness and Convergence Analysis of PML Method for Time-Dependent Acoustic Scattering Problems Over a Locally Rough Surface 局部粗糙表面上时变声散射问题PML方法的适定性和收敛性分析
IF 1.3 4区 数学
Computational Methods in Applied Mathematics Pub Date : 2023-01-17 DOI: 10.48550/arXiv.2301.06686
Hongxia Guo, G. Hu
{"title":"Well-Posedness and Convergence Analysis of PML Method for Time-Dependent Acoustic Scattering Problems Over a Locally Rough Surface","authors":"Hongxia Guo, G. Hu","doi":"10.48550/arXiv.2301.06686","DOIUrl":"https://doi.org/10.48550/arXiv.2301.06686","url":null,"abstract":"Abstract We aim to analyze and calculate time-dependent acoustic wave scattering by a bounded obstacle and a locally perturbed non-selfintersecting curve. The scattering problem is equivalently reformulated as an initial-boundary value problem of the wave equation in a truncated bounded domain through a well-defined transparent boundary condition. Well-posedness and stability of the reduced problem are established. Numerically, we adopt the perfect matched layer (PML) scheme for simulating the propagation of perturbed waves. By designing a special absorbing medium in a semi-circular PML, we show the well-posedness and stability of the truncated initial-boundary value problem. Finally, we prove that the PML solution converges exponentially to the exact solution in the physical domain. Numerical results are reported to verify the exponential convergence with respect to absorbing medium parameters and thickness of the PML.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44600549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A Convergent Entropy-Dissipating BDF2 Finite-Volume Scheme for a Population Cross-Diffusion System 一类群体交叉扩散系统的收敛熵耗散BDF2有限体积格式
IF 1.3 4区 数学
Computational Methods in Applied Mathematics Pub Date : 2023-01-09 DOI: 10.48550/arXiv.2301.03200
A. Jüngel, M. Vetter
{"title":"A Convergent Entropy-Dissipating BDF2 Finite-Volume Scheme for a Population Cross-Diffusion System","authors":"A. Jüngel, M. Vetter","doi":"10.48550/arXiv.2301.03200","DOIUrl":"https://doi.org/10.48550/arXiv.2301.03200","url":null,"abstract":"Abstract A second-order backward differentiation formula (BDF2) finite-volume discretization for a nonlinear cross-diffusion system arising in population dynamics is studied. The numerical scheme preserves the Rao entropy structure and conserves the mass. The existence and uniqueness of discrete solutions and their large-time behavior as well as the convergence of the scheme are proved. The proofs are based on the G-stability of the BDF2 scheme, which provides an inequality for the quadratic Rao entropy and hence suitable a priori estimates. The novelty is the extension of this inequality to the system case. Some numerical experiments in one and two space dimensions underline the theoretical results.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47747958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Fast Barrier Option Pricing by the COS BEM Method in Heston Model (with Matlab Code) Heston模型中COS BEM方法的快速障碍期权定价（含Matlab代码）
IF 1.3 4区 数学
Computational Methods in Applied Mathematics Pub Date : 2023-01-02 DOI: 10.1515/cmam-2022-0088
A. Aimi, C. Guardasoni, L. Ortiz-Gracia, S. Sanfelici
{"title":"Fast Barrier Option Pricing by the COS BEM Method in Heston Model (with Matlab Code)","authors":"A. Aimi, C. Guardasoni, L. Ortiz-Gracia, S. Sanfelici","doi":"10.1515/cmam-2022-0088","DOIUrl":"https://doi.org/10.1515/cmam-2022-0088","url":null,"abstract":"Abstract In this work, the Fourier-cosine series (COS) method has been combined with the Boundary Element Method (BEM) for a fast evaluation of barrier option prices. After a description of its use in the Black and Scholes (BS) model, the focus of the paper is on the application of the proposed methodology to the barrier option evaluation in the Heston model, where its contribution is fundamental to improve computational efficiency and to make BEM appealing among finance practitioners as a valid alternative to Monte Carlo (MC) or other more traditional approaches. An error analysis is provided on the number of terms used in the Fourier-cosine series expansion, where the error bound estimation is based on the characteristic function of the log-asset price process. A Matlab code implementing this technique is attached at the end of the paper.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"23 1","pages":"301 - 331"},"PeriodicalIF":1.3,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44504945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 2
BEM-Based Magnetic Field Reconstruction by Ensemble Kálmán Filtering 基于bem的集成Kálmán滤波磁场重建
IF 1.3 4区 数学
Computational Methods in Applied Mathematics Pub Date : 2022-12-15 DOI: 10.1515/cmam-2022-0121
M. Liebsch, S. Russenschuck, S. Kurz
{"title":"BEM-Based Magnetic Field Reconstruction by Ensemble Kálmán Filtering","authors":"M. Liebsch, S. Russenschuck, S. Kurz","doi":"10.1515/cmam-2022-0121","DOIUrl":"https://doi.org/10.1515/cmam-2022-0121","url":null,"abstract":"Abstract Magnetic fields generated by normal or superconducting electromagnets are used to guide and focus particle beams in storage rings, synchrotron light sources, mass spectrometers, and beamlines for radiotherapy. The accurate determination of the magnetic field by measurement is critical for the prediction of the particle beam trajectory and hence the design of the accelerator complex. In this context, state-of-the-art numerical field computation makes use of boundary-element methods (BEM) to express the magnetic field. This enables the accurate computation of higher-order partial derivatives and local expansions of magnetic potentials used in efficient numerical codes for particle tracking. In this paper, we present an approach to infer the boundary data of an indirect BEM formulation from magnetic field measurements by ensemble Kálmán filtering. In this way, measurement uncertainties can be propagated to the boundary data, magnetic field and potentials, and to the beam related quantities derived from particle tracking. We provide results obtained from real measurement data of a curved dipole magnet using a Hall probe mapper system.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"23 1","pages":"405 - 424"},"PeriodicalIF":1.3,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47308358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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