Pub Date : 2024-09-20DOI: 10.1016/j.matcom.2024.09.009
Lei Liu , Xuan-Xuan Zhou , Xi-Yang Xie , Wen-Rong Sun
In this paper, we numerically investigate vector solitons with oscillatory phase backgrounds in the integrable coupled nonlinear Schrödinger equations, which are widely applied to varieties of physical contexts such as the simultaneous propagation of nonlinear optical pulses and the dynamics of two-components Bose–Einstein condensates. We develop the time-splitting Chebyshev–Galerkin method based on a transformation to accurately compute the vector soliton solutions. Compared to the finite difference method, numerical experiments show that the method with spectral accuracy and high efficiency is necessary for simulating the dynamics evolution of vector solitons. Combined with modulation instability conditions, linear stability analysis and direct numerical simulation, we reveal that the bright-dark and dark-dark solitons with various combinations of parameters under perturbations have qualitative differences. Particularly, vector solitons in unstable background with different wave numbers present distinct dynamics evolutions. The results help us to understand soliton dynamics with oscillatory phase backgrounds and the superposition between nonlinear waves.
{"title":"Numerical study of vector solitons with the oscillatory phase backgrounds in the integrable coupled nonlinear Schrödinger equations","authors":"Lei Liu , Xuan-Xuan Zhou , Xi-Yang Xie , Wen-Rong Sun","doi":"10.1016/j.matcom.2024.09.009","DOIUrl":"10.1016/j.matcom.2024.09.009","url":null,"abstract":"<div><div>In this paper, we numerically investigate vector solitons with oscillatory phase backgrounds in the integrable coupled nonlinear Schrödinger equations, which are widely applied to varieties of physical contexts such as the simultaneous propagation of nonlinear optical pulses and the dynamics of two-components Bose–Einstein condensates. We develop the time-splitting Chebyshev–Galerkin method based on a transformation to accurately compute the vector soliton solutions. Compared to the finite difference method, numerical experiments show that the method with spectral accuracy and high efficiency is necessary for simulating the dynamics evolution of vector solitons. Combined with modulation instability conditions, linear stability analysis and direct numerical simulation, we reveal that the bright-dark and dark-dark solitons with various combinations of parameters under perturbations have qualitative differences. Particularly, vector solitons in unstable background with different wave numbers present distinct dynamics evolutions. The results help us to understand soliton dynamics with oscillatory phase backgrounds and the superposition between nonlinear waves.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"228 ","pages":"Pages 466-484"},"PeriodicalIF":4.4,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142328103","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}
Pub Date : 2024-09-19DOI: 10.1016/j.matcom.2024.09.013
Gala Navarro-Martínez, Jaime Martínez-Turégano, Ramon Blasco-Gimenez
Grid forming wind turbines are crucial for achieving a 100% renewable based grid. The mechanical control of the wind turbines is usually designed for maximum power tracking operation. This paper includes the development of a wind turbine pitch controller considering the wider operational range of a grid forming wind turbine. The proposed controller tracks the optimal generation characteristic of the wind turbine when grid connected and is designed to cater for the different power levels when the wind turbine is operated in islanded mode (or grid-connected at partial power). The proposed controller does not require wind speed estimation for its operation and shows better performance than standard pitch controllers during grid-forming operation, particularly, limiting wind turbine speed excursion during block de-loading. Moreover, the proposed controller does not increase the mechanical loads of the key wind turbine elements. The performance of the proposed control is validated in a black start procedure with a full wind farm realistic real-time simulator, including detailed electrical and aeroelastic models of the wind turbine generator, wind farm and connecting HVDC link. Time and frequency domain validation using the real-time model has shown the performance of the proposed controller during black start operation.
{"title":"Control of a 15MW off-shore wind turbine for black-start operation","authors":"Gala Navarro-Martínez, Jaime Martínez-Turégano, Ramon Blasco-Gimenez","doi":"10.1016/j.matcom.2024.09.013","DOIUrl":"10.1016/j.matcom.2024.09.013","url":null,"abstract":"<div><div>Grid forming wind turbines are crucial for achieving a 100% renewable based grid. The mechanical control of the wind turbines is usually designed for maximum power tracking operation. This paper includes the development of a wind turbine pitch controller considering the wider operational range of a grid forming wind turbine. The proposed controller tracks the optimal generation characteristic of the wind turbine when grid connected and is designed to cater for the different power levels when the wind turbine is operated in islanded mode (or grid-connected at partial power). The proposed controller does not require wind speed estimation for its operation and shows better performance than standard pitch controllers during grid-forming operation, particularly, limiting wind turbine speed excursion during block de-loading. Moreover, the proposed controller does not increase the mechanical loads of the key wind turbine elements. The performance of the proposed control is validated in a black start procedure with a full wind farm realistic real-time simulator, including detailed electrical and aeroelastic models of the wind turbine generator, wind farm and connecting HVDC link. Time and frequency domain validation using the real-time model has shown the performance of the proposed controller during black start operation.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"229 ","pages":"Pages 15-31"},"PeriodicalIF":4.4,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142358547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-19DOI: 10.1016/j.matcom.2024.09.006
Emiliano Cristiani , Nadia Loy , Marta Menci , Andrea Tosin
In this paper, we derive a kinetic description of swarming particle dynamics in an interacting multi-agent system featuring emerging leaders and followers. Agents are classically characterized by their position and velocity plus a continuous parameter quantifying their degree of leadership. The microscopic processes ruling the change of velocity and degree of leadership are independent, non-conservative and non-local in the physical space, so as to account for long-range interactions. Out of the kinetic description, we obtain then a macroscopic model under a hydrodynamic limit reminiscent of that used to tackle the hydrodynamics of weakly dissipative granular gases, thus relying in particular on a regime of small non-conservative and short-range interactions. Numerical simulations in one- and two-dimensional domains show that the limiting macroscopic model is consistent with the original particle dynamics and furthermore can reproduce classical emerging patterns typically observed in swarms.
{"title":"Kinetic description and macroscopic limit of swarming dynamics with continuous leader–follower transitions","authors":"Emiliano Cristiani , Nadia Loy , Marta Menci , Andrea Tosin","doi":"10.1016/j.matcom.2024.09.006","DOIUrl":"10.1016/j.matcom.2024.09.006","url":null,"abstract":"<div><div>In this paper, we derive a kinetic description of swarming particle dynamics in an interacting multi-agent system featuring emerging leaders and followers. Agents are classically characterized by their position and velocity plus a continuous parameter quantifying their degree of leadership. The microscopic processes ruling the change of velocity and degree of leadership are independent, non-conservative and non-local in the physical space, so as to account for long-range interactions. Out of the kinetic description, we obtain then a macroscopic model under a hydrodynamic limit reminiscent of that used to tackle the hydrodynamics of weakly dissipative granular gases, thus relying in particular on a regime of small non-conservative and short-range interactions. Numerical simulations in one- and two-dimensional domains show that the limiting macroscopic model is consistent with the original particle dynamics and furthermore can reproduce classical emerging patterns typically observed in swarms.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"228 ","pages":"Pages 362-385"},"PeriodicalIF":4.4,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142323341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-19DOI: 10.1016/j.matcom.2024.09.008
T.A. Midhun, K. Murugesan
This study introduces a novel stochastic SICR (susceptible, infected, cervical cancer and recovered) model to illustrate HPV (Human papillomavirus) infection dynamics and its impact on cervical cancer in the female population of India. We prove the existence of a unique positive global solution that ensures stochastic boundedness and permanence. Moreover, sufficient conditions for HPV extinction are established through the stochastic extinction parameter , indicating that the infection will die out if . Conversely, the persistence of HPV is established by the existence and uniqueness of an ergodic stationary distribution of the solution when the stochastic threshold , using the suitable selection of Lyapunov functions. Furthermore, data on cervical cancer cases in India from 2016 to 2020 is fitted to the model, providing parameter values suitable for the region. The theoretical findings are validated using the Positive-Preserving Truncated Euler–Maruyama method. Additionally, effective control strategies for India are suggested based on model predictions and sensitivity of key parameters.
{"title":"A study of stochastically perturbed epidemic model of HPV infection and cervical cancer in Indian female population","authors":"T.A. Midhun, K. Murugesan","doi":"10.1016/j.matcom.2024.09.008","DOIUrl":"10.1016/j.matcom.2024.09.008","url":null,"abstract":"<div><div>This study introduces a novel stochastic SICR (susceptible, infected, cervical cancer and recovered) model to illustrate HPV (Human papillomavirus) infection dynamics and its impact on cervical cancer in the female population of India. We prove the existence of a unique positive global solution that ensures stochastic boundedness and permanence. Moreover, sufficient conditions for HPV extinction are established through the stochastic extinction parameter <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>e</mi></mrow></msubsup></math></span>, indicating that the infection will die out if <span><math><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>e</mi></mrow></msubsup><mo><</mo><mn>1</mn></mrow></math></span>. Conversely, the persistence of HPV is established by the existence and uniqueness of an ergodic stationary distribution of the solution when the stochastic threshold <span><math><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>s</mi></mrow></msubsup><mo>></mo><mn>1</mn></mrow></math></span>, using the suitable selection of Lyapunov functions. Furthermore, data on cervical cancer cases in India from 2016 to 2020 is fitted to the model, providing parameter values suitable for the region. The theoretical findings are validated using the Positive-Preserving Truncated Euler–Maruyama method. Additionally, effective control strategies for India are suggested based on model predictions and sensitivity of key parameters.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"228 ","pages":"Pages 431-465"},"PeriodicalIF":4.4,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142328102","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}
Pub Date : 2024-09-19DOI: 10.1016/j.matcom.2024.09.012
Fan Zhang , Po-Wei Li , Yan Gu , Chia-Ming Fan
In this paper, the space-time generalized finite difference scheme is applied to solve the nonlinear high-order Korteweg-de Vries equations in multiple dimensions. The proposed numerical scheme combines the space-time generalized finite difference method, the Levenberg-Marquardt algorithm, and a time-marching approach. The space-time generalized finite difference method treats the temporal axis as a spatial axis, enabling the proposed scheme to discretize all derivatives in the governing equation. This is accomplished through Taylor series expansion and the moving least squares method. Due to the expandability of the Taylor series to any order, the proposed numerical scheme excels in efficiently handling mixed and higher-order derivatives. These capabilities are distinct advantages of the proposed scheme. The resulting system of algebraic equations is sparse but overdetermined. Therefore, the Levenberg-Marquardt algorithm is directly applied to solve this nonlinear algebraic system. During the calculation process, the time-marching approach reduces computational effort and improves efficiency by dividing the space-time domain.
{"title":"A space-time generalized finite difference scheme for long wave propagation based on high-order Korteweg-de Vries type equations","authors":"Fan Zhang , Po-Wei Li , Yan Gu , Chia-Ming Fan","doi":"10.1016/j.matcom.2024.09.012","DOIUrl":"10.1016/j.matcom.2024.09.012","url":null,"abstract":"<div><div>In this paper, the space-time generalized finite difference scheme is applied to solve the nonlinear high-order Korteweg-de Vries equations in multiple dimensions. The proposed numerical scheme combines the space-time generalized finite difference method, the Levenberg-Marquardt algorithm, and a time-marching approach. The space-time generalized finite difference method treats the temporal axis as a spatial axis, enabling the proposed scheme to discretize all derivatives in the governing equation. This is accomplished through Taylor series expansion and the moving least squares method. Due to the expandability of the Taylor series to any order, the proposed numerical scheme excels in efficiently handling mixed and higher-order derivatives. These capabilities are distinct advantages of the proposed scheme. The resulting system of algebraic equations is sparse but overdetermined. Therefore, the Levenberg-Marquardt algorithm is directly applied to solve this nonlinear algebraic system. During the calculation process, the time-marching approach reduces computational effort and improves efficiency by dividing the space-time domain.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"228 ","pages":"Pages 298-312"},"PeriodicalIF":4.4,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142312014","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}
Pub Date : 2024-09-18DOI: 10.1016/j.matcom.2024.09.010
E. Barrena , S. Bermudo , A.G. Hernández-Díaz , A.D. López-Sánchez , J.A. Zamudio
In this work, we propose, analyze, and solve a generalization of the -dominating set problem in a graph, when we consider a weighted graph. Given a graph with weights in its edges, a set of vertices is a -weighted dominating set if for every vertex outside the set, the sum of the weights from it to its adjacent vertices in the set is bigger than or equal to . The -weighted domination number is the minimum cardinality among all -weighted dominating sets. Since the problem of finding the -weighted domination number is -hard, we have proposed several problem-adapted construction and reconstruction techniques and embedded them in an Iterated Greedy algorithm. The resulting sixteen variants of the Iterated Greedy algorithm have been compared with an exact algorithm. Computational results show that the proposal is able to find optimal or near-optimal solutions within a short computational time. To the best of our knowledge, the -weighted dominating set problem has never been studied before in the literature and, therefore, there is no other state-of-the-art algorithm to solve it. We have also included a comparison with a particular case of our problem, the minimum dominating set problem and, on average, we achieve same quality results within around 50% of computation time.
在这项研究中，我们提出、分析并解决了图中 k 主集问题的一般化，即考虑加权图。给定一个边上有权重的图，如果该图外的每个顶点到图中相邻顶点的权重之和大于或等于 k，则该顶点集是一个 k 加权支配集。由于求 k 加权支配数的问题是 NP 难问题，我们提出了几种与问题相适应的构造和重构技术，并将它们嵌入到迭代贪婪算法中。我们将迭代贪心算法的 16 个变体与精确算法进行了比较。计算结果表明，该建议能够在较短的计算时间内找到最优或接近最优的解决方案。据我们所知，文献中从未研究过 k 加权支配集问题，因此也没有其他最先进的算法来解决这个问题。我们还将其与我们问题的一种特殊情况--最小支配集问题--进行了比较，平均而言，我们只用了大约 50% 的计算时间就获得了相同质量的结果。
{"title":"Finding the minimum k-weighted dominating sets using heuristic algorithms","authors":"E. Barrena , S. Bermudo , A.G. Hernández-Díaz , A.D. López-Sánchez , J.A. Zamudio","doi":"10.1016/j.matcom.2024.09.010","DOIUrl":"10.1016/j.matcom.2024.09.010","url":null,"abstract":"<div><div>In this work, we propose, analyze, and solve a generalization of the <span><math><mi>k</mi></math></span>-dominating set problem in a graph, when we consider a weighted graph. Given a graph with weights in its edges, a set of vertices is a <span><math><mi>k</mi></math></span>-weighted dominating set if for every vertex outside the set, the sum of the weights from it to its adjacent vertices in the set is bigger than or equal to <span><math><mi>k</mi></math></span>. The <span><math><mi>k</mi></math></span>-weighted domination number is the minimum cardinality among all <span><math><mi>k</mi></math></span>-weighted dominating sets. Since the problem of finding the <span><math><mi>k</mi></math></span>-weighted domination number is <span><math><mi>NP</mi></math></span>-hard, we have proposed several problem-adapted construction and reconstruction techniques and embedded them in an Iterated Greedy algorithm. The resulting sixteen variants of the Iterated Greedy algorithm have been compared with an exact algorithm. Computational results show that the proposal is able to find optimal or near-optimal solutions within a short computational time. To the best of our knowledge, the <span><math><mi>k</mi></math></span>-weighted dominating set problem has never been studied before in the literature and, therefore, there is no other state-of-the-art algorithm to solve it. We have also included a comparison with a particular case of our problem, the minimum dominating set problem and, on average, we achieve same quality results within around 50% of computation time.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"228 ","pages":"Pages 485-497"},"PeriodicalIF":4.4,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142328104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-17DOI: 10.1016/S0378-4754(24)00358-6
{"title":"IMACS Calendar of Events","authors":"","doi":"10.1016/S0378-4754(24)00358-6","DOIUrl":"10.1016/S0378-4754(24)00358-6","url":null,"abstract":"","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"227 ","pages":"Page 570"},"PeriodicalIF":4.4,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0378475424003586/pdfft?md5=804e6437cfbd3238ba4cf79f078803d5&pid=1-s2.0-S0378475424003586-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142242678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-17DOI: 10.1016/S0378-4754(24)00357-4
{"title":"News of IMACS","authors":"","doi":"10.1016/S0378-4754(24)00357-4","DOIUrl":"10.1016/S0378-4754(24)00357-4","url":null,"abstract":"","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"227 ","pages":"Page 569"},"PeriodicalIF":4.4,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142242677","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}
Pub Date : 2024-09-12DOI: 10.1016/j.matcom.2024.09.001
Subarna Roy, Pankaj Kumar Tiwari
This study focuses on unraveling key factors influencing predator–prey interactions with Crowley–Martin functional response. Specifically, it explores the roles of additional food sources, harvesting practices, hunting cooperation, fear and its carry-over effects. We analyze equilibrium points and their stability properties through rigorous mathematical methods. Numerical illustrations showcase a diverse range of bifurcations including Hopf, saddle–node, and transcritical, providing a comprehensive understanding of the system’s dynamics. We find that the collaboration among predators during hunting induces instability in the system, leading to the emergence of population cycles from a stable state. Further, we place emphasis on investigating the impact of seasonal forcing by introducing time-varying parameters into our model. We reveal the emergence of periodic solutions, higher periodic solutions and chaotic dynamics due to the seasonal variations of the prey’s birth rate and the degree of hunting cooperation. We also emphasize the significance of incorporating different periodicity of seasonally forced parameters, leading to a more precise understanding of predator–prey dynamics.
{"title":"Bistability in a predator–prey model characterized by the Crowley–Martin functional response: Effects of fear, hunting cooperation, additional foods and nonlinear harvesting","authors":"Subarna Roy, Pankaj Kumar Tiwari","doi":"10.1016/j.matcom.2024.09.001","DOIUrl":"10.1016/j.matcom.2024.09.001","url":null,"abstract":"<div><p>This study focuses on unraveling key factors influencing predator–prey interactions with Crowley–Martin functional response. Specifically, it explores the roles of additional food sources, harvesting practices, hunting cooperation, fear and its carry-over effects. We analyze equilibrium points and their stability properties through rigorous mathematical methods. Numerical illustrations showcase a diverse range of bifurcations including Hopf, saddle–node, and transcritical, providing a comprehensive understanding of the system’s dynamics. We find that the collaboration among predators during hunting induces instability in the system, leading to the emergence of population cycles from a stable state. Further, we place emphasis on investigating the impact of seasonal forcing by introducing time-varying parameters into our model. We reveal the emergence of periodic solutions, higher periodic solutions and chaotic dynamics due to the seasonal variations of the prey’s birth rate and the degree of hunting cooperation. We also emphasize the significance of incorporating different periodicity of seasonally forced parameters, leading to a more precise understanding of predator–prey dynamics.</p></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"228 ","pages":"Pages 274-297"},"PeriodicalIF":4.4,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142242599","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}
Pub Date : 2024-09-12DOI: 10.1016/j.matcom.2024.09.004
M. Naimi, M. Lamnii
In this work, we are interested in the resolution of the Laplace equation with Dirichlet boundary condition in a closed surface in , which is – topologically – equivalent to the unit disc . It is known that for a function represented in polar coordinates on , certain boundary conditions must be satisfied by so that the surface is of class . More precisely, we construct an approximant of class on as a tensor product of two quasi-interpolants, one based on UAT-splines and the other based on classical B-splines. Some numerical results are given to validate the work.
在这项工作中，我们感兴趣的是在 R2 中的封闭曲面 S 上解决带有 Dirichlet 边界条件的拉普拉斯方程 -Δu=f 的问题，该曲面在拓扑上等价于单位圆盘 D={x,y|x2+y2⩽1}。众所周知，对于在 D 上以极坐标表示的函数 u，u 必须满足某些边界条件，这样曲面 S 才属于 C0 类。更确切地说，我们在 D 上构建了一个 C0 类近似值，它是两个准内插值的张量乘积，一个基于 UAT 样条曲线，另一个基于经典 B 样条曲线。我们给出了一些数值结果来验证这项工作。
{"title":"Solving the Laplace equation on the disc using the UAT spline","authors":"M. Naimi, M. Lamnii","doi":"10.1016/j.matcom.2024.09.004","DOIUrl":"10.1016/j.matcom.2024.09.004","url":null,"abstract":"<div><div>In this work, we are interested in the resolution of the Laplace equation <span><math><mrow><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>=</mo><mi>f</mi></mrow></math></span> with Dirichlet boundary condition in a closed surface <span><math><mi>S</mi></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, which is – topologically – equivalent to the unit disc <span><math><mrow><mi>D</mi><mo>=</mo><mrow><mo>{</mo><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced><mo>|</mo><mspace></mspace><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⩽</mo><mn>1</mn><mo>}</mo></mrow></mrow></math></span>. It is known that for a function <span><math><mi>u</mi></math></span> represented in polar coordinates on <span><math><mi>D</mi></math></span>, certain boundary conditions must be satisfied by <span><math><mi>u</mi></math></span> so that the surface <span><math><mi>S</mi></math></span> is of class <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span>. More precisely, we construct an approximant of class <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> on <span><math><mi>D</mi></math></span> as a tensor product of two quasi-interpolants, one based on UAT-splines and the other based on classical B-splines. Some numerical results are given to validate the work.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"228 ","pages":"Pages 534-548"},"PeriodicalIF":4.4,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357111","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}
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