Pub Date : 2022-10-01DOI: 10.1016/j.amc.2022.127351
Kaipeng Ji, P. Zhao, X. Zhou, Yuhong Chen, Zhengyang Dong, Jianguo Zheng, Jianzhong Fu, Huamin Zhou
{"title":"Uniform Initialization in Response Space for PSO and its Applications","authors":"Kaipeng Ji, P. Zhao, X. Zhou, Yuhong Chen, Zhengyang Dong, Jianguo Zheng, Jianzhong Fu, Huamin Zhou","doi":"10.1016/j.amc.2022.127351","DOIUrl":"https://doi.org/10.1016/j.amc.2022.127351","url":null,"abstract":"","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"139 1","pages":"127351"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91429374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-01DOI: 10.1016/j.amc.2022.127349
Lin Zhu, Weiwei Che, Xiao‐Zheng Jin
{"title":"Dynamic event-triggered tracking control for model-free networked control systems","authors":"Lin Zhu, Weiwei Che, Xiao‐Zheng Jin","doi":"10.1016/j.amc.2022.127349","DOIUrl":"https://doi.org/10.1016/j.amc.2022.127349","url":null,"abstract":"","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"1 1","pages":"127349"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83653063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-29DOI: 10.48550/arXiv.2209.14892
M. Ciallella, Elena Gaburro, Marco Lorini, M. Ricchiuto
In this work we propose a simple but effective high order polynomial correction allowing to enhance the consistency of all kind of boundary conditions for the Euler equations (Dirichlet, characteristic far-field and slip-wall), both in 2D and 3D, preserving a high order of accuracy without the need of curved meshes. The method proposed is a simplified reformulation of the Shifted Boundary Method (SBM) and relies on a correction based on the extrapolated value of the in cell polynomial to the true geometry, thus not requiring the explicit evaluation of high order Taylor series. Moreover, this strategy could be easily implemented into any already existing finite element and finite volume code. Several validation tests are presented to prove the convergence properties up to order four for 2D and 3D simulations with curved boundaries, as well as an effective extension to flows with shocks.
{"title":"Shifted boundary polynomial corrections for compressible flows: high order on curved domains using linear meshes","authors":"M. Ciallella, Elena Gaburro, Marco Lorini, M. Ricchiuto","doi":"10.48550/arXiv.2209.14892","DOIUrl":"https://doi.org/10.48550/arXiv.2209.14892","url":null,"abstract":"In this work we propose a simple but effective high order polynomial correction allowing to enhance the consistency of all kind of boundary conditions for the Euler equations (Dirichlet, characteristic far-field and slip-wall), both in 2D and 3D, preserving a high order of accuracy without the need of curved meshes. The method proposed is a simplified reformulation of the Shifted Boundary Method (SBM) and relies on a correction based on the extrapolated value of the in cell polynomial to the true geometry, thus not requiring the explicit evaluation of high order Taylor series. Moreover, this strategy could be easily implemented into any already existing finite element and finite volume code. Several validation tests are presented to prove the convergence properties up to order four for 2D and 3D simulations with curved boundaries, as well as an effective extension to flows with shocks.","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"123 1","pages":"127698"},"PeriodicalIF":0.0,"publicationDate":"2022-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86674402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-08DOI: 10.48550/arXiv.2209.03795
E. Abreu, Elena Bachini, J. Pérez, M. Putti
We present a Lagrangian-Eulerian scheme to solve the shallow water equations in the case of spatially variable bottom geometry. Using a local curvilinear reference system anchored on the bottom surface, we develop an effective first-order and high-resolution space-time discretization of the no-flow surfaces and solve a Lagrangian initial value problem that describes the evolution of the balance laws governing the geometrically intrinsic shallow water equations. The evolved solution set is then projected back to the original surface grid to complete the proposed Lagrangian-Eulerian formulation. The resulting scheme maintains monotonicity and captures shocks without providing excessive numerical dissipation also in the presence of non-autonomous fluxes such as those arising from the geometrically intrinsic shallow water equation on variable topographies. We provide a representative set of numerical examples to illustrate the accuracy and robustness of the proposed Lagrangian-Eulerian formulation for two-dimensional surfaces with general curvatures and discontinuous initial conditions.
{"title":"A geometrically intrinsic Lagrangian-Eulerian scheme for 2D Shallow Water Equations with variable topography and discontinuous data","authors":"E. Abreu, Elena Bachini, J. Pérez, M. Putti","doi":"10.48550/arXiv.2209.03795","DOIUrl":"https://doi.org/10.48550/arXiv.2209.03795","url":null,"abstract":"We present a Lagrangian-Eulerian scheme to solve the shallow water equations in the case of spatially variable bottom geometry. Using a local curvilinear reference system anchored on the bottom surface, we develop an effective first-order and high-resolution space-time discretization of the no-flow surfaces and solve a Lagrangian initial value problem that describes the evolution of the balance laws governing the geometrically intrinsic shallow water equations. The evolved solution set is then projected back to the original surface grid to complete the proposed Lagrangian-Eulerian formulation. The resulting scheme maintains monotonicity and captures shocks without providing excessive numerical dissipation also in the presence of non-autonomous fluxes such as those arising from the geometrically intrinsic shallow water equation on variable topographies. We provide a representative set of numerical examples to illustrate the accuracy and robustness of the proposed Lagrangian-Eulerian formulation for two-dimensional surfaces with general curvatures and discontinuous initial conditions.","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"30 1","pages":"127776"},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82437333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-30DOI: 10.48550/arXiv.2208.14477
R. Abgrall, Wasilij Barsukow
We propose an arbitrarily high-order accurate numerical method for conservation laws that is based on a continuous approximation of the solution. The degrees of freedom are point values at cell interfaces and moments of the solution inside the cell. To lowest ($3^text{rd}$) order this method reduces to the Active Flux method. The update of the moments is achieved immediately by integrating the conservation law over the cell, integrating by parts and employing the continuity across cell interfaces. We propose two ways how the point values can be updated in time: either by first deriving a semi-discrete method that uses a finite-difference-type formula to approximate the spatial derivative, and integrating this method e.g. with a Runge-Kutta scheme, or by using a characteristics-based update, which is inspired by the original (fully discrete) Active Flux method. We analyze stability and accuracy of the resulting methods.
{"title":"A hybrid finite element - finite volume method for conservation laws","authors":"R. Abgrall, Wasilij Barsukow","doi":"10.48550/arXiv.2208.14477","DOIUrl":"https://doi.org/10.48550/arXiv.2208.14477","url":null,"abstract":"We propose an arbitrarily high-order accurate numerical method for conservation laws that is based on a continuous approximation of the solution. The degrees of freedom are point values at cell interfaces and moments of the solution inside the cell. To lowest ($3^text{rd}$) order this method reduces to the Active Flux method. The update of the moments is achieved immediately by integrating the conservation law over the cell, integrating by parts and employing the continuity across cell interfaces. We propose two ways how the point values can be updated in time: either by first deriving a semi-discrete method that uses a finite-difference-type formula to approximate the spatial derivative, and integrating this method e.g. with a Runge-Kutta scheme, or by using a characteristics-based update, which is inspired by the original (fully discrete) Active Flux method. We analyze stability and accuracy of the resulting methods.","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"39 1","pages":"127846"},"PeriodicalIF":0.0,"publicationDate":"2022-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85647373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-22DOI: 10.48550/arXiv.2208.10501
D. Cortellessa, Nicola Ferro, S. Perotto, S. Micheletti
We propose a new algorithm for the design of topologically optimized lightweight structures, under a minimum compliance requirement. The new process enhances a standard level set formulation in terms of computational efficiency, thanks to the employment of a strategic computational mesh. We pursue a twofold goal, i.e., to deliver a final layout characterized by a smooth contour and reliable mechanical properties. The smoothness of the optimized structure is ensured by the employment of an anisotropic adapted mesh, which sharply captures the material/void interface. A robust mechanical performance is guaranteed by a uniform tessellation of the internal part of the optimized configuration. A thorough numerical investigation corroborates the effectiveness of the proposed algorithm as a reliable and computationally affordable design tool, both in two- and three-dimensional contexts.
{"title":"Enhancing level set-based topology optimization with anisotropic graded meshes","authors":"D. Cortellessa, Nicola Ferro, S. Perotto, S. Micheletti","doi":"10.48550/arXiv.2208.10501","DOIUrl":"https://doi.org/10.48550/arXiv.2208.10501","url":null,"abstract":"We propose a new algorithm for the design of topologically optimized lightweight structures, under a minimum compliance requirement. The new process enhances a standard level set formulation in terms of computational efficiency, thanks to the employment of a strategic computational mesh. We pursue a twofold goal, i.e., to deliver a final layout characterized by a smooth contour and reliable mechanical properties. The smoothness of the optimized structure is ensured by the employment of an anisotropic adapted mesh, which sharply captures the material/void interface. A robust mechanical performance is guaranteed by a uniform tessellation of the internal part of the optimized configuration. A thorough numerical investigation corroborates the effectiveness of the proposed algorithm as a reliable and computationally affordable design tool, both in two- and three-dimensional contexts.","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"33 1","pages":"127903"},"PeriodicalIF":0.0,"publicationDate":"2022-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76239552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we consider the Heston-CIR model with L'{e}vy process for pricing in the foreign exchange (FX) market by providing a new formula that better fits the distribution of prices. To do that, first, we study the existence and uniqueness of the solution to this model. Second, we examine the strong convergence of the L'{e}vy process with stochastic domestic short interest rates, foreign short interest rates and stochastic volatility. Then, we apply Least Squares Monte Carlo (LSM) method for pricing American options under our model with stochastic volatility and stochastic interest rate. Finally, by considering real-world market data, we illustrate numerical results for the four-factor Heston-CIR L'{e}vy model.
在本文中，我们考虑具有L {e}vy过程的赫斯顿- cir模型在外汇(FX)市场上的定价，通过提供一个新的公式，更好地拟合价格分布。为此，我们首先研究了该模型解的存在唯一性。其次，我们考察了随机国内短期利率、随机国外短期利率和随机波动率对L {e}vy过程的强收敛性。然后，在随机波动率和随机利率的模型下，应用最小二乘蒙特卡罗方法对美式期权进行定价。最后，通过考虑现实市场数据，我们举例说明了四因子Heston-CIR L {e}vy模型的数值结果。
{"title":"Foreign Exchange Options on Heston-CIR Model Under Lévy Process Framework","authors":"G. Ascione, F. Mehrdoust, G. Orlando, O. Samimi","doi":"10.2139/ssrn.4185466","DOIUrl":"https://doi.org/10.2139/ssrn.4185466","url":null,"abstract":"In this paper, we consider the Heston-CIR model with L'{e}vy process for pricing in the foreign exchange (FX) market by providing a new formula that better fits the distribution of prices. To do that, first, we study the existence and uniqueness of the solution to this model. Second, we examine the strong convergence of the L'{e}vy process with stochastic domestic short interest rates, foreign short interest rates and stochastic volatility. Then, we apply Least Squares Monte Carlo (LSM) method for pricing American options under our model with stochastic volatility and stochastic interest rate. Finally, by considering real-world market data, we illustrate numerical results for the four-factor Heston-CIR L'{e}vy model.","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"10 1","pages":"127851"},"PeriodicalIF":0.0,"publicationDate":"2022-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81679527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-01DOI: 10.1016/j.amc.2022.127110
S. Mukherjee, G. C. Shit
{"title":"Mathematical modeling of electrothermal couple stress nanofluid flow and entropy in a porous microchannel under injection process","authors":"S. Mukherjee, G. C. Shit","doi":"10.1016/j.amc.2022.127110","DOIUrl":"https://doi.org/10.1016/j.amc.2022.127110","url":null,"abstract":"","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"88 1","pages":"127110"},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76793905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-01DOI: 10.1016/j.amc.2022.127111
Akbar Shirilord, M. Dehghan
{"title":"Single step iterative method for linear system of equations with complex symmetric positive semi-definite coefficient matrices","authors":"Akbar Shirilord, M. Dehghan","doi":"10.1016/j.amc.2022.127111","DOIUrl":"https://doi.org/10.1016/j.amc.2022.127111","url":null,"abstract":"","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"34-35 1","pages":"127111"},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74310136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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