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Author (up) Escapil-Inchauspe, P.; Jerez-Hanckes, C. doi  openurl
  Title Bi-parametric operator preconditioning Type
  Year 2021 Publication Computers & Mathematics With Applications Abbreviated Journal Comput. Math. Appl.  
  Volume 102 Issue Pages 220-232  
  Keywords Operator preconditioning; Galerkin methods; Numerical approximation; Iterative linear solvers  
  Abstract We extend the operator preconditioning framework Hiptmair (2006) [10] to Petrov-Galerkin methods while accounting for parameter-dependent perturbations of both variational forms and their preconditioners, as occurs when performing numerical approximations. By considering different perturbation parameters for the original form and its preconditioner, our bi-parametric abstract setting leads to robust and controlled schemes. For Hilbert spaces, we derive exhaustive linear and super-linear convergence estimates for iterative solvers, such as h-independent convergence bounds, when preconditioning with low-accuracy or, equivalently, with highly compressed approximations.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0898-1221 ISBN Medium  
  Area Expedition Conference  
  Notes Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1471  
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Author (up) Gonzalez, E.; Villena, M.J. doi  openurl
  Title On the spatial dynamics of vaccination: A spatial SIRS-V model Type
  Year 2020 Publication Computers & Mathematics With Applications Abbreviated Journal Comput. Math. Appl.  
  Volume 80 Issue 5 Pages 733-743  
  Keywords Epidemic dynamics; Spatial SIR model; Vaccination strategy; Non-linear system of partial differential equations; Numerical modeling  
  Abstract In this paper, we analyze the effects of vaccination from a spatial perspective. We propose a spatial deterministic SIRS-V model, which considers a non-linear system of partial differential equations with explicit attrition and diffusion terms for the vaccination process. The model allows us to simulate numerically the spatial and temporal dynamics of an epidemic, considering different spatial strategies for the vaccination policy. In particular, in our first example we analyze the classical SIRS-V evolution with the addition of movements due to diffusion, while in the second one we focus on modeling one ring vaccination policy. We expect this model can improve spatial predictions of SIR vaccination models by taking into account the spatial dimension of the problem. (C) 2020 Elsevier Ltd. All rights reserved.  
  Address [Gonzalez, Eduardo] Univ Finis Terrae, Fac Engn, Santiago, Chile, Email: e.gonzalez@ieee.org;  
  Corporate Author Thesis  
  Publisher Pergamon-Elsevier Science Ltd Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0898-1221 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000557765800010 Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1220  
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Author (up) Gonzalez, E.; Villena, M.J. pdf  doi
openurl 
  Title Spatial attrition modeling: Stability conditions for a 2D + t FD formulation Type
  Year 2011 Publication Computers & Mathematics With Applications Abbreviated Journal Comput. Math. Appl.  
  Volume 61 Issue 11 Pages 3246-3257  
  Keywords PDE; Stability; Reaction-diffusion; Spatial attrition modeling  
  Abstract A new general formulation for the spatial modeling of combat is presented, where the main drivers are movement attitudes and struggle evolution. This model in its simplest form is represented by a linear set of two coupled partial differential equations for two independent functions of the space and time variables. Even though the problem has a linear shape, non-negative values for the two functions render this problem as nonlinear. In contrast with other attempts, this model ensures stability and theoretical consistency with the original Lanchester Equations, allowing for a better understanding and interpretation of the spatial modeling. As a numerical illustration a simple combat situation is developed. The model is calibrated to simulate different troop movement tactics that allow an invader force to provoke maximum damage at a minimum cost. The analysis provided here reviews the trade-off between spatial grid and time stepping for attrition cases and then extends it to a new method for guaranteeing good numerical behavior when the solution is expected to grow along the time variable. There is a wide variety of spatial problems that could benefit from this analysis. (C) 2011 Elsevier Ltd. All rights reserved.  
  Address [Gonzalez, E; Villena, MJ] Univ Adolfo Ibanez, Fac Sci & Engn, Santiago, Chile, Email: eduardo.gonzalez@uai.cl  
  Corporate Author Thesis  
  Publisher Pergamon-Elsevier Science Ltd Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0898-1221 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000292573000005 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 155  
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