The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
A. Borzì - One of the best experts on this subject based on the ideXlab platform.
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a Multigrid Scheme for solving convection diffusion integral optimal control problems
Computing and Visualization in Science, 2019Co-Authors: Duncan Kioi Gathungu, A. BorzìAbstract:The fast Multigrid solution of an optimal control problem governed by a convection–diffusion partial-integro differential equation is investigated. This optimization problem considers a cost functional of tracking type and a constrained distributed control. The optimal control sought is characterized by the solution to the corresponding optimality system, which is approximated by a finite volume and quadrature discretization Schemes and solved by Multigrid techniques. The proposed Multigrid approach combines a Multigrid method for the governing model with a fast Multigrid integration method. The convergence of this solution procedure is analyzed by local Fourier analysis and validated by results of numerical experiments.
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A Multigrid Scheme for solving convection–diffusion-integral optimal control problems
Computing and Visualization in Science, 2019Co-Authors: Duncan Kioi Gathungu, A. BorzìAbstract:The fast Multigrid solution of an optimal control problem governed by a convection–diffusion partial-integro differential equation is investigated. This optimization problem considers a cost functional of tracking type and a constrained distributed control. The optimal control sought is characterized by the solution to the corresponding optimality system, which is approximated by a finite volume and quadrature discretization Schemes and solved by Multigrid techniques. The proposed Multigrid approach combines a Multigrid method for the governing model with a fast Multigrid integration method. The convergence of this solution procedure is analyzed by local Fourier analysis and validated by results of numerical experiments.
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Multigrid Solution of an Elliptic Fredholm Partial Integro-Differential Equation with a Hilbert-Schmidt Integral Operator
Applied Mathematics-a Journal of Chinese Universities Series B, 2017Co-Authors: Duncan Kioi Gathungu, A. BorzìAbstract:An efficient Multigrid finite-differences Scheme for solving elliptic Fredholm partial integro-differential equations (PIDE) is discussed. This Scheme combines a second-order accurate finite difference discretization of the PIDE problem with a Multigrid Scheme that includes a fast multilevel integration of the Fredholm operator allowing the fast solution of the PIDE problem. Theoretical estimates of second-order accuracy and results of local Fourier analysis of convergence of the proposed Multigrid Scheme are presented. Results of numerical experiments validate these estimates and demonstrate optimal computational complexity of the proposed framework.
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A FEM-Multigrid Scheme for Elliptic Nash-Equilibrium Multiobjective Optimal Control Problems
Numerical Mathematics-theory Methods and Applications, 2015Co-Authors: Mohammad Tanvir Rahman, A. BorzìAbstract:AbstractA finite-element Multigrid Scheme for elliptic Nash-equilibrium multiobjective optimal control problems with control constraints is investigated. The Multigrid computational framework implements a nonlinear Multigrid strategy with collective smoothing for solving the multiobjective optimality system discretized with finite elements. Error estimates for the optimal solution and two-grid local Fourier analysis of the Multigrid Scheme are presented. Results of numerical experiments are presented to demonstrate the effectiveness of the proposed framework.
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Second-order approximation and fast Multigrid solution of parabolic bilinear optimization problems
Advances in Computational Mathematics, 2015Co-Authors: A. Borzì, Sergio González AndradeAbstract:An accurate and fast solution Scheme for parabolic bilinear optimization problems is presented. Parabolic models where the control plays the role of a reaction coefficient and the objective is to track a desired trajectory are formulated and investigated. Existence and uniqueness of optimal solution are proved. A space-time discretization is proposed and second-order accuracy for the optimal solution is discussed. The resulting optimality system is solved with a nonlinear Multigrid strategy that uses a local semismooth Newton step as smoothing Scheme. Results of numerical experiments validate the theoretical accuracy estimates and demonstrate the ability of the Multigrid Scheme to solve the given optimization problems with mesh-independent efficiency.
G. Wittum - One of the best experts on this subject based on the ideXlab platform.
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Adaptive Local Multigrid Methods for the Solution of Time Harmonic Eddy Current Problems
2020Co-Authors: O. Sterz, A. Hauser, G. WittumAbstract:The efficient computation of large eddy current problems with finite elements requires adaptive methods and fast optimal iterative solvers like Multigrid methods. This paper provides an overview of the most important implementation aspects of an adaptive Multigrid Scheme for time-harmonic eddy currents. It is shown how the standard Multigrid Scheme can be modified to yield an O(N) complexity even for general adaptive refinement strategies, where the number of unknowns N can grow slowly from one to the next refinement level. Algorithmic details and numerical examples are given.
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Adaptive local Multigrid methods for solving time-harmonic eddy-current problems
IEEE Transactions on Magnetics, 2006Co-Authors: O. Sterz, A. Hauser, G. WittumAbstract:The efficient computation of large eddy-current problems with finite elements requires adaptive methods and fast optimal iterative solvers such as Multigrid methods. This paper provides an overview of the most important implementation aspects of an adaptive Multigrid Scheme for time-harmonic eddy currents. Numerical experiments show that the standard Multigrid Scheme can be modified to yield an O(N) complexity even for general adaptive refinement strategies, where the number of unknowns N can grow slowly from one to the next refinement level. Algorithmic details and numerical examples are given.
Romain Teyssier - One of the best experts on this subject based on the ideXlab platform.
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a simple Multigrid Scheme for solving the poisson equation with arbitrary domain boundaries
Journal of Computational Physics, 2011Co-Authors: Thomas Guillet, Romain TeyssierAbstract:We present a new Multigrid Scheme for solving the Poisson equation with Dirichlet boundary conditions on a Cartesian grid with irregular domain boundaries. This Scheme was developed in the context of the Adaptive Mesh Refinement (AMR) Schemes based on a graded-octree data structure. The Poisson equation is solved on a level-by-level basis, using a ''one-way interface'' Scheme in which boundary conditions are interpolated from the previous coarser level solution. Such a Scheme is particularly well suited for self-gravitating astrophysical flows requiring an adaptive time stepping strategy. By constructing a Multigrid hierarchy covering the active cells of each AMR level, we have designed a memory-efficient algorithm that can benefit fully from the Multigrid acceleration. We present a simple method for capturing the boundary conditions across the Multigrid hierarchy, based on a second-order accurate reconstruction of the boundaries of the Multigrid levels. In case of very complex boundaries, small scale features become smaller than the discretization cell size of coarse Multigrid levels and convergence problems arise. We propose a simple solution to address these issues. Using our Scheme, the convergence rate usually depends on the grid size for complex grids, but good linear convergence is maintained. The proposed method was successfully implemented on distributed memory architectures in the RAMSES code, for which we present and discuss convergence and accuracy properties as well as timing performances.
Ioannis K Nikolos - One of the best experts on this subject based on the ideXlab platform.
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using a parallel spatial angular agglomeration Multigrid Scheme to accelerate the fvm radiative heat transfer computation part i methodology
Numerical Heat Transfer Part B-fundamentals, 2014Co-Authors: Georgios N Lygidakis, Ioannis K NikolosAbstract:A parallel spatial/angular agglomeration Multigrid Scheme is developed to accelerate the finite-volume method (FVM) for the computation of radiative heat transfer in absorbing, emitting, and scattering gray media. The Multigrid Scheme is based on the solution of the radiative transfer equation (RTE) with the full approximation Scheme (FAS) on successively coarser spatial and angular resolutions, derived from the initial finest ones through the fusion of the adjacent control volumes and control angles, respectively. The numerical tests reveal the improvement of efficiency employing the aforementioned technique, especially in cases considering scattering media and reflecting boundaries.
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Using a Parallel Spatial/Angular Agglomeration Multigrid Scheme to Accelerate the FVM Radiative Heat Transfer Computation—Part I: Methodology
Numerical Heat Transfer Part B-fundamentals, 2014Co-Authors: Georgios N Lygidakis, Ioannis K NikolosAbstract:A parallel spatial/angular agglomeration Multigrid Scheme is developed to accelerate the finite-volume method (FVM) for the computation of radiative heat transfer in absorbing, emitting, and scattering gray media. The Multigrid Scheme is based on the solution of the radiative transfer equation (RTE) with the full approximation Scheme (FAS) on successively coarser spatial and angular resolutions, derived from the initial finest ones through the fusion of the adjacent control volumes and control angles, respectively. The numerical tests reveal the improvement of efficiency employing the aforementioned technique, especially in cases considering scattering media and reflecting boundaries.
O. Sterz - One of the best experts on this subject based on the ideXlab platform.
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Adaptive Local Multigrid Methods for the Solution of Time Harmonic Eddy Current Problems
2020Co-Authors: O. Sterz, A. Hauser, G. WittumAbstract:The efficient computation of large eddy current problems with finite elements requires adaptive methods and fast optimal iterative solvers like Multigrid methods. This paper provides an overview of the most important implementation aspects of an adaptive Multigrid Scheme for time-harmonic eddy currents. It is shown how the standard Multigrid Scheme can be modified to yield an O(N) complexity even for general adaptive refinement strategies, where the number of unknowns N can grow slowly from one to the next refinement level. Algorithmic details and numerical examples are given.
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Adaptive local Multigrid methods for solving time-harmonic eddy-current problems
IEEE Transactions on Magnetics, 2006Co-Authors: O. Sterz, A. Hauser, G. WittumAbstract:The efficient computation of large eddy-current problems with finite elements requires adaptive methods and fast optimal iterative solvers such as Multigrid methods. This paper provides an overview of the most important implementation aspects of an adaptive Multigrid Scheme for time-harmonic eddy currents. Numerical experiments show that the standard Multigrid Scheme can be modified to yield an O(N) complexity even for general adaptive refinement strategies, where the number of unknowns N can grow slowly from one to the next refinement level. Algorithmic details and numerical examples are given.