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Computational advances in quasi-optimal domain decomposition methods for time-harmonic electromagnetic wave problems Marsic, Nicolas ; Vion, Alexandre ; Geuzaine, Christophe Conference (2015) In this talk we will present recent advances in the construction of quasi-optimal domain decomposition methods for time-harmonic electromagnetic wave problems. In particular, we will discuss the parallel ... [more ▼] In this talk we will present recent advances in the construction of quasi-optimal domain decomposition methods for time-harmonic electromagnetic wave problems. In particular, we will discuss the parallel implementation and computational efficiency of sweeping-type preconditioners, as well as the use of high order finite element discretizations, potentially mixing orders for the volume and interface formulations. Results on several large scale test cases will be analysed. [less ▲] Detailed reference viewed: 31 (2 ULg)Multi-Domain Approaches for the Solution of High-Frequency Time-Harmonic Propagation Problems Vion, Alexandre Doctoral thesis (2014) The numerical solution of high-frequency time-harmonic propagation problems by volumic discretization methods is a challenging task, most notably because of the very large size of the resulting linear ... [more ▼] The numerical solution of high-frequency time-harmonic propagation problems by volumic discretization methods is a challenging task, most notably because of the very large size of the resulting linear systems. We present a framework for a class of iterative methods that distribute the work between several CPUs and exchange information between physical or artificial interfaces. The goal is to define subproblems of manageable sizes, and to exploit the power of parallel supercomputers. [less ▲] Detailed reference viewed: 93 (25 ULg)Double Sweep Preconditioners for propagation problems solved by Optimized Schwarz Methods Vion, Alexandre ; Geuzaine, Christophe in Proceedings of the 6th International Conference on Advanced COmputational Methods in ENgineering, ACOMEN 2014 (2014, June) Detailed reference viewed: 25 (7 ULg)Parallel Double Sweep Preconditioner for the Optimized Schwarz Algorithm Applied to High Frequency Helmholtz and Maxwell Equations Vion, Alexandre ; Geuzaine, Christophe Scientific conference (2014, May) Detailed reference viewed: 39 (2 ULg)Double sweep preconditioner for optimized Schwarz methods applied to the Helmholtz problem Vion, Alexandre ; Geuzaine, Christophe in Journal of Computational Physics (2014), 266 Detailed reference viewed: 31 (8 ULg)Double sweep preconditioner for Schwarz methods applied to the Helmholtz equation Vion, Alexandre ; Geuzaine, Christophe in Proceedings of the 22nd International Conference on Domain Decomposition Methods (2013, September) Observing that the optimized Schwarz algorithm is equivalent to the solution of a linear system, we design a new preconditioner as an approximate inverse of the iteration operator, in the particular case ... [more ▼] Observing that the optimized Schwarz algorithm is equivalent to the solution of a linear system, we design a new preconditioner as an approximate inverse of the iteration operator, in the particular case of a layered decomposi- tion. We show that it can be rewritten as two independent sequences of subproblem solves (forward and back- ward), hence the name ‘double sweep’. The whole algorithm is implemented as a matrix-free GMRES iteration, that requires no more additional preprocessing than the original algorithm. Numerical experiments indicate that the convergence rate is independent of the wavenumber and number of subdomains when good approximations of the DtN maps are used, in both homogeneous and non-homogeneous cases. [less ▲] Detailed reference viewed: 20 (5 ULg)Optimized Schwarz Algorithm with Double Sweep Preconditioner for the Helmholtz Equation Vion, Alexandre ; Geuzaine, Christophe in Proceedings of the 9th International Symposium on Electric and Magnetic Fields, EMF 2013 (2013, April) Detailed reference viewed: 14 (0 ULg)A DDM double sweep preconditioner for the Helmholtz equation with matrix probing of the DtN map Vion, Alexandre ; ; et al in Proceedings of the 11th International Conference on Mathematical and Numerical Aspects of Waves (WAVES 2013) (2013) Detailed reference viewed: 18 (2 ULg)Acceleration of the convergence of a non-overlapping domain decomposition method by an approximate deflation technique for high-frequency wave propagation Vion, Alexandre ; ; Geuzaine, Christophe in Proceedings of the 15th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC2012) (2012) The analysis of a non-overlapping domain decom- position method with optimized transmission conditions, applied to a simplified 1-D problem discretized by finite elements, is performed to better ... [more ▼] The analysis of a non-overlapping domain decom- position method with optimized transmission conditions, applied to a simplified 1-D problem discretized by finite elements, is performed to better understand the spectral properties of the method. An approximate deflation preconditioner is then introduced to modify the spectrum of the iteration operator, and speed up the convergence of the GMRES algorithm used to solve the substructured problem. [less ▲] Detailed reference viewed: 20 (4 ULg)Improved Domain Decomposition Method for the Helmholtz Equation Thierry, Bertrand ; ; et al in Proceedings of the 21th International Conference on Domain Decomposition Methods (DD21) (2012, June) Detailed reference viewed: 48 (4 ULg)A Model Reduction Algorithm for Solving Multiple Scattering Problems Using Iterative Methods Vion, Alexandre ; Vazquez Sabariego, Ruth ; Geuzaine, Christophe in IEEE Transactions on Magnetics (2011), 47(5), 1470-1473 Detailed reference viewed: 22 (7 ULg)An Amplitude Finite Element Formulation for Multiple-Scattering by a Collection of Convex Obstacles Geuzaine, Christophe ; Vion, Alexandre ; Gaignaire, Roman et al in IEEE Transactions on Magnetics (2010), 46(8), 2963-2966 We present a multiple-scattering solver for nonconvex geometries obtained as the union of a finite number of convex obstacles. The algorithm is a finite element reformulation of a high-frequency integral ... [more ▼] We present a multiple-scattering solver for nonconvex geometries obtained as the union of a finite number of convex obstacles. The algorithm is a finite element reformulation of a high-frequency integral equation technique proposed previously. It is based on an iterative solution of the scattering problem, where each iteration leads to the resolution of a single scattering problem in terms of a slowly oscillatory amplitude. [less ▲] Detailed reference viewed: 82 (21 ULg)A model reduction algorithm for solving multiple scattering problems using iterative methods Vion, Alexandre ; V Sabariego, Ruth ; Geuzaine, Christophe in Proceedings of the 14th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC2010) (2010, May) This paper presents a new method for solving scattering problems by multiple objects. A model reduction algorithm based on the Macro Basis Functions (MBFs) method is used to find an approximate solution ... [more ▼] This paper presents a new method for solving scattering problems by multiple objects. A model reduction algorithm based on the Macro Basis Functions (MBFs) method is used to find an approximate solution within a subspace of solutions, that are the solutions of several single scattering subproblems. Different iterative methods for the generation of the MBFs are compared. The whole process relies on a finite element approach and is applied to convex obstacles scattering. [less ▲] Detailed reference viewed: 44 (13 ULg)Iterative solution of high-frequency multiple-scattering problems using finite elements Geuzaine, Christophe ; Vion, Alexandre ; V Sabariego, Ruth in Proceedings of the IVth European Conference on Computational Mechanics (ECCM 2010) (2010) Detailed reference viewed: 40 (17 ULg) |
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