Insulation analyses for vacuum interrupter using multigrid and finite element method
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High precision domain discretization and field solution efficiency is the barrier of electric field numerical simulation for multi-dielectrics and complex structure by finite element method (FEM). In this paper, by applying the adaptive control strategy in the transformation between coarse grid and fine grid, an adaptive multigrid-finite element method (AMG-FEM) based on non-structure grid is presented. For simulating the multi-dielectrics and complex electric filed, domain decomposition method (DDM) is employed. And the feasibility and validity of the proposed AMG-FEM/DDM with higher precision and efficiency is verified by calculating the electric field of a vacuum interrupter (VI). And the electric field distributions of the VI with different opening strokes have been figured out dynamically.Keywords:
Multigrid method
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The coupled Discrete Element (DEM) - Lattice Boltzmann Method (LBM) often suffers from the high computational cost due to the fine meshes used. The intrinsic parallel nature of DEM-LBM makes it possible to be applied to the analysis of realistic engineering problems using parallel computer. In this paper the domain decomposition is implemented in the validated coupled DEM-LBM code FPS-BHAM and its performance is tested. A parallel efficiency of 0.72 has been achieved by using 32 processors, which shows a very good parallel behaviour of the DEM-LBM. Besides, the feature of ‘pseudo-vector processing capacity’ boosts the parallel behaviour of LBM with domain decomposition.
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Multigrid method
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Fast simulations of cardiac electrical phenomena demand fast matrix solvers for both the elliptic and parabolic parts of the bidomain equations. It is well known that fast matrix solvers for the elliptic part must address multiple physical scales in order to show robust behavior. Recent research on finding the proper solution method for the bidomain equations has addressed this issue whereby multigrid preconditioned conjugate gradients has been used as a solver. In this paper, a more robust multigrid method, called Black Box Multigrid, is presented as an alternative to conventional geometric multigrid, and the effect of discontinuities on solver performance for the elliptic and parabolic part is investigated. Test problems with discontinuities arising from inserted plunge electrodes and naturally occurring myocardial discontinuities are considered. For these problems, we explore the advantages to using a more advanced multigrid method like Black Box Multigrid over conventional geometric multigrid. Results will indicate that for certain discontinuous bidomain problems Black Box Multigrid provides 60% faster simulations than using conventional geometric multigrid. Also, for the problems examined, it will be shown that a direct usage of conventional multigrid leads to faster simulations than an indirect usage of conventional multigrid as a preconditioner unless there are sharp discontinuities.
Multigrid method
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Graphics processor units (GPUs) have started becoming an integral part of high performance computing. We develop a GPU based 3D-unstructured geometric multigrid solver, which is extensively used in Computational Fluid Dynamics (CFD) applications. Parallelization for GPUs is not straightforward because of the irregularity of the mesh. Using combination of graph coloring and greedy maximal independent set computations, we obtain significant performance improvements in the multigrid solver and its parallelization. We use NVIDIAs CUDA programming model for the implementation. In our experiments, we solve heat conduction problems on unstructured 3D meshes. Different schemes for implementing the multigrid algorithm are evaluated. For a mesh of size 1.6 million, our multigrid GPU implementation gives 24 times speed up compared to multigrid serial implementation and 1630 times speed up compared to non-multigrid serial implementation.
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Parallel multigrid is widely used as preconditioners in solving large-scale sparse linear systems. However, the current multigrid library still needs more satisfactory performance for structured grid problems regarding speed and scalability. To this end, we design and implement StructMG, a fast and scalable multigrid that constructs hierarchical grids automatically based on the original matrix. As a preconditioner, StructMG can achieve both low cost per iteration and good convergence. Two idealized and five real-world problems from four application fields, including radiation hydrodynamics, petroleum reservoir simulation, numerical weather prediction, and solid mechanics, are evaluated on ARM and X86 platforms. In comparison to hypre's multigrid preconditioners, StructMG achieves the fastest time-to-solutions in all cases with average speedups of 17.6x, 5.7x, 4.6x, 8.5x over SMG, PFMG, SysPFMG, and BoomerAMG, respectively. Additionally, StructMG significantly improves strong and weak scaling efficiencies in most tests.
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The formulation of good discretization schemes is of course the first step in any numerical solution of continuous equations. For multigrid solutions, some additional considerations enter. First, discrete equations should be written for general meshsizes h, including large ones (to be used on coarse grids). Also, the multigrid processes offer several simplifications of the discretization procedures.
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