Scalability Analysis of Direct and Iterative Solvers Used to Model Charging of Non-insulated Superconducting Pancake Solenoids

Mohebujjaman, M.; Shiraiwa, S.; LaBombard, B.; Wright, J. C.; Uppalapati, K.

doi:10.48550/arxiv.2007.15410

Cited by 3 publications

(3 citation statements)

References 33 publications

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“…For simulations of MHD systems, it is considered important to enforce the solenoidal constraint ∇ • B = 0 in discrete level to the machine precision [29]. This is because the condition is induced by the induction equation for all time if the initial magnetic field is divergence free [49], which is a precise physical law. Moreover, it has been shown that for MHD flow simulations ∇ • B = 0 can produce large errors in the solution [12].…”

Section: Numerical Experimentsmentioning

confidence: 99%

High order efficient algorithm for computation of MHD flow ensembles

Mohebujjaman¹

2021

Preprint

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In this paper, we propose, analyze, and test a new fully discrete, efficient, decoupled, stable, and practically second-order time-stepping algorithm for computing MHD ensemble flow averages under uncertainties in the initial conditions and forcing. For each viscosity and magnetic diffusivity pair, the algorithm picks the largest possible parameter θ ∈ [0, 1] to avoid the instability that arises due to the presence of some explicit viscous terms. At each time step, the algorithm shares the same system matrix with all J realizations but with different right-hand-side vectors. That saves assembling time and computer memory, allows the reuse of the same preconditioner, and can take the advantage of block linear solvers. For the proposed algorithm, we prove stability and convergence rigorously. To illustrate the predicted convergence rates of our analysis, numerical experiments with manufactured solutions are given on a unit square domain. Finally, we test the scheme on a benchmark channel flow over a step problem and it performs well.

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Section: Numerical Experimentsmentioning

confidence: 99%

High order efficient algorithm for computation of MHD flow ensembles

Mohebujjaman¹

2021

Preprint

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“…The reduction of the nonlinearity implies the reduction of the test mass resonance frequency, which in turn increases the gravity gradiometer sensitivity at low frequencies. Finite element modeling is a powerful tool for modeling superconducting devices [23][24][25]. We set up a model with the finite element method in COMSOL Multiphysics ® simulation software and compared it with experimental results [26].…”

Section: Introductionmentioning

confidence: 99%

Superconducting pancake coil FEM analysis for very low frequency levitated gravity accelerometers

Paula¹,

Moody²,

Norton³

et al. 2022

Supercond. Sci. Technol.

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State-of-the-art detectors are necessary to measure very tiny variations of gravity produced by spiraling neutron stars, merging black holes, moving tectonic plates. We are developing a superconducting gravity gradiometer and aim to achieve 0.1 mE Hz^{-1/2} in the frequency band of 0.1 mHz to 0.1 Hz. The superconducting test masses are levitated by a superconducting current-carrying monolayer pancake coil, which is one of the key components of the instrument. However, the nonlinear aspect of the magnetic field trapped between the test mass and the pancake coil imposes one of the main constraints to achieve that such low frequencies. In this paper, we investigated the causes of that nonlinearity by finite element method using COMSOL Multiphysics® simulation software. First, inductances were measured with an experimental setup where a gap spacing, created by a pancake coil and a niobium plate, could be adjustable. The inductances computed with a 2D axis-symmetric model satisfactorily agreed to the experimental data. Finally, we extensively studied several mechanisms for cancelling the nonlinearity of the inductance. A solenoid next to the pancake coil is the most effective and practical way to mitigate it. Furthermore, our approach can also be useful for those seeking a simple and effective model to study magnetostatic problems in a superconductor

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“…We will explore for more appropriate physical boundary conditions rather than the Dirichlet boundary conditions in Elsässer variables. It has been shown in [37], for Maxwell equations simulation, in presence of extremely different time scales, the iterative solver combination (FGMRES-GMRES) in conjunction with the parallel Auxiliary Space Maxwell (AMS) solver preconditioner outperforms over the direct solver. We plan to employ FGMRES-GMRES-AMS solver for solving complex problems using this scheme.…”

mentioning

confidence: 99%

An efficient algorithm for simulating ensembles of parameterized MHD flow problems

Mohebujjaman,

Wang,

Rebholz

et al. 2021

Preprint

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In this paper, we propose, analyze, and test an efficient algorithm for computing ensemble average of incompressible magnetohydrodynamics (MHD) flows, where instances/members correspond to varying kinematic viscosity, magnetic diffusivity, body forces, and initial conditions. The algorithm is decoupled in Elsässer variables and permits a shared coefficient matrix for all members at each time-step. Thus, the algorithm is much more computationally efficient than separately computing simulations for each member using usual MHD algorithms. We prove the proposed algorithm is unconditionally stable and convergent. Several numerical tests are given to support the predicted convergence rates. Finally, we test the proposed scheme and observe how the physical behavior changes as the coupling number increases in a lid-driven cavity problem with mean Reynolds number Re ≈ 15000, and as the deviation of uncertainties in the initial and boundary conditions increases in a channel flow past a step problem.

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Scalability Analysis of Direct and Iterative Solvers Used to Model Charging of Non-insulated Superconducting Pancake Solenoids

Cited by 3 publications

References 33 publications

High order efficient algorithm for computation of MHD flow ensembles

High order efficient algorithm for computation of MHD flow ensembles

Superconducting pancake coil FEM analysis for very low frequency levitated gravity accelerometers

An efficient algorithm for simulating ensembles of parameterized MHD flow problems

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