Approximation and Reconstruction of the Electrostatic Field in Wire–Plate Precipitators by a Low-Order Model

Beux, F.; Iollo, Angelo; Salvetti, Maria Vittoria; Soldati, Alfredo

doi:10.1006/jcph.2001.6773

Cited by 10 publications

(9 citation statements)

References 19 publications

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“…However, when the KL decomposition is used to approximate , the construction of a snapshot basis is needed and, thus, preliminary computations must be carried out, which imply the solution of the reduced Maxwell problem. Nevertheless, as shown in [17], a limited number of snapshots and, thus, of preliminary simulations, is sufficient to obtain an accurate approximation. Thus, the proposed procedure remains interesting when many different configurations must be computed, as in optimization or control applications.…”

Section: Discussionmentioning

confidence: 99%

“…Remembering that the potential is equal to zero at the plate, can simply be expressed as follows: (6) One possible drawback of this construction is that information from only the second component of the electric field has been used. Moreover, in this way we have an accumulation of approximation errors moving away from the plate, i.e., when decreases (see also [17]).…”

Section: A Electrostatic Field Construction From a Given Current-denmentioning

confidence: 99%

“…As for the numerical discretization of (1) and (2), the present approach is based on a finite-difference (FD) method close to the one defined in [5], but here a constant value of and a nonuniform grid system are used. This method is certainly not the most efficient among those proposed in the literature; however, tests on grid independence and comparisons with experimental and numerical data have shown that accurate solutions can be obtained [17]. On the basis of those tests, all the computations presented here are carried out on a 23 34 nonuniform grid, with points clustered near the wire (point A) in both directions.…”

Section: Problem Description and Numerical Solvermentioning

confidence: 99%

“…For the problem under consideration, it has been shown by a priori tests [17] that only three or four modes are typically needed to obtain an accurate representation of . The coefficients are determined here by an optimization algorithm aimed to obtain a wire potential value close to , i.e., as previously, by minimizing the function .…”

Section: Kl Decompositionmentioning

confidence: 99%

“…• computation of : charge-density and potential fields are obtained using (5) and (6); • updating of the mode coefficients using a gradient descent method (14) in which the derivatives of can be explicitly obtained by using the expression of from (6) and introducing the field and its parameterization, i.e., [17].…”

Section: Kl Decompositionmentioning

confidence: 99%

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Current-density approximation for efficient computation of the electrostatic field in wire-plate precipitators

Beux

Iollo

Salvetti

et al. 2002

IEEE Trans. on Ind. Applicat.

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The problem is defined by a reduced set of the Maxwell equations. The efficiency of numerical iterative computations is significantly improved by deriving an initial field as close as possible to the final solution from an approximation of the current density field J. Different techniques to approximate J are proposed. A first analytical approximation is derived, which verifies by construction the boundary conditions of the problem, and, in particular, gives the correct average value at the plate. A second analytical approximation is also considered, which contains a free parameter that can be computed by an optimization procedure based on the known value of the potential at the wire. Finally, proper orthogonal decomposition (POD) is used and the current density field is expressed. The coefficients can be determined again by an optimization algorithm. Starting from these approximated J fields, a procedure is proposed to obtain an estimate of the complete electrostatic field. It is shown that this estimate, which is obtained at negligible computational cost, is in all cases much closer to the exact solution than guesses typically employed in the literature. Hence, it can be used as initialization for standard numerical solvers, leading to a significant gain in the efficiency of the numerical algorithm, especially when the POD decomposition of J is considered

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Section: Discussionmentioning

confidence: 99%

Section: A Electrostatic Field Construction From a Given Current-denmentioning

confidence: 99%