A functional optimization approach to an inverse magneto-convection problem

Sampath, Rajiv; Zabaras, Nicholas

doi:10.1016/s0045-7825(00)00222-x

Cited by 25 publications

(19 citation statements)

References 29 publications

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“…The CGM in conjunction with an appropriate stopping rule can serve as a regularization method, and it has been applied to various inverse problems, e.g. the inverse heat conduction problem, with great success [23][24][25][26][27]. Its basic idea is to cease the iterative procedure at an appropriate step according to the noise level in the data to guarantee its convergence, where the number of iterations assumes the role of a regularization parameter.…”

Section: Conjugate Gradient Methodsmentioning

confidence: 99%

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Conjugate gradient method for the Robin inverse problem associated with the Laplace equation

Jin

2007

Numerical Meth Engineering

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SUMMARYThis paper studies a non-linear inverse problem associated with the Laplace equation of identifying the Robin coefficient from boundary measurements. A variational formulation of the problem is suggested, thereby transforming it into an optimization problem. Mathematical properties relevant to its numerical computation are established. The optimization problem is solved using the conjugate gradient method in conjunction with the discrepancy principle, and the algorithm is implemented using the boundary element method. Numerical results are presented for several benchmark problems with both exact and noisy data, and the convergence of the algorithm with respect to mesh refinement and decreasing the amount of noise in the data is investigated.

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Section: Conjugate Gradient Methodsmentioning

confidence: 99%

“…An arbitrarily function 0 may be specified as an initial guess for the Robin coefficient on the boundary i . In our computations, the initial guess has been chosen as (27) for all the examples, and note that the initial guess is faraway from the exact solution.…”

Section: Examplementioning

confidence: 99%

Conjugate gradient method for the Robin inverse problem associated with the Laplace equation

Jin

2007

Numerical Meth Engineering

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“…Note that the adjoint equations described in Box IV are reduced to the form reported by Yang and Zabaras [18] in the absence of any external magnetic ÿeld. Further details on the development of the present adjoint equations can be found in Reference [43].…”

Section: Adjoint Methods Formulationmentioning

confidence: 99%

“…In our recent paper [46], we have conducted exhaustive numerical testing of the proposed formulation for various inverse magneto-convection problems in a ÿxed domain. For each problem examined, a unique solution was shown to exist that corresponded to a zero cost functional.…”

Section: The Conjugate Gradient Algorithmmentioning

confidence: 99%

Inverse design of directional solidification processes in the presence of a strong external magnetic field

Sampath

Zabaras

2001

Numerical Meth Engineering

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SUMMARYA computational method for the design of directional alloy solidiÿcation processes is addressed such that a desired growth velocity v f under stable growth conditions is achieved. An externally imposed magnetic ÿeld is introduced to facilitate the design process and to reduce macrosegregation by the damping of melt ow. The design problem is posed as a functional optimization problem. The unknowns of the design problem are the thermal boundary conditions. The cost functional is taken as the square of the L 2 norm of an expression representing the deviation of the freezing interface thermal conditions from the conditions corresponding to local thermodynamic equilibrium. The adjoint method for the inverse design of continuum processes is adopted in this work. A continuum adjoint system is derived to calculate the adjoint temperature, concentration, velocity and electric potential ÿelds such that the gradient of the L 2 cost functional can be expressed analytically. The cost functional minimization process is realized by the conjugate gradient method via the FE solutions of the continuum direct, sensitivity and adjoint problems. The developed formulation is demonstrated with an example of designing the boundary thermal uxes for the directional growth of a germanium melt with dopant impurities in the presence of an externally applied magnetic ÿeld. The design is shown to achieve a stable interface growth at a prescribed desired growth rate.

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“…If the enthalpy extraction was not sufficient to avoid the need for a scramjet engine, the MHD power generator could still lower inlet temperatures to tolerable levels. As well the addition of a bypass system to further accelerate the exhaust gases could increase the specific thrust of the engine during off-design conditions and flow control [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Combined Magnetohydrodynamic and Geometric Optimization of a Hypersonic Inlet

Subbarao

Goss

2009

International Journal of Aerospace Engineering

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This paper considers the numerical optimization of a double ramp scramjet inlet using magnetohydrodynamic (MHD) effects together with inlet ramp angle changes. The parameter being optimized is the mass capture at the throat of the inlet, such that spillage effects for less than design Mach numbers are reduced. The control parameters for the optimization include the MHD effects in conjunction with ramp angle changes. To enhance the MHD effects different ionization scenarios depending upon the alignment of the magnetic field are considered. The flow solution is based on the Advection Upstream Splitting Method (AUSM) that accounts for the MHD source terms as well. A numerical Broyden-Flecher-Goldfarb-Shanno-(BFGS-) based procedure is utilized to optimize the inlet mass capture. Numerical validation results compared to published results in the literature as well as the outcome of the optimization procedure are summarized to illustrate the efficacy of the approach.

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A functional optimization approach to an inverse magneto-convection problem

Cited by 25 publications

References 29 publications

Conjugate gradient method for the Robin inverse problem associated with the Laplace equation

Conjugate gradient method for the Robin inverse problem associated with the Laplace equation

Inverse design of directional solidification processes in the presence of a strong external magnetic field

Combined Magnetohydrodynamic and Geometric Optimization of a Hypersonic Inlet

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