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Second-order cross terms in monte carlo differential operator perturbation estimates.

DE2001776530

Publication Date	2001
Personal Author	Favorite, J. A.; Parsons, D. K.
Page Count	17
Abstract	Given some initial, unperturbed problem and a desired perturbation, a second-order accurate Taylor series perturbation estimate for a Monte Carlo tally that is a function of two or more perturbed variables can be obtained using an implementation of the differential operator method that ignores cross terms, such as in MCNP4C(trademark). This requires running a base case defined to be halfway between the perturbed and unperturbed states of all of the perturbed variables and doubling the first-order estimate of the effect of perturbing from the 'midpoint' base case to the desired perturbed case. The difference between such a midpoint perturbation estimate and the standard perturbation estimate (using the endpoints) is a second-order estimate of the sum of the second-order cross terms of the Taylor series expansion. This technique is demonstrated on an analytic fixed-source problem, a Godiva k(sub eff) eigenvalue problem, and a concrete shielding problem. The effect of ignoring the cross terms in all three problems is significant.
Keywords	Concretes Shielding Eigenvalues Implementation Series expansion
Source Agency	Technical Information Center Oak Ridge Tennessee
NTIS Subject Category	77F - Radiation Shielding, Protection, & Safety
Corporate Authors	Los Alamos National Lab., NM.; Department of Energy, Washington, DC.
Document Type	Conference Proceedings
NTIS Issue Number	200125
Contract Number	W-7405-ENG-36

Second-order cross terms in monte carlo differential operator perturbation estimates.

Second-order cross terms in monte carlo differential operator perturbation estimates.
DE2001776530

Publication Date	2001
Personal Author	Favorite, J. A.; Parsons, D. K.
Page Count	17
Abstract	Given some initial, unperturbed problem and a desired perturbation, a second-order accurate Taylor series perturbation estimate for a Monte Carlo tally that is a function of two or more perturbed variables can be obtained using an implementation of the differential operator method that ignores cross terms, such as in MCNP4C(trademark). This requires running a base case defined to be halfway between the perturbed and unperturbed states of all of the perturbed variables and doubling the first-order estimate of the effect of perturbing from the 'midpoint' base case to the desired perturbed case. The difference between such a midpoint perturbation estimate and the standard perturbation estimate (using the endpoints) is a second-order estimate of the sum of the second-order cross terms of the Taylor series expansion. This technique is demonstrated on an analytic fixed-source problem, a Godiva k(sub eff) eigenvalue problem, and a concrete shielding problem. The effect of ignoring the cross terms in all three problems is significant.
Keywords	Concretes Shielding Eigenvalues Implementation Series expansion
Source Agency	Technical Information Center Oak Ridge Tennessee
NTIS Subject Category	77F - Radiation Shielding, Protection, & Safety
Corporate Authors	Los Alamos National Lab., NM.; Department of Energy, Washington, DC.
Document Type	Conference Proceedings
NTIS Issue Number	200125
Contract Number	W-7405-ENG-36