Article

# The accurate numerical inversion of laplace transforms

01/1979; DOI: 10.1093/imamat/23.1.97

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**ABSTRACT:**[1] A flowing partially penetrating well with infinitesimal well skin is a mixed boundary because a Cauchy condition is prescribed along the screen length and a Neumann condition of no flux is stipulated over the remaining unscreened part. An analytical approach based on the integral transform technique is developed to determine the Laplace domain solution for such a mixed boundary problem in a confined aquifer of finite thickness. First, the mixed boundary is changed into a homogeneous Neumann boundary by substituting the Cauchy condition with a Neumann condition in terms of well bore flux that varies along the screen length and is time dependent. Despite the well bore flux being unknown a priori, the modified model containing this homogeneous Neumann boundary can be solved with the Laplace and the finite Fourier cosine transforms. To determine well bore flux, screen length is discretized into a finite number of segments, to which the Cauchy condition is reinstated. This reinstatement also restores the relation between the original model and the solutions obtained. For a given time, the numerical inversion of the Laplace domain solution yields the drawdown distributions, well bore flux, and the well discharge. This analytical approach provides an alternative for dealing with the mixed boundary problems, especially when aquifer thickness is assumed to be finite.Water Resources Research. 06/2002; 38(6). - [Show abstract] [Hide abstract]

**ABSTRACT:**A review has been made for the previous studies on safety of a geologic repository for high-level radioactive wastes (HLW) related to autocatalytic criticality phenomena with positive reactivity feedback. Neutronic studies on geometric and materials configuration consisting of rock, water and thermally fissile materials and the radionuclide migration and accumulation studies were performed previously for the Yucca Mountain Repository and a hypothetical water-saturated repository for vitrified HLW. In either case, it was concluded that it would be highly unlikely for an autocatalytic criticality event to happen at a geologic repository. Remaining scenarios can be avoided by careful selection of a repository site, engineered-barrier design and conditioning of solidified HLW. Thus, criticality safety should be properly addressed in regulations and site selection criteria. The models developed for radiological safety assessment to obtain conservatively overestimated exposure dose rates to the public may not be used directly for the criticality safety assessment, where accumulated fissile materials mass needs to be conservatively overestimated. The models for criticality safety also require more careful treatment of geometry and heterogeneity in transport paths because a minimum critical mass is sensitive to geometry of fissile materials accumulation.Nuclear Engineering and Technology 01/2006; 38(6). · 0.58 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**New methods are proposed for the numerical evaluation of f(𝐀) or f(𝐀)b, where f(𝐀) is a function such as 𝐀 1/2 or log(𝐀) with singularities in (-∞,0] and 𝐀 is a matrix with eigenvalues on or near (0,∞). The methods are based on combining contour integrals evaluated by the periodic trapezoid rule with conformal maps involving Jacobi elliptic functions. The convergence is geometric, so that the computation of f(𝐀)b is typically reduced to one or two dozen linear system solves, which can be carried out in parallel.SIAM Journal on Numerical Analysis 01/2008; 46(5). · 1.48 Impact Factor

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