An implementation of a Fourier series method for the numerical inversion of the Laplace transform

D’Amore, Luisa; Laccetti, Giuliano; Murli, A.

doi:10.1145/326147.326148

Cited by 52 publications

(35 citation statements)

References 15 publications

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“…In order to show that these assumptions are reasonable and to show the error resulting from decoupling of the whole process, the results from the present model are compared with those from numerical simulator TOUGH 2. An automatic Laplace inversion technique developed by D' Amore et al [53] based on Fourier series is used in the present model to obtain the values in the time space. Figure 2 shows spatial discretization of the rock formation for the numerical calculation by using TOUGH2.…”

Section: Methods Validationmentioning

confidence: 99%

An Approximate Solution for Predicting the Heat Extraction and Preventing Heat Loss from a Closed-Loop Geothermal Reservoir

Feng

et al. 2017

Geofluids

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Approximate solutions are found for a mathematical model developed to predict the heat extraction from a closed-loop geothermal system which consists of two vertical wells (one for injection and the other for production) and one horizontal well which connects the two vertical wells. Based on the feature of slow heat conduction in rock formation, the fluid flow in the well is divided into three stages, that is, in the injection, horizontal, and production wells. The output temperature of each stage is regarded as the input of the next stage. The results from the present model are compared with those obtained from numerical simulator TOUGH2 and show first-order agreement with a temperature difference less than 4 ∘ C for the case where the fluid circulated for 2.74 years. In the end, a parametric study shows that (1) the injection rate plays dominant role in affecting the output performance, (2) higher injection temperature produces larger output temperature but decreases the total heat extracted given a specific time, (3) the output performance of geothermal reservoir is insensitive to fluid viscosity, and (4) there exists a critical point that indicates if the fluid releases heat into or absorbs heat from the surrounding formation.

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Section: Methods Validationmentioning

confidence: 99%

An Approximate Solution for Predicting the Heat Extraction and Preventing Heat Loss from a Closed-Loop Geothermal Reservoir

Feng

et al. 2017

Geofluids

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“…Based on Fourier series, D'Amore et al [11] presented another inversion algorithm and made a suitable choice of the free parameters by means of the error analysis. Their solution is expressed as [11]:…”

Section: From Talbot Methods To Fixed-talbot Algorithmmentioning

confidence: 99%

Performance comparison of numerical inversion methods for Laplace and Hankel integral transforms in engineering problems

Naeeni

Campagna

Eskandari‐Ghadi

et al. 2015

Applied Mathematics and Computation

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“…However the convergence is slow and the method is computationally prohibitive when multiple time domain evaluations are needed. The Fourier Series technique of De Hoog (De Hoog et al 1982;D'Amore et al 1999) is a good choice because it is highly efficient for multiple time evaluations and straightforward to program. In this algorithm, the path of the contour integration of (11) is discretized as:…”

Section: Inversion Of the Laplace Transformmentioning

confidence: 99%

Parameter estimation for a leaky integrate-and-fire neuronal model from ISI data

Mullowney

Iyengar

2007

J Comput Neurosci

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The Ornstein-Uhlenbeck process has been proposed as a model for the spontaneous activity of a neuron. In this model, the firing of the neuron corresponds to the first passage of the process to a constant boundary, or threshold. While the Laplace transform of the first-passage time distribution is available, the probability distribution function has not been obtained in any tractable form. We address the problem of estimating the parameters of the process when the only available data from a neuron are the interspike intervals, or the times between firings. In particular, we give an algorithm for computing maximum likelihood estimates and their corresponding confidence regions for the three identifiable (of the five model) parameters by numerically inverting the Laplace transform. A comparison of the two-parameter algorithm (where the time constant tau is known a priori) to the three-parameter algorithm shows that significantly more data is required in the latter case to achieve comparable parameter resolution as measured by 95% confidence intervals widths. The computational methods described here are a efficient alternative to other well known estimation techniques for leaky integrate-and-fire models. Moreover, it could serve as a template for performing parameter inference on more complex integrate-and-fire neuronal models.

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An implementation of a Fourier series method for the numerical inversion of the Laplace transform

Cited by 52 publications

References 15 publications

An Approximate Solution for Predicting the Heat Extraction and Preventing Heat Loss from a Closed-Loop Geothermal Reservoir

An Approximate Solution for Predicting the Heat Extraction and Preventing Heat Loss from a Closed-Loop Geothermal Reservoir

Performance comparison of numerical inversion methods for Laplace and Hankel integral transforms in engineering problems

Parameter estimation for a leaky integrate-and-fire neuronal model from ISI data

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