A Matlab Implementation of an Algorithm for Computing Integrals of Products of Bessel Functions

Deun, Joris Van; Cools, Ronald

doi:10.1007/11832225_29

Cited by 4 publications

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References 23 publications

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“…The main motivation for writing this paper is that the algorithm presented here effectively improves the performance of the program in [24]. For the test set discussed in [25], the number of evaluations of the incomplete gamma function is reduced from 2,027 to 177, with a reduction in time from 0.57 to 0.08 s (there is some organisational overhead in the recurrence relation).…”

Section: Introductionmentioning

confidence: 99%

A stable recurrence for the incomplete gamma function with imaginary second argument

Deun

Cools

2006

Numer. Math.

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Even though the two term recurrence relation satisfied by the incomplete gamma function is asymptotically stable in at least one direction, for an imaginary second argument there can be a considerable loss of correct digits before stability sets in. We present an approach to compute the recurrence relation to full precision, also for small values of the arguments, when the first argument is negative and the second one is purely imaginary. A detailed analysis shows that this approach works well for all values considered.

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Section: Introductionmentioning

confidence: 99%

A stable recurrence for the incomplete gamma function with imaginary second argument

Deun

Cools

2006

Numer. Math.

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Electromagnetic Response of a Large Circular Loop Source on a Layered Earth: A New Computation Method

Singh

Mogi

2005

Pure appl. geophys.

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Integral expressions of electromagnetic (EM) field components due to a large circular loop source carrying an alternating (ac) current and placed on or above the surface of a layered earth model are transformed to such suitable forms that facilitate numerical computation of field response in quasi-static as well as non-quasi-static regions. The improper integrals occurring in expressions of EM field components are evaluated by converting these integrals into the convergent integrals using the process of subtraction or addition of an integral expression inside the integral sign and subsequently adjusting it or its equivalent analytic expression outside the integral sign. The adjusted integral expressions, in turn, are evaluated using the functional relationships described in this paper. The computation method based on this formulation takes into consideration the effects of both conduction as well as displacement currents, and is well suitable for any position of the source loop either in the air or on the surface of the model, in contrary to the earlier methods which face convergence problem. Moreover, the formulation is equally efficient for computing the EM response at any arbitrary receiver position either inside or outside the source loop. For illustrating the accuracy and applicability of the method and studying the nature of EM response of a loop source over a layered earth model, we have applied it for the computation of amplitude and phase of H z field over the various 2-layer and 3-layer models. Results show their characteristic variations, and depict good resolution for the subsurface layering. The results are in agreement with those of the published results for the quasi-static region, and are new extension of quasi-static variation in the non-quasi-static region. The agreement of computed results with published results demonstrates the accuracy of the method. Moreover, this is the initial presentation of numerical results for an arbitrary in-loop point (other than the center point) inside a large circular loop source.

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Note on ``Electromagnetic Response of a Large Circular Loop Source on a Layered Earth: A New Computation Method'' by N. P. Singh and T. Mogi

Deun

Cools

2007

Pure appl. geophys.

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A Matlab Implementation of an Algorithm for Computing Integrals of Products of Bessel Functions

Cited by 4 publications

References 23 publications

A stable recurrence for the incomplete gamma function with imaginary second argument

A stable recurrence for the incomplete gamma function with imaginary second argument

Electromagnetic Response of a Large Circular Loop Source on a Layered Earth: A New Computation Method

Note on ``Electromagnetic Response of a Large Circular Loop Source on a Layered Earth: A New Computation Method'' by N. P. Singh and T. Mogi

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