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Adaptive quadrature for sharply spiked integrands

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Abstract

A new adaptive quadrature algorithm that places a greater emphasis on cost reduction while still maintaining an acceptable accuracy is demonstrated. The different needs of science and engineering applications are highlighted as the existing algorithms are shown to be inadequate. The performance of the new algorithm is compared with the well known adaptive Simpson, Gauss-Lobatto and Gauss-Kronrod methods. Finally, scenarios where the proposed algorithm outperforms the existing ones are discussed.

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References

  1. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables. Dover, New York (1965)

    Google Scholar 

  2. Bowen, R.C., Frensley, W.R., Klimeck, G., Lake, R.K.: Transmission resonances and zeros in multiband models. Phys. Rev. B 52(4), 2754–2765 (1995). doi:10.1103/PhysRevB.52.2754

    Article  Google Scholar 

  3. Datta, S.: Quantum Transport. Cambridge University Press, Cambridge (2005)

    MATH  Google Scholar 

  4. Gander, W., Gautschi, W.: Adaptive quadrature–revisited. BIT Numer. Math. 40(1), 84–101 (2000). doi:10.1023/A:1022318402393

    Article  MathSciNet  Google Scholar 

  5. Klimeck, G., Lake, R., Bowen, R.C., Frensley, W.R., Moise, T.S.: Quantum device simulation with a generalized tunneling formula. Appl. Phys. Lett. 67(17), 2539–2541 (1995). doi:10.1063/1.114451. URL http://link.aip.org/link/?APL/67/2539/1

    Article  Google Scholar 

  6. Klimeck, G., Lake, R.K., Bowen, R.C., Fernando, C.L., Frensley, W.R.: Resolution of resonances in a general purpose quantum device simulator (NEMO). VLSI Des. 6(1–4), 107–110 (1998). doi:10.1155/1998/43043

    Article  Google Scholar 

  7. Kronrod, A.S.: Nodes and Weights of Quadrature Formulas. Sixteen-place Tables. Consultants Bureau, New York (1965)

    MATH  Google Scholar 

  8. McKeeman, W.M.: Algorithm 145: adaptive numerical integration by Simpson’s rule. Commun. ACM 5(12), 604 (1962). http://doi.acm.org/10.1145/355580.369102

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Purdue University, West Lafayette, IN, 47907, USA

    Samarth Agarwal

  2. School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, 47907, USA

    Michael Povolotskyi, Tillmann Kubis & Gerhard Klimeck

Authors
  1. Samarth Agarwal
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  2. Michael Povolotskyi
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  3. Tillmann Kubis
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  4. Gerhard Klimeck
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Correspondence to Samarth Agarwal.

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Agarwal, S., Povolotskyi, M., Kubis, T. et al. Adaptive quadrature for sharply spiked integrands. J Comput Electron 9, 252–255 (2010). https://doi.org/10.1007/s10825-010-0338-3

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  • DOI: https://doi.org/10.1007/s10825-010-0338-3

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