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A New Class of Grid-Free Monte Carlo Algorithms for Elliptic Boundary Value Problems

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Numerical Methods and Applications (NMA 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2542))

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Abstract

In this paper we consider the following mathematical model: an elliptic boundary value problem, where the partial differential equation contains advection, diffusion, and deposition parts. A Monte Carlo (MC) method to solve this equation uses a local integral representation by the Green's function and a random process called “Walks on Balls”(WOB). A new class of grid free MC algorithms for solving the above elliptic boundary value problem is suggested and studied. We prove that the integral transformation kernel can be taken as a transition density function in the Markov chain in the case when the deposition part is equal to zero. An acceptance-rejection (AR) and an inversetransformation methods are used to sample the next point in the Markov chain. An estimate for the efficiency of the AR method is obtained.

Supported by Center of Excellence BIS-21 grant ICA1-2000-70016 and by the NSF of Bulgaria under Grants I-1201/02 and MM-902/99

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Author information

Authors and Affiliations

  1. Central Laboratory for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev St., bl. 25A, 1113, Sofia, Bulgaria

    R.J. Papancheva, I. T. Dimov & T. V. Gurov

Authors
  1. R.J. Papancheva
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  2. I. T. Dimov
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  3. T. V. Gurov
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Editor information

Editors and Affiliations

  1. Central Laboratory for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, bl. 25A, 1113, Sofia, Bulgaria

    Ivan Dimov , Ivan Lirkov  & Svetozar Margenov ,  & 

  2. National Environmental Research Institute, Frederiksborgvej 399, P.O. Box 358, 4000, Roskilde, Denmark

    Zahari Zlatev

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© 2003 Springer-Verlag Berlin Heidelberg

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Papancheva, R., Dimov, I.T., Gurov, T.V. (2003). A New Class of Grid-Free Monte Carlo Algorithms for Elliptic Boundary Value Problems. In: Dimov, I., Lirkov, I., Margenov, S., Zlatev, Z. (eds) Numerical Methods and Applications. NMA 2002. Lecture Notes in Computer Science, vol 2542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36487-0_14

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  • DOI: https://doi.org/10.1007/3-540-36487-0_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00608-4

  • Online ISBN: 978-3-540-36487-0

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