Reproducing kernel particle method and its modification

Vratislava Mošová

Mathematica Bohemica (2010)

  • Volume: 135, Issue: 4, page 383-392
  • ISSN: 0862-7959

Abstract

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Meshless methods have become an effective tool for solving problems from engineering practice in last years. They have been successfully applied to problems in solid and fluid mechanics. One of their advantages is that they do not require any explicit mesh in computation. This is the reason why they are useful in the case of large deformations, crack propagations and so on. Reproducing kernel particle method (RKPM) is one of meshless methods. In this contribution we deal with some modifications of the RKPM. The construction of the methods considered is given together with simple examples of their applications to solving boundary value problems.

How to cite

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Mošová, Vratislava. "Reproducing kernel particle method and its modification." Mathematica Bohemica 135.4 (2010): 383-392. <http://eudml.org/doc/196669>.

@article{Mošová2010,
abstract = {Meshless methods have become an effective tool for solving problems from engineering practice in last years. They have been successfully applied to problems in solid and fluid mechanics. One of their advantages is that they do not require any explicit mesh in computation. This is the reason why they are useful in the case of large deformations, crack propagations and so on. Reproducing kernel particle method (RKPM) is one of meshless methods. In this contribution we deal with some modifications of the RKPM. The construction of the methods considered is given together with simple examples of their applications to solving boundary value problems.},
author = {Mošová, Vratislava},
journal = {Mathematica Bohemica},
keywords = {meshless method; partition of unity; reproducing kernel particle method; reproducing kernel hierarchical partition of unity; enriched reproducing kernel particle method; meshless method; partition of unity; reproducing kernel particle method; reproducing kernel hierarchical partition of unity; enriched reproducing kernel particle method},
language = {eng},
number = {4},
pages = {383-392},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Reproducing kernel particle method and its modification},
url = {http://eudml.org/doc/196669},
volume = {135},
year = {2010},
}

TY - JOUR
AU - Mošová, Vratislava
TI - Reproducing kernel particle method and its modification
JO - Mathematica Bohemica
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 135
IS - 4
SP - 383
EP - 392
AB - Meshless methods have become an effective tool for solving problems from engineering practice in last years. They have been successfully applied to problems in solid and fluid mechanics. One of their advantages is that they do not require any explicit mesh in computation. This is the reason why they are useful in the case of large deformations, crack propagations and so on. Reproducing kernel particle method (RKPM) is one of meshless methods. In this contribution we deal with some modifications of the RKPM. The construction of the methods considered is given together with simple examples of their applications to solving boundary value problems.
LA - eng
KW - meshless method; partition of unity; reproducing kernel particle method; reproducing kernel hierarchical partition of unity; enriched reproducing kernel particle method; meshless method; partition of unity; reproducing kernel particle method; reproducing kernel hierarchical partition of unity; enriched reproducing kernel particle method
UR - http://eudml.org/doc/196669
ER -

References

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  4. Joyot, P., Trunzier, J., Chinesta, F., Enriched reproducing kernel approximation: Reproducing functions with discontinuous derivatives, Meshfree methods for partial differential equation II, Springer, Berlin, 2004, pp. 93-107. MR2278265
  5. Li, S., Liu, W. K., 10.1002/(SICI)1097-0207(19990530)45:3<251::AID-NME583>3.0.CO;2-I, Internat. J. Numer. Methods Engrg. 45 (1999), 251-317. (1999) Zbl0945.74079MR1688030DOI10.1002/(SICI)1097-0207(19990530)45:3<251::AID-NME583>3.0.CO;2-I

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