### Abstract

A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously nonhomogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The analyzed domain is covered by small subdomains with a simple geometry. A weak formulation for the set of governing equations is transformed into local integral equations on local subdomains by using a unit test function. Nodal points are randomly distributed in the 3D analyzed domain and each node is surrounded by a spherical subdomain to which a local integral equation is applied. The meshless approximation based on the Moving Least-Squares (MLS) method is employed for the implementation. Several example problems with Dirichlet, mixed, and/or convection boundary conditions, are presented to demonstrate the veracity and effectiveness of the numerical approach.

Original language | English |
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Pages (from-to) | 161-174 |

Number of pages | 14 |

Journal | CMES - Computer Modeling in Engineering and Sciences |

Volume | 32 |

Issue number | 3 |

State | Published - Dec 4 2008 |

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### Keywords

- Heaviside step function
- Laplace transform
- Local weak form
- Meshless method
- Moving least squares interpolation

### Cite this

*CMES - Computer Modeling in Engineering and Sciences*,

*32*(3), 161-174.