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 non- homogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The an- alyzed 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 ran- domly distributed in the 3D analyzed domain and each node is surrounded by a spherical subdo- main to which a local integral equation is applied. The meshless approximation based on the Mov- ing Least-Squares (MLS) method is employed for the implementation. Several example problems with Dirichlet, mixed, and/or convection bound- ary conditions, are presented to demonstrate the veracity and effectiveness of the numerical ap-
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