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An improved meshless method with almost interpolation property for isotropic heat conduction problems. (English) Zbl 1287.80007
Summary: In the paper an improved element free Galerkin method is presented for heat conduction problems with heat generation and spatially varying conductivity. In order to improve computational efficiency of meshless method based on Galerkin weak form, the nodal influence domain of meshless method is extended to have arbitrary polygon shape. When the dimensionless size of the nodal influence domain approaches 1, the Gauss quadrature point only contributes to those nodes in whose background cell the Gauss quadrature point is located. Thus, the bandwidth of global stiff matrix decreases obviously and the node search procedure is also avoided. Moreover, the shape functions almost possess the Kronecker delta function property, and essential boundary conditions can be implemented without any difficulties. Numerical results show that arbitrary polygon shape nodal influence domain not only has high computational accuracy, but also enhances computational efficiency of meshless method greatly.

MSC:
80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
80A20 Heat and mass transfer, heat flow (MSC2010)
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