Meshless fragile points methods based on Petrov‐Galerkin weak‐forms for transient heat conduction problems in complex anisotropic nonhomogeneous media

Regularized meshless method for nonhomogeneous problems

The regularized meshless method is a novel boundary-type meshless method but by now has largely been confined to homogeneous problems. In this paper, we apply the regularized meshless method to the nonhomogeneous problems in conjunction with the dual reciprocity technique in the evaluation of the particular solution. Numerical experiments of three benchmark nonhomogeneous problems demonstrate t...

A Meshless Method Based on Least-souares Approach for Steady- and Unsteady-state Heat Conduction Problems

The meshles.i method based on the least-squares approach, the rneshle.is weighted leastsquares (MWLS) method, is extended to soive conduction heat transfer problems. The MWLS formulation is first established for steady-state problems and then extended to unsteady-state problems with time-stepping schemes. Theoretiiai analy.us antl numerical examples indicate that larger time steps can be used i...

A Meshless Method Based on Least-squares Approach for Steady- and Unsteady-state Heat Conduction Problems

The meshless method based on the least-squares approach, the meshless weighted leastsquares (MWLS) method, is extended to solve conduction heat transfer problems. The MWLS formulation is first established for steady-state problems and then extended to unsteady-state problems with time-stepping schemes. Theoretical analysis and numerical examples indicate that larger time steps can be used in th...

Numerical solution of transient heat conduction problems using improved meshless local Petrov-Galerkin method

Meshless Local Petrov-Galerkin Method for Heat Conduction Problem in an Anisotropic Medium

Meshless methods based on the local Petrov-Galerkin approach are proposed for solution of steady and transient heat conduction problem in a continuously nonhomogeneous anisotropic medium. Fundamental solution of the governing partial differential equations and the Heaviside step function are used as the test functions in the local weak form. It is leading to derive local boundary integral equat...