Heat conduction analysis by a Truly Meshless Method

The first part of this book discusses a numerical approach to solve two-dimensional heat conduction problems of layer composites with steady and transient states by implementing a Meshless Local Petrove-Galerkin (MLPG) method. At the second part, a similar approach is applied for analysis of three-dimensional steady state heat conduction problems. The penalty method is adopted to efficiently enforce the essential boundary condition. Among interpolation functions, due to the high continuity of the approximation function, the moving least squares (MLS) interpolation is selected. Also the Heaviside step function is considered as the test function. To resolve the problem of discontinuity in layers of composites, a new technique is proposed for the numerical integration process. To deal with time derivatives, the forward time differences are employed. Several numerical examples have been illustrated in both parts to prove the efficiency and accuracy of the considered approach.