| Author | Pattaramon Tantichattanont |
| Call Number | AIT Thesis no. ST-01-4 |
| Subject(s) | Heat--Conduction
|
| Note | A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering, School of Engineering and Technology |
| Publisher | Asian Institute of Technology |
| Abstract | The mesh-based finite element method (FEM) and several recently developed meshfree methods obtain solutions for an entire problem domain, even if the solution is required only at a small set of points. In computing their respective solutions, integration of a weak form of the governing partial differential equations is typically carried out over the entire problem domain. Two approaches to eliminate the need for numerically integrating the weak form, and thus significantly reduce the computational effort required to obtain accurate solutions, are presented. The first approach, termed the meshless random walk (MR W) method, has the added benefit that it can generate solutions at a single point or a particular subset of the problem domain. In the MRW approach, Monte Carlo methods are applied to probabilistically determine a solution to the deterministic 2D boundary value problem. The second approach, termed the iterative moving least-squares (IMLS) method, generates solutions by applying a penalty method for imposing natural boundary conditions to the governing equations. A Galerkin approximation of the independent variables is then constructed using moving least-squares (MLS) approximation functions. Nodal unknowns are written as a function of the corresponding values at all visible nodes. The nodal solutions are then obtained by a Gauss-Seidel iterative process starting with an initial guess at each node and iterating until convergence of the solution is achieved. The versatility, simplicity and accuracy of the proposed methods are verified through a variety of numerical examples in 2D heat-conduction. With further refinements and extension of the proposed methods to solve problem in 2D elastostatics, it is expected that significant computational savings may be achieved when compared to currently employed meshless or mesh-based numerical methods. |
| Year | 2001 |
| Type | Thesis |
| School | School of Engineering and Technology (SET) |
| Department | Department of Civil and Infrastucture Engineering (DCIE) |
| Academic Program/FoS | Structural Engineering (STE) /Former Name = Structural Engineering and Construction (ST) |
| Chairperson(s) | Barry, William J.; |
| Examination Committee(s) | Pennung Warnitchai;Pichai Nimityongskul; |
| Scholarship Donor(s) | Asian Institute of Technology (Partial Scholarship) |
| Degree | Thesis (M.Eng.) - Asian Institute of Technology, 2001 |