Finite Element Computation Of Linearized Thermoelectric Effectswith P-Adaptivity
| dc.contributor.author | Tan, Yi Fung | |
| dc.date.accessioned | 2019-10-02T08:22:33Z | |
| dc.date.available | 2019-10-02T08:22:33Z | |
| dc.date.issued | 2010-12 | |
| dc.description.abstract | With advances in microsystem technology, multiphysics simulations in which more than one physical nature are considered become increasingly important and pose challenges on the efficiency of their implementations through the finite element method (FEM). The research work was to implement an efficient yet accurate FEM computation of thermoelectric problems where two natures, heat and electric potential mutually interact. A set of partial differential equations (PDEs) describing thermoelectric effects were first formulated for three dimensional problems and transformed into the weak form using the Galerkin’s method. For a more efficient computation, constitutive thermoelectric equations were linearized with a reference temperature. Theoretically, the speedup of the linear approach is at least twofold of the nonlinear one. By using a direct or strong coupling, the method retains positive definiteness and symmetry of the system matrix. The algebraic equations were consequently amenable to the widely available matrix solver technology including preconditioned iterative solvers like the Conjugate Gradient with Successive Over-Relaxation (SORCG) method. Besides, padaptivity was implemented to reduce the discretization error by increasing the polynomial order of the approximation function in a similar manner as in single physics problem. The adaptivity strategy was achieved with an a posteriori error estimator, which was an explicit error estimation based on element-wise residuals and jumps at element boundaries. It was observed that although the error indicator did not fully contribute to theoretical convergence rate in error for three dimensional problems, it provided useful information on the quality of the local solution to effectively drive the p-adaptation. The method established in this work strongly suggests that the thermoelectric problems may well be computed with the p-adaptivity so that accurate results can be achieved without an excessive use of computational resources. | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/8915 | |
| dc.language.iso | en | en_US |
| dc.publisher | Universiti Sains Malaysia | en_US |
| dc.subject | Linearized Thermoelectric | en_US |
| dc.subject | Effectswith P-Adaptivity | en_US |
| dc.title | Finite Element Computation Of Linearized Thermoelectric Effectswith P-Adaptivity | en_US |
| dc.type | Thesis | en_US |
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