Finite Element Computation Of Linearized Thermoelectric Effectswith P-Adaptivity
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Date
2010-12
Authors
Tan, Yi Fung
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
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.
Description
Keywords
Linearized Thermoelectric , Effectswith P-Adaptivity