Abstract
This paper investigates the a posteriori finite element bound method applied to a heat transfer problem in a multi-material electronic components array. The temperature field is obtained by solving Poisson equations and convection–diffusion equations in different regions of the computational domain. The bound method calculates very sharp lower and upper bounds of the temperature of the hottest component which is assumed to be the engineering output of interest. This paper shows that for this two-dimensional problem the bound method can yield more than an 80-fold reduction in simulation time over a fine mesh calculation (330,050 d.o.f.) while still maintaining quantitative control over the accuracy of the engineering output of interest. Parallel implementation on a Beowulf cluster is also reported.
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