Abstract
This paper presents a substantially more economical technique for the boundary element analysis (BEA) of a large class of nonlinear heat transfer problems including those with temperature dependent conductivity, temperature dependent convection coefficients, and radiation boundary conditions. The technique involves an exact static condensation of boundary element zones in a multi-zone boundary element model. The condensed boundary element zone contributions to be overall sparse blocked boundary element system matrices are formed once in the first step of the iterative nonlinear solution process and subsequently reused as the nonlinear parts of the overall problem are evolved to a convergent solution. Through a series of example problems it is demonstrated that the zone condensation technique facilitates the use of highly convergent iterative strategies for the solution of the nonlinear heat transfer problem involving modification and subsequent factorization of the overall boundary element system left had side matrix. For heat transfer problems with localized nonlinear effects, the condensation technique is shown to allow for the solution of nonlinear problems in less than half the CPU time required by methods that do not employ condensation.
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Communicated by S. N. Atluri, November 6, 1989
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Kane, J.H., Wang, H. & Kumar, B.L.K. Nonlinear thermal analysis with a boundary element zone condensation technique. Computational Mechanics 7, 107–122 (1990). https://doi.org/10.1007/BF00375925
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DOI: https://doi.org/10.1007/BF00375925