Compression of the Radiative Heat Transfer BEM Matrix of an Inductive Heating System Using a Block-Oriented Wavelet Transform

摘要

Inductive heating processes become more and more important, and therefore the interest in thermal effects of an inductive heating system increases. Radiative heat transfers are normally neglected even though these transfers affect the temperature of the inductive heating system up to ten percent. To compute radiative heat transfers a boundary element method (BEM) is of first choice, due to a surface-to-surface heat transfer. To counteract the general disadvantage of a BEM—the quadratic growth of the system matrix—an application is presented using an adapted version of the JPEG2000 standard, a file format for compressing graphic images. Furthermore, an arbitrary number $N$ of degree of freedom (DOF) can be used to set up the BEM system matrix, while an adapted block-oriented fast wavelet transform compresses the preponderant populated BEM system matrix. Finally, the BEM system of linear equations is solved at compressed state using a normal iterative solver with nearly the same number of iterative steps as in uncompressed state.