We solve the transient heat conduction equation in an L- shaped region using domain decomposition and boundary integrals. The iterations need to be carried out only on the interfaces between the subdomains unlike finite difference or finite element methods where the iterations are to be performed in the entire domain. Numerically, the problem reduces to the multiplication of dense matrices by vectors of boundary or initial values. The DAUB4 wavelet transform is used to compress the matrices which leads to computational advantage without loss of accuracy. This procedure, capable of parallel implementation, is an extension of the work of Zarantonello and Elton for Laplace equation in overlapping circular discs.
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