Doubly asymptotic approximations (DAAs) are approximate temporal impedance relations for a medium in contact with a flexible body. In this paper, the method of operator matching previously used for external acoustic domains is used to develop first- and second-order boundary integral DAAs for internal acoustic domains. Corresponding boundary element forms permit the numerical solution of transient structural acoustics problems with complex geometry. The accuracy of the DAAs is assessed in the following companion paper by comparing DAA and exact solutions for a canonical problem with spherical geometry.

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