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Abstract We give here a space‐time variational formula to the problem of the transient acoustic scattering by a free (pressure release) surface, using the retarded potential technique. From this formula, we obtain new schemes for the calculation of the potential density. We prove stability and convergence of such schemes: these are as far as we know, the first results in that direction for such problem. The case of a hard obstacle will be treated in the second part of the paper.
Duong et al. (Wed,) studied this question.