Abstract
As previously demonstrated, the generalized Adams method (GAM) is effective for solving underwater acoustic wave-propagation problems. In this paper, we describe how to modify an earlier GAM implementation to substantially improve its efficiency. An approximation to the matrix exponential is required to implement a GAM. By using a rational approximation implicitily, the sparsity of the matrix can be exploited to produce a significantly more efficient implementation for a wide class of problems. A further improvement in efficiency can be gained by using a Restricted-Pade approximation to the matrix exponential, rather than the more traditional Pade approximation. To demonstrate the effectiveness of this approach, an underwater acoustic wave-propagation problem in a wedge-shaped region is solved by both the modified and unmodified GAM implementations.
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