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A 4th-order Implicit Procedure for the Simulation of Acoustics

This article is concerned with a new fourth-order implicit time-stepping scheme for the simulation of acoustic waves. For an enhanced efficiency, the new scheme is incorporated with a locally one-dimensional (LOD) procedure. Its stability and accuracy are analyzed and compared with those of the standard explicit fourth-order scheme. It has been observed from various experiments that the computational cost of the implicit LOD algorithm is only about 40% higher than that of the explicit method, for the problems of the same size in two space variables; the implicit procedure produces less dispersive solutions in heterogeneous media.