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A 27-point optimal scheme for 3D frequency-domain scalar wave equation was recently developed. This scheme includes 9 optimization coefficients, and is relatively complicated. To simplify this scheme, a 19-point average-derivative optimal scheme for 3D frequency-domain scalar wave equation is constructed in this paper. This new 19-point scheme includes only 5 optimization coefficients, but maintains similar advantages of the 27-point optimal scheme. Compared to the classical 7-point scheme, the number of grid points per shortest wavelength is reduced from approximately 13 to approximately 4 by this 19-point optimal scheme for equal directional sampling intervals and unequal directional sampling intervals as well. Two numerical examples are presented to demonstrate the theoretical analysis.
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