The phrase "as a benchmark solution" is correct and usable in written English.
It can be used when referring to a standard or reference point against which other solutions or performances can be measured.
Example: "We will evaluate the effectiveness of our new strategy as a benchmark solution to improve our overall performance."
Alternatives: "as a reference solution" or "as a standard solution".
The results obtained can be used as a benchmark solution.
This exact solution can serve as a benchmark solution for various approximate solutions.
Extended results are obtained to serve as a benchmark solution for other numerical techniques and specialized applications.
The presented solution can serve as a benchmark solution to the general problem of 3D acoustic scattering from axisymmetric inhomogeneities in ocean waveguides at low frequencies.
The offline scenario solution serves as a benchmark solution to check feasibility and optimality of generated trajectory subject to constraints on the states and controls.
The closed-form solution obtained in this paper can be used as a benchmark solution for the transient vibration of a two-span beam.
Thus, in this section, based on a benchmark solution as well as insights provided in last section, we will analyze the online scheduling with the assumption that the transmitter only has the knowledge of the energy amount of the current block and the probability density function of the harvesting energy and the channel gains.
Detailed simulation results at different flow and radiative regimes, as well as benchmark solutions, are presented and discussed.
The results obtained with the proposed hybrid approach are compared with direct Monte Carlo simulations, which have been considered as the benchmark solution.
The results of simulation using the coupled method are in excellent agreement with those of the pure DSMC method, which is taken as the benchmark solution.
A variety of new vibration results including frequencies and mode shapes for composite laminated cylindrical, conical, spherical shells and annular plates with classical and elastic restraints as well as different geometric and material parameters are presented, which may serve as benchmark solution for future researches.
