Sentence examples for benchmark problems are developed from inspiring English sources

Benchmark problems are developed to examine the accuracy and efficiency of the proposed element for a wide range of material properties including the limiting cases of shear compliant and shear rigid laminates.

A previous benchmark problem was developed by one of the authors (RPG) for two similar oil well logging problems (Gardner and Verghese, 1991, [1]).

But problems were developing under the surface.

Several numerical benchmark problems are analyzed.

Some benchmark problems are solved to support our discussion.

Several benchmark problems are solved using the proposed method.

Numerical results for typical benchmark problems are presented and analyzed.

Implementations of the benchmark problems are provided as Additional files 2 and 3.

In comparison, our benchmark problems are typically smaller and address the more specific need of evaluating algorithms identifying both structure and parameters, fully specifying problems as optimization problems.

The design method is applied to the JSAE-SICE benchmark problem which is developed using GT-SUITE of Gamma Technologies, Inc. and integrated with Simulink / MATLAB.

A system of benchmark problems is proposed for future reference.