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We establish the accuracy of the PC representations within a reasonable error threshold through systematic convergence studies.
The DFT code has high systematic convergence properties, very good performances, and excellent efficiency on parallel computation.
A systematic convergence study is conducted to establish the accuracy of the method for long time inviscid simulations.
For this purpose, a systematic convergence measurement is usually implemented to adjust the design during the whole construction, and consequently deadly hazards can be prevented.
This allows for efficient calculation of the electronic structure of clusters (and molecules) with high accuracy and systematic convergence properties without the need for any artificial periodicity.
The key success factor for all the case studies presented in this study seems to come from the systematic convergence of technological competence and the visionary role of the development team.
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An overall second-order accuracy of the algorithm is verified in two systematic grid convergence tests.
Numerical results for several problems, including systematic grid convergence studies, MHD bow-shock flows, and global modelling of solar wind flow are discussed to demonstrate the accuracy and efficiency of the proposed solution procedure, along with assessment of parallel computing scalability for up to thousands of computing cores.
Thirdly, based on the relationship properties between the normalizing signal and all the signals in the closed-loop system and on some important mathematical tools on discrete-time systems, as in the continuous-time case, a systematic stability and convergence analysis approach to the discrete indirect MRAC scheme is developed rigorously.
Incremental passivity enables a systematic approach to study convergence to the steady state with zero frequency deviation and to design the controller in the presence of time-varying voltages, whereas the internal-model principle is applied to tackle the uncertain nature of the loads.
The key features are (a) systematic low-level moisture convergence with retained conservation of vertically integrated moist static energy, and (b) the use of three cumulus cloud types (congestus, stratiform, and deep convective) together with their differing vertical heating structures.
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