Errors due to split time stepping are discussed for an explicit free–surface ocean model. In commonly used split time stepping, the way of time integration for the barotropic momentum equation is not compatible with ...Errors due to split time stepping are discussed for an explicit free–surface ocean model. In commonly used split time stepping, the way of time integration for the barotropic momentum equation is not compatible with that of the baroclinic one. The baroclinic equation has three–time–level structure because of leapfrog scheme. The barotropic one, however, has two–time–level structure when represented in terms of the baroclinic time level, on which the baroclinic one is integrated. This incompatibility results in the splitting errors as shown in this paper. The proper split time stepping is therefore proposed in such a way that the compatibility is kept between the barotropic and baroclinic equations. Its splitting errors are shown extremely small, so that it is particularly relevant to long–term integration for climate studies. It is applied to a free–surface model for the North Pacific Ocean.展开更多
An error correction technique to achieve a 14-bit successive approximation register analog-to-digital converter(SAR ADC) is proposed. A tunable split capacitor is designed to eliminate the mismatches caused by parasit...An error correction technique to achieve a 14-bit successive approximation register analog-to-digital converter(SAR ADC) is proposed. A tunable split capacitor is designed to eliminate the mismatches caused by parasitic capacitors. The linearity error of capacitor array caused by process mismatch is calibrated by a novel calibration capacitor array that can improve the sampling rate. The dual-comparator topology ensures both the speed and precision of the ADC. The simulation results show that the SAR ADC after calibration achieves 83.07 dB SNDR and 13.5 bit ENOB at 500 kilosamples/s.展开更多
In this paper,the transient Navier-Stokes equations with damping are considered.Firstly,the semi-discrete scheme is discussed and optimal error estimates are derived.Secondly,a linearized backward Euler scheme is prop...In this paper,the transient Navier-Stokes equations with damping are considered.Firstly,the semi-discrete scheme is discussed and optimal error estimates are derived.Secondly,a linearized backward Euler scheme is proposed.By the error split technique,the Stokes operator and the H^(-1)-norm estimate,unconditional optimal error estimates for the velocity in the norms L^(∞)(L^(2)) and L^(∞)(H^(1)),and the pressure in the norm L^(∞)(L^(2))are deduced.Finally,two numerical examples are provided to confirm the theoretical analysis.展开更多
基金Hundred Talent Program of Chinese Academy of Sciences under Grant No. 0300YQ000101. Partly supported by the National Natural Sci
文摘Errors due to split time stepping are discussed for an explicit free–surface ocean model. In commonly used split time stepping, the way of time integration for the barotropic momentum equation is not compatible with that of the baroclinic one. The baroclinic equation has three–time–level structure because of leapfrog scheme. The barotropic one, however, has two–time–level structure when represented in terms of the baroclinic time level, on which the baroclinic one is integrated. This incompatibility results in the splitting errors as shown in this paper. The proper split time stepping is therefore proposed in such a way that the compatibility is kept between the barotropic and baroclinic equations. Its splitting errors are shown extremely small, so that it is particularly relevant to long–term integration for climate studies. It is applied to a free–surface model for the North Pacific Ocean.
基金Supported by National Science and Technology Major Project of China(No.2012ZX03004008)
文摘An error correction technique to achieve a 14-bit successive approximation register analog-to-digital converter(SAR ADC) is proposed. A tunable split capacitor is designed to eliminate the mismatches caused by parasitic capacitors. The linearity error of capacitor array caused by process mismatch is calibrated by a novel calibration capacitor array that can improve the sampling rate. The dual-comparator topology ensures both the speed and precision of the ADC. The simulation results show that the SAR ADC after calibration achieves 83.07 dB SNDR and 13.5 bit ENOB at 500 kilosamples/s.
基金supported by Fundamental Research Funds for the Henan Provincial Colleges and Universities(No.20A110002).
文摘In this paper,the transient Navier-Stokes equations with damping are considered.Firstly,the semi-discrete scheme is discussed and optimal error estimates are derived.Secondly,a linearized backward Euler scheme is proposed.By the error split technique,the Stokes operator and the H^(-1)-norm estimate,unconditional optimal error estimates for the velocity in the norms L^(∞)(L^(2)) and L^(∞)(H^(1)),and the pressure in the norm L^(∞)(L^(2))are deduced.Finally,two numerical examples are provided to confirm the theoretical analysis.
