The cross sections of $e^+e^- \rightarrow K^+K^-J/\psi$ at center-of-mass energies from 4.127 to 4.600~GeV are measured based on 15.6 fb$^{-1}$ data collected with the BESIII detector operating at the BEPCII storage ring. Two resonant structures are observed in the line shape of the cross sections. The mass and width of the first structure are measured to be ($4225.3\pm2.3\pm21.5$) MeV and ($72.9\pm6.1\pm30.8$)~MeV, respectively. They are consistent with those of the established $Y(4230)$. The second structure is observed for the first time with a statistical significance greater than 8$\sigma$, denoted as $Y(4500)$. Its mass and width are determined to be ($4484.7\pm13.3\pm24.1$) MeV and ($111.1\pm30.1\pm15.2$) MeV, respectively. The first presented uncertainties are statistical and the second ones are systematic. The product of the electronic partial width with the decay branching fraction $ \Gamma(Y(4230)\to e^+ e^-) \mathcal{B}(Y(4230) \to K^+ K^- J/\psi)$ is reported.Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

The proposed parallel state transformation procedures (PSTP) of fiber beam-column elements and multi-layered shell elements, combined with the parallel factorization of Jacobian (PF), are incorporated into a finite element program. In PSTP, elements are classified into different levels of workload prior to state determination in order to balance workload among different threads. In PF, the multi-threaded version of OpenBLAS is adopted to compute super-nodes. A case study on four super high-rise buildings, i.e. S1~S4, has demonstrated that the combination of PSTP and PF does not have any observable influence on computational accuracy. As number of elements and DOFs increases, the ratio of time consumed in the formation of the Jacobian to that consumed in the solution of algebraic equations tends to decrease. The introduction of parallel solver can yield a substantial reduction in computational cost. Combination of PSTP and PF can give rise to a further significant reduction. The acceleration ratios associated with PSTP do not exhibit a significant decrease as PGA level increases. Even PGA level is equal to 2.0g, PSTP still can result in acceleration ratios of 2.56 and 1.92 for S1 and S4, respectively. It is verified that it is more effective to accelerate analysis by reducing the time spent in solving algebraic equations rather than reducing that spent in the formation of the Jacobian for super high-rise buildings.

The integrated luminosities of the XYZ data samples collected in 2016--2017 at center-of-mass energies between 4.19 and 4.28 GeV are measured with a precision better than 1% by analyzing large-angle Bhabha scattering events. The integrated luminosities of the data sets collected in 2010--2014 are updated by considering an additional correction related to the detector performance. These results are essential for precision measurements of the production cross sections of the charmonium and charmonium-like states.

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Using inclusive decays of the J/ψ, a precise determination of the number of J/ψ events collected with the BESIII detector is performed. For the two data sets taken in 2009 and 2012, the numbers of J/ψ events are recalculated to be (224.0±1.3)×10^6 and (1088.5±4.4)×10^6 respectively, which are in good agreement with the previous measurements. For the J/ψ sample taken in 2017–2019, the number of events is determined to be (8774.0±39.4)×10^6. The total number of J/ψ events collected with the BESIII detector is determined to be (10087±44)×10^6, where the uncertainty is dominated by systematic effects and the statistical uncertainty is negligible. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.