基于泰勒级数的P波旅行时方程的计算精度受到具有垂直对称轴的横向各向同性(Transverse Isotropy Medium with Vertical Symmetry Axis,VTI)介质的影响,为了改善这种情况,提出一种基于平方处理与系数匹配的计算方法。首先,利用平方处理...基于泰勒级数的P波旅行时方程的计算精度受到具有垂直对称轴的横向各向同性(Transverse Isotropy Medium with Vertical Symmetry Axis,VTI)介质的影响,为了改善这种情况,提出一种基于平方处理与系数匹配的计算方法。首先,利用平方处理将非平方形式的基于泰勒级数的旅行时公式转换为包含高阶项的平方形式;再使用系数匹配法处理旅行时平方公式的高阶项,保持方程炮检距的最高阶为常用的4阶;然后,在简化参数形式与优化旅行时平方公式计算的基础上,得到与各向异性参数相关的新系数y;最后,形成了含有y的基于平方处理与系数匹配的4阶P波旅行时计算方法。基于水平层状VTI介质模型的实验结果表明,与有理近似算法、三射线广义时差近似计算法和扩展广义时差计算法相比,该方法计算误差更小,同时远炮检距处的计算能力得到一定提高,从而给以旅行时方程为基础的应用提供了更多选择。展开更多
We sttidy the problem of scheduling n jobs on m parallel bounded batch machines to minimize the sum of squared machine loads. Each batch contains at most B jobs, and the processing time of a batch is equal to the long...We sttidy the problem of scheduling n jobs on m parallel bounded batch machines to minimize the sum of squared machine loads. Each batch contains at most B jobs, and the processing time of a batch is equal to the longest processing time of the jobs in this batch. We prove this problem to be NP-hard. Furthermore, we present a polynomial time approximation scheme （PTAS） and a fully polynomial time approximation scheme （FPTAS） for this problem.展开更多
With the intermediate flow states predicted by local two phase Riemann problem,the modified ghost fluid method(MGFM)and its variant(r GFM)have been widely employed to resolve the interface condition in the simulation ...With the intermediate flow states predicted by local two phase Riemann problem,the modified ghost fluid method(MGFM)and its variant(r GFM)have been widely employed to resolve the interface condition in the simulation of compressible multi-medium flows.In this work,the drawback of the construction procedure of local two phase Riemann problem in r GFM was investigated in detail,and a refined version of the construction procedure was specially developed to make the simulation of underwater explosion bubbles more accurate and robust.Beside the refined r GFM,the fast and accurate particle level set method was also adopted to achieve a more effective and computationally efficient capture of the evolving multi-medium interfaces during the simulation.To demonstrate the improvement brought by current refinement,several typical numerical examples of underwater explosion bubbles were performed with original r GFM and refined r GFM,respectively.The results indicate that,when compared with original r GFM,numerical oscillations were effectively removed with the proposed refinement.Accordingly,with present refined treatment of interface condition,a more accurate and robust simulation of underwater explosion bubbles was accomplished in this work.展开更多
文摘基于泰勒级数的P波旅行时方程的计算精度受到具有垂直对称轴的横向各向同性(Transverse Isotropy Medium with Vertical Symmetry Axis,VTI)介质的影响,为了改善这种情况,提出一种基于平方处理与系数匹配的计算方法。首先,利用平方处理将非平方形式的基于泰勒级数的旅行时公式转换为包含高阶项的平方形式;再使用系数匹配法处理旅行时平方公式的高阶项,保持方程炮检距的最高阶为常用的4阶;然后,在简化参数形式与优化旅行时平方公式计算的基础上,得到与各向异性参数相关的新系数y;最后,形成了含有y的基于平方处理与系数匹配的4阶P波旅行时计算方法。基于水平层状VTI介质模型的实验结果表明,与有理近似算法、三射线广义时差近似计算法和扩展广义时差计算法相比,该方法计算误差更小,同时远炮检距处的计算能力得到一定提高,从而给以旅行时方程为基础的应用提供了更多选择。
文摘We sttidy the problem of scheduling n jobs on m parallel bounded batch machines to minimize the sum of squared machine loads. Each batch contains at most B jobs, and the processing time of a batch is equal to the longest processing time of the jobs in this batch. We prove this problem to be NP-hard. Furthermore, we present a polynomial time approximation scheme （PTAS） and a fully polynomial time approximation scheme （FPTAS） for this problem.
基金supported by the National Natural Science Foundation of China(Grant Nos.041322062 and 51075004)the Foundation of Zhejiang Educational Committee(Grant No.529003+G21144)
文摘With the intermediate flow states predicted by local two phase Riemann problem,the modified ghost fluid method(MGFM)and its variant(r GFM)have been widely employed to resolve the interface condition in the simulation of compressible multi-medium flows.In this work,the drawback of the construction procedure of local two phase Riemann problem in r GFM was investigated in detail,and a refined version of the construction procedure was specially developed to make the simulation of underwater explosion bubbles more accurate and robust.Beside the refined r GFM,the fast and accurate particle level set method was also adopted to achieve a more effective and computationally efficient capture of the evolving multi-medium interfaces during the simulation.To demonstrate the improvement brought by current refinement,several typical numerical examples of underwater explosion bubbles were performed with original r GFM and refined r GFM,respectively.The results indicate that,when compared with original r GFM,numerical oscillations were effectively removed with the proposed refinement.Accordingly,with present refined treatment of interface condition,a more accurate and robust simulation of underwater explosion bubbles was accomplished in this work.
