A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems i...A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.展开更多
A general and efficient parallel approach is proposed for the first time to parallelize the hybrid finiteelement-boundary-integral-multi-level fast multipole algorithm （FE-BI-MLFMA）. Among many algorithms of FE-BI-M...A general and efficient parallel approach is proposed for the first time to parallelize the hybrid finiteelement-boundary-integral-multi-level fast multipole algorithm （FE-BI-MLFMA）. Among many algorithms of FE-BI-MLFMA, the decomposition algorithm （DA） is chosen as a basis for the parallelization of FE-BI-MLFMA because of its distinct numerical characteristics suitable for parallelization. On the basis of the DA, the parallelization of FE-BI-MLFMA is carried out by employing the parallelized multi-frontal method for the matrix from the finiteelement method and the parallelized MLFMA for the matrix from the boundary integral method respectively. The programming and numerical experiments of the proposed parallel approach are carried out in the high perfor- mance computing platform CEMS-Liuhui. Numerical experiments demonstrate that FE-BI-MLFMA is efficiently parallelized and its computational capacity is greatly improved without losing accuracy, efficiency, and generality.展开更多
In order to master the magnetic field distribution of submarines in the air completely and exactly and study the magnetic stealthy performance of submarine,a mathematic model of submarine magnetic field extrapolation ...In order to master the magnetic field distribution of submarines in the air completely and exactly and study the magnetic stealthy performance of submarine,a mathematic model of submarine magnetic field extrapolation is built based on the boundary element method(BEM).An experiment is designed to measure three components of magnetic field on the envelope surface surrounding a model submarine.The data in different heights above the model submarine are obtained by use of tri-axial magnetometers.The results show that this extrapolation model has good stabilities and high accuracies compared the measured data with the extrapolated data.Moreover,the model can reflect the submarine magnetic field distribution in the air exactly,and is valuable in practical engineering.展开更多
研究了复杂微细导线电容矩阵提取边界元法(boundary element method,BEM)的边界离散问题以及增强计算精度和数值稳定性的有效措施,分析了开阔边界尺寸、开阔边界离散、导线离散对计算精度的影响以及伪解、矩阵奇异性问题,提出了基于导...研究了复杂微细导线电容矩阵提取边界元法(boundary element method,BEM)的边界离散问题以及增强计算精度和数值稳定性的有效措施,分析了开阔边界尺寸、开阔边界离散、导线离散对计算精度的影响以及伪解、矩阵奇异性问题,提出了基于导线离散迭代和开阔边界迭代两阶段自动迭代边界元算法(automatic iterative boundary element method,AIBEM),并结合实例阐述了全域法和区域分解法两种多层介质问题系数矩阵生成方法。研究结果表明,边界环内生成的系数矩阵存在误差均衡协调问题,对复杂模型需合理选择各线段离散单元数及开阔边界尺寸,通过AIBEM可以获得经济的离散参数,有效避免矩阵奇异性,并提高收敛稳定性。将计算结果与有限元法、解析法、传输线法、矩量法进行了对比分析,证实了算法的可靠性。展开更多
传统有限元法对大坝-不规则地基-库水系统进行建模时存在一定的局限性。基于ABAQUS二次开发接口,实现了比例边界有限元方法(scaled boundary finite element method,SBFEM)与八叉树网格的结合,建立了一种考虑真实地形的高拱坝-不规则地...传统有限元法对大坝-不规则地基-库水系统进行建模时存在一定的局限性。基于ABAQUS二次开发接口,实现了比例边界有限元方法(scaled boundary finite element method,SBFEM)与八叉树网格的结合,建立了一种考虑真实地形的高拱坝-不规则地基-库水系统自动建模方法。利用构建的八叉树比例边界有限元法对某重力坝地震响应进行了数值验证。随后对NG5拱坝系统分别基于平整地基和不规则地基进行线弹性和非线性动力响应分析。结果表明:在地震作用下,相较于简化的平整地基拱坝系统,不规则地基拱坝系统坝顶与坝底横河向相对位移以及第一主应力峰值变化较大,分别增加了73.5%和103.6%;考虑拱坝横缝以及材料非线性的情况下,坝顶与坝底横河向相对位移以及顺河向相对位移和相对速度分别增加了43.9%、32.0%和56.6%,同时边缝的法向开度增加尤为显著,增加了388.9%和381.8%,开度峰值增加了105%,在应力和损伤方面,第一主应力峰值增加了81.6%,损伤较大的区域也沿着坝体底部进行了扩展。展开更多
三轴试验离散元模拟是探究砂土等岩土材料变形破坏机制的一种重要手段,合理地模拟侧向边界是三轴试验离散元模拟的一个重要环节。基于有限差分法(finite difference method,简称FDM)-离散元法(discrete element method,简称DEM)FDM-DEM...三轴试验离散元模拟是探究砂土等岩土材料变形破坏机制的一种重要手段,合理地模拟侧向边界是三轴试验离散元模拟的一个重要环节。基于有限差分法(finite difference method,简称FDM)-离散元法(discrete element method,简称DEM)FDM-DEM耦合开展了柔性侧向边界条件下砂土三轴固结排水和不排水试验的数值模拟,并与相应的刚性侧向边界三轴数值试验进行了对比分析。结果表明:相比刚性侧向边界,基于FDM-DEM耦合的柔性侧向边界三轴试验能更好地再现室内砂土三轴试样的宏观力学响应和微观颗粒运动学特征;对于所模拟的砂土三轴固结排水试验,柔性侧向边界试样峰值强度后的应变软化和剪胀性明显弱于刚性侧向边界试样;对于所模拟的砂土三轴固结不排水试验,当轴向应变较大时,柔性侧向边界试样的偏应力小于刚性侧向边界试样,且产生绝对值较小的负孔压;三轴固结不排水试验中,当轴向应变较大时,柔性侧向边界对试样的约束和支撑作用弱于刚性侧向边界,其力链的稳定性较低,力链屈曲数较多,剪切带形成较早,故其各向异性和偏应力均较低。展开更多
文摘A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.
文摘A general and efficient parallel approach is proposed for the first time to parallelize the hybrid finiteelement-boundary-integral-multi-level fast multipole algorithm （FE-BI-MLFMA）. Among many algorithms of FE-BI-MLFMA, the decomposition algorithm （DA） is chosen as a basis for the parallelization of FE-BI-MLFMA because of its distinct numerical characteristics suitable for parallelization. On the basis of the DA, the parallelization of FE-BI-MLFMA is carried out by employing the parallelized multi-frontal method for the matrix from the finiteelement method and the parallelized MLFMA for the matrix from the boundary integral method respectively. The programming and numerical experiments of the proposed parallel approach are carried out in the high perfor- mance computing platform CEMS-Liuhui. Numerical experiments demonstrate that FE-BI-MLFMA is efficiently parallelized and its computational capacity is greatly improved without losing accuracy, efficiency, and generality.
文摘In order to master the magnetic field distribution of submarines in the air completely and exactly and study the magnetic stealthy performance of submarine,a mathematic model of submarine magnetic field extrapolation is built based on the boundary element method(BEM).An experiment is designed to measure three components of magnetic field on the envelope surface surrounding a model submarine.The data in different heights above the model submarine are obtained by use of tri-axial magnetometers.The results show that this extrapolation model has good stabilities and high accuracies compared the measured data with the extrapolated data.Moreover,the model can reflect the submarine magnetic field distribution in the air exactly,and is valuable in practical engineering.
文摘研究了复杂微细导线电容矩阵提取边界元法(boundary element method,BEM)的边界离散问题以及增强计算精度和数值稳定性的有效措施,分析了开阔边界尺寸、开阔边界离散、导线离散对计算精度的影响以及伪解、矩阵奇异性问题,提出了基于导线离散迭代和开阔边界迭代两阶段自动迭代边界元算法(automatic iterative boundary element method,AIBEM),并结合实例阐述了全域法和区域分解法两种多层介质问题系数矩阵生成方法。研究结果表明,边界环内生成的系数矩阵存在误差均衡协调问题,对复杂模型需合理选择各线段离散单元数及开阔边界尺寸,通过AIBEM可以获得经济的离散参数,有效避免矩阵奇异性,并提高收敛稳定性。将计算结果与有限元法、解析法、传输线法、矩量法进行了对比分析,证实了算法的可靠性。
文摘传统有限元法对大坝-不规则地基-库水系统进行建模时存在一定的局限性。基于ABAQUS二次开发接口,实现了比例边界有限元方法(scaled boundary finite element method,SBFEM)与八叉树网格的结合,建立了一种考虑真实地形的高拱坝-不规则地基-库水系统自动建模方法。利用构建的八叉树比例边界有限元法对某重力坝地震响应进行了数值验证。随后对NG5拱坝系统分别基于平整地基和不规则地基进行线弹性和非线性动力响应分析。结果表明:在地震作用下,相较于简化的平整地基拱坝系统,不规则地基拱坝系统坝顶与坝底横河向相对位移以及第一主应力峰值变化较大,分别增加了73.5%和103.6%;考虑拱坝横缝以及材料非线性的情况下,坝顶与坝底横河向相对位移以及顺河向相对位移和相对速度分别增加了43.9%、32.0%和56.6%,同时边缝的法向开度增加尤为显著,增加了388.9%和381.8%,开度峰值增加了105%,在应力和损伤方面,第一主应力峰值增加了81.6%,损伤较大的区域也沿着坝体底部进行了扩展。
文摘三轴试验离散元模拟是探究砂土等岩土材料变形破坏机制的一种重要手段,合理地模拟侧向边界是三轴试验离散元模拟的一个重要环节。基于有限差分法(finite difference method,简称FDM)-离散元法(discrete element method,简称DEM)FDM-DEM耦合开展了柔性侧向边界条件下砂土三轴固结排水和不排水试验的数值模拟,并与相应的刚性侧向边界三轴数值试验进行了对比分析。结果表明:相比刚性侧向边界,基于FDM-DEM耦合的柔性侧向边界三轴试验能更好地再现室内砂土三轴试样的宏观力学响应和微观颗粒运动学特征;对于所模拟的砂土三轴固结排水试验,柔性侧向边界试样峰值强度后的应变软化和剪胀性明显弱于刚性侧向边界试样;对于所模拟的砂土三轴固结不排水试验,当轴向应变较大时,柔性侧向边界试样的偏应力小于刚性侧向边界试样,且产生绝对值较小的负孔压;三轴固结不排水试验中,当轴向应变较大时,柔性侧向边界对试样的约束和支撑作用弱于刚性侧向边界,其力链的稳定性较低,力链屈曲数较多,剪切带形成较早,故其各向异性和偏应力均较低。
