In this paper,we apply Fokas unified method to study the initial boundary value(IBV)problems for nonlinear integrable equation with 3×3 Lax pair on the finite interval[0,L].The solution can be expressed by the so...In this paper,we apply Fokas unified method to study the initial boundary value(IBV)problems for nonlinear integrable equation with 3×3 Lax pair on the finite interval[0,L].The solution can be expressed by the solution of a 3×3 Riemann-Hilbert(RH)problem.The relevant jump matrices are written in terms of matrix-value spectral functions s(k),S(k),S_(l)(k),which are determined by initial data at t=0,boundary values at x=0 and boundary values at x=L,respectively.What's more,since the eigenvalues of 3×3 coefficient matrix of k spectral parameter in Lax pair are three different values,search for the path of analytic functions in RH problem becomes a very interesting thing.展开更多
In this paper, a meshfree boundary integral equation （BIE） method, called the moving Kriging interpolation- based boundary node method （MKIBNM）, is developed for solving two-dimensional potential problems. This st...In this paper, a meshfree boundary integral equation （BIE） method, called the moving Kriging interpolation- based boundary node method （MKIBNM）, is developed for solving two-dimensional potential problems. This study combines the DIE method with the moving Kriging interpolation to present a boundary-type meshfree method, and the corresponding formulae of the MKIBNM are derived. In the present method, the moving Kriging interpolation is applied instead of the traditional moving least-square approximation to overcome Kronecker＇s delta property, then the boundary conditions can be imposed directly and easily. To verify the accuracy and stability of the present formulation, three selected numerical examples are presented to demonstrate the efficiency of MKIBNM numerically.展开更多
应用任意地形河谷沉积层散射波源的格林函数公式,基于间接边界积分方程法(indirect boundary integral equation method,IBIEM),分析了SH波斜入射下梯形沉积河谷场地地震动特性和分布规律,研究了地震波斜入射角度、斜坡坡度、介质阻抗...应用任意地形河谷沉积层散射波源的格林函数公式,基于间接边界积分方程法(indirect boundary integral equation method,IBIEM),分析了SH波斜入射下梯形沉积河谷场地地震动特性和分布规律,研究了地震波斜入射角度、斜坡坡度、介质阻抗比对地震动特性及非一致分布规律的影响机制,深入分析了河谷散射效应对地基截断边界地震动场的影响规律。结果表明:斜入射使得河谷表面峰值位移的放大效应和非一致效应显著增强,最大峰值位移达入射地震动峰值的5倍以上;当河谷底宽较大时,沉积河谷的边缘效应明显;当底宽较小时,沉积河谷的聚焦效应明显,表面最大值出现在河谷中心处;斜坡坡度对楔形体内、外表面附近地表处的地震反应影响强烈,该现象可以由地表折射波干涉区域与斜坡坡度、入射角、波速的确定函数关系得到解释;随着阻抗比的增大,位移幅值放大越来越显著;当斜入射时,刚度越小的软弱沉积层对地震波传播起到的屏障作用越大;无论是空心河谷还是沉积河谷,散射效应对边界处地震动场影响都较为明显,相对于平坦基岩自由场,底边界、右边界误差最大可达30.8%,54.8%,应考虑将散射效应的总场作为输入。展开更多
针对声学边界元法中解的非唯一性和奇异积分问题,基于组合亥姆霍兹积分方程公式(combined helmholtz integral equation formulation,CHIEF)法思想,将常规边界元方程和等效源方程进行联立,并利用两者方程系数矩阵间的耦合等价关系,间接...针对声学边界元法中解的非唯一性和奇异积分问题,基于组合亥姆霍兹积分方程公式(combined helmholtz integral equation formulation,CHIEF)法思想,将常规边界元方程和等效源方程进行联立,并利用两者方程系数矩阵间的耦合等价关系,间接替换计算常规边界元法中的奇异系数矩阵,进而提出一种具有全频域唯一解、高计算精度和高稳定性的耦合CHIEF法。该方法将等效源方程作为补充方程,不仅解决了传统CHIEF法内点补充方程失效的问题,而且矩阵的间接替换计算避免了直接计算奇异积分,显著提高了计算效率和精度。通过声辐射和声散射的典型算例对比了所提方法、常规边界元法、常规Burton-Miller法和等效源法的计算效果。结果表明,所提方法不仅在全波数域内均能获得唯一解,且其计算精度和效率均优于常规边界元法和常规Burton-Miller方法,其系数矩阵条件数远低于等效源法。展开更多
基金supported by the National Natural Science Foundation of China(11901167,11971313 and 51879045)Key scientific research projects of higher education institutions in Henan,China(18B110008).
文摘In this paper,we apply Fokas unified method to study the initial boundary value(IBV)problems for nonlinear integrable equation with 3×3 Lax pair on the finite interval[0,L].The solution can be expressed by the solution of a 3×3 Riemann-Hilbert(RH)problem.The relevant jump matrices are written in terms of matrix-value spectral functions s(k),S(k),S_(l)(k),which are determined by initial data at t=0,boundary values at x=0 and boundary values at x=L,respectively.What's more,since the eigenvalues of 3×3 coefficient matrix of k spectral parameter in Lax pair are three different values,search for the path of analytic functions in RH problem becomes a very interesting thing.
基金Project supported by the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.10902076)the Natural Science Foundation of Shanxi Province of China(Grant No.2007011009)+1 种基金the Scientific Research and Development Program of the Shanxi Higher Education Institutions(Grant No.20091131)the Doctoral Startup Foundation of Taiyuan University of Science and Technology(Grant No.200708)
文摘In this paper, a meshfree boundary integral equation （BIE） method, called the moving Kriging interpolation- based boundary node method （MKIBNM）, is developed for solving two-dimensional potential problems. This study combines the DIE method with the moving Kriging interpolation to present a boundary-type meshfree method, and the corresponding formulae of the MKIBNM are derived. In the present method, the moving Kriging interpolation is applied instead of the traditional moving least-square approximation to overcome Kronecker＇s delta property, then the boundary conditions can be imposed directly and easily. To verify the accuracy and stability of the present formulation, three selected numerical examples are presented to demonstrate the efficiency of MKIBNM numerically.
文摘应用任意地形河谷沉积层散射波源的格林函数公式,基于间接边界积分方程法(indirect boundary integral equation method,IBIEM),分析了SH波斜入射下梯形沉积河谷场地地震动特性和分布规律,研究了地震波斜入射角度、斜坡坡度、介质阻抗比对地震动特性及非一致分布规律的影响机制,深入分析了河谷散射效应对地基截断边界地震动场的影响规律。结果表明:斜入射使得河谷表面峰值位移的放大效应和非一致效应显著增强,最大峰值位移达入射地震动峰值的5倍以上;当河谷底宽较大时,沉积河谷的边缘效应明显;当底宽较小时,沉积河谷的聚焦效应明显,表面最大值出现在河谷中心处;斜坡坡度对楔形体内、外表面附近地表处的地震反应影响强烈,该现象可以由地表折射波干涉区域与斜坡坡度、入射角、波速的确定函数关系得到解释;随着阻抗比的增大,位移幅值放大越来越显著;当斜入射时,刚度越小的软弱沉积层对地震波传播起到的屏障作用越大;无论是空心河谷还是沉积河谷,散射效应对边界处地震动场影响都较为明显,相对于平坦基岩自由场,底边界、右边界误差最大可达30.8%,54.8%,应考虑将散射效应的总场作为输入。
文摘针对声学边界元法中解的非唯一性和奇异积分问题,基于组合亥姆霍兹积分方程公式(combined helmholtz integral equation formulation,CHIEF)法思想,将常规边界元方程和等效源方程进行联立,并利用两者方程系数矩阵间的耦合等价关系,间接替换计算常规边界元法中的奇异系数矩阵,进而提出一种具有全频域唯一解、高计算精度和高稳定性的耦合CHIEF法。该方法将等效源方程作为补充方程,不仅解决了传统CHIEF法内点补充方程失效的问题,而且矩阵的间接替换计算避免了直接计算奇异积分,显著提高了计算效率和精度。通过声辐射和声散射的典型算例对比了所提方法、常规边界元法、常规Burton-Miller法和等效源法的计算效果。结果表明,所提方法不仅在全波数域内均能获得唯一解,且其计算精度和效率均优于常规边界元法和常规Burton-Miller方法,其系数矩阵条件数远低于等效源法。
