Numerical Computation of Solitary Waves in Infinite Cylindrical Domains
Numerical Computation of Solitary Waves in Infinite Cylindrical Domains
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无限柱域中孤立波的数值计算
DOI：
10.1137/s003614299833734x
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
A. Scheel
中科院分区：
文献类型：
--
作者：
G. Lord;Daniela Peterhof;Bjorn Sandstede;A. Scheel
研究了半线性椭圆型方程在无限圆柱区域上孤立波的数值计算。该方程不是在无限圆柱体上求解，而是通过有限圆柱体上的边值问题来近似。这种方法的收敛性和稳定性的结果。本文还证明了Galerkin近似可以用来计算有限圆柱上椭圆问题的孤立波。此外，它表明，上述程序简化的情况下，椭圆方程承认一个额外的可逆性结构。最后，理论预测与数值计算进行了比较。特别是，后屈曲的无限长的圆柱壳轴向压缩下，它是数值示出，对于一个固定的空间截断，截断尺度的误差与长度的圆柱体的理论预测。
The numerical computation of solitary waves to semilinear elliptic equations in infinite cylindrical domains is investigated. Rather than solving on the infinite cylinder, the equation is approximated by a boundary-value problem on a finite cylinder. Convergence and stability results for this approach are given. It is also shown that Galerkin approximations can be used to compute solitary waves of the elliptic problem on the finite cylinder. In addition, it is demonstrated that the aforementioned procedures simplify in cases where the elliptic equation admits an additional reversibility structure. Finally, the theoretical predictions are compared with numerical computations. In particular, post buckling of an infinitely long cylindrical shell under axial compression is considered; it is shown numerically that, for a fixed spatial truncation, the error in the truncation scales with the length of the cylinder as predicted theoretically.