FINITE-ELEMENT APPROXIMATION TO 2-DIMENSIONAL SINE-GORDON SOLITONS
FINITE-ELEMENT APPROXIMATION TO 2-DIMENSIONAL SINE-GORDON SOLITONS
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DOI：
10.1016/0045-7825(91)90136-t
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发表时间：
1991-03-01
影响因子：
7.2
通讯作者：
HEINRICH, JC
中科院分区：
文献类型：
--
作者：
ARGYRIS, J;HAASE, M;HEINRICH, JC
本文提出了一种有限元算法的正弦戈登方程的数值解在两个空间维度，因为它出现，例如，在矩形大面积约瑟夫森结。色散非线性偏微分方程的系统允许孤子型的解决方案，一个普遍存在的现象，在各种各样的物理问题。一个简单的四节点双线性有限元结合广义Newmark积分方案的基础上的半离散Galerkin方法在整个文件中使用，并在各种情况下进行测试。与有限差分解的比较表明，该算法的上级性能非常准确，数值稳定和物理一致的孤立波解。结果支持本数值模型的信心，它应该能够处理更复杂的情况下，涉及孤子型相互作用。
The paper presents a finite element algorithm for the numerical solution of the sine-Gordon equation in two spatial dimensions, as it arises, for example, in rectangular large-area Josephson junctions. The dispersive nonlinear partial differential equation of the system allows for soliton-type solutions, an ubiquitous phenomenon in a large variety of physical problems. A semidiscrete Galerkin approach based on simple four-noded bilinear finite elements in combination with a generalized Newmark integration scheme is used throughout the paper and is tested in a variety of cases. Comparisons with finite difference solutions show the superior performance of the proposed algorithm leading to very accurate, numerically stable and physically consistent solitary wave solutions. The results support the confidence in the present numerical model which should be capable to treat also more complex situations involving soliton-type interactions.