首页> 外文学位 >Numerical solution of Schroedinger equations using finite element methods.
【24h】

Numerical solution of Schroedinger equations using finite element methods.

机译:使用有限元方法对Schroedinger方程进行数值求解。

获取原文
获取原文并翻译 | 示例

摘要

This dissertation concerns the numerical solution of Schrodinger equations using finite element methods. Two particular equations are considered, the cubic nonlinear Schrodinger equation in one space variable, which has application in several areas of physics, and the two-dimensional parabolic equation of Tappert, which is used in the solution of problems arising in underwater acoustic wave propagation.;For the solution of the cubic Schrodinger equation, three spatial discretizations are examined. Two Galerkin-type methods are considered, both using product approximation to handle the nonlinear term. The L;The parabolic equation of Tappert is solved in the case of horizontally stratified media using an orthogonal spline collocation semi-discretization and ordinary differential equations software. An error analysis is presented for this method, as are numerical results for several test problems from the literature. A "space-time" finite element approach to the problem is also introduced, both for horizontally layered media and for the case of sloping interfaces.
机译:本文涉及有限元方法对薛定inger方程的数值求解。考虑了两个特定的方程,一个空间变量中的三次非线性Schrodinger方程已在物理的多个领域中应用,而Tappert的二维抛物方程则用于解决在水下声波传播中产生的问题。 ;对于三次薛定inger方程的解,检验了三个空间离散化。考虑了两种Galerkin型方法,均使用乘积近似来处理非线性项。在水平分层介质的情况下,使用正交样条搭配半离散化和常微分方程软件来求解Tappert的L;抛物型方程。对该方法进行了误差分析,文献中的一些测试问题的数值结果也是如此。还针对水平分层介质和倾斜界面的情况引入了针对该问题的“时空”有限元方法。

著录项

  • 作者

    Robinson, Mark Preuss.;

  • 作者单位

    University of Kentucky.;

  • 授予单位 University of Kentucky.;
  • 学科 Mathematics.;Physics Acoustics.
  • 学位 Ph.D.
  • 年度 1991
  • 页码 170 p.
  • 总页数 170
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 数学;声学;
  • 关键词

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱:kefu@zhangqiaokeyan.com

京公网安备:11010802029741号 ICP备案号:京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有
  • 客服微信

  • 服务号