Study on Complex Geometric Boundary Problems in Hamiltonian system

机译：哈密顿体系中复杂几何边界问题的研究

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Based on the Hamiltonian system, a numerical method of boundary integral is proposed for solving the problems of mechanical boundary conditions, especially those with complex geometric boundary. This method is based on the eigensolution of analytic form and realizes the solution of the problem through twice integration. On the one hand, the eigenvalue equation is established by directly integrating the eigenvalues of analytic form on the boundary, and the eigenvalues corresponding to the eigenvalues can meet the boundary conditions in an average sense; on the other hand, taking the eigenvalues of each order as the weight function, through the weighted integration on the boundary, the algebraic equations on the expansion of the eigenvalues are established to realize the Effective handling.

机译：基于哈密顿系统，提出了一种边界积分的数值方法来解决机械边界条件，特别是那些具有复杂几何边界的边界条件的问题。该方法基于解析形式的本征解，并且通过两次积分来实现问题的解。一方面，特征值方程是通过在边界上直接积分解析形式的特征值而建立的，与特征值相对应的特征值在平均意义上可以满足边界条件。另一方面，以各阶特征值作为权重函数，通过边界上的加权积分，建立了特征值扩展的代数方程，实现了有效处理。

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《International Conference on Electron Device and Mechanical Engineering》|2020年|621-624|共4页
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WX Zhang;
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boundary integral; complex geometric boundary; eigenvalue equation; zero eigensolution; weighted integration; algebraic equation;

机译：边界积分;复杂几何边界;特征值方程;零特征解;加权积分;代数方程;

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3. Hamiltonian geometric connection associated with adiabatically perturbed Hamiltonian systems and the existence of adiabatic invariants [J] . Ya. A. Prykarpats’kyi Ukrainian mathematical journal . 2008,第3期

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4. On the Complexity of Commuting Local Hamiltonians, and Tight Conditions for Topological Order in Such Systems [C] . Aharonov Dorit, Eldar Lior 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science . 2011

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5. An automated code generator for three-dimensional acoustic wave propagation with geometrically complex solid-wall boundaries. [D] . Dyson, Rodger William, Jr. 1999

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6. Multiple twinning in cubic crystals: geometric/algebraic study and its application for the identification of the Σ3n grain boundaries [O] . Cyril Cayron -1

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7. On the Hamiltonian structures of the second and the fourth Painleve hierarchies, and the degenerate Garnier systems(Algebraic, Analytic and Geometric Aspects of Complex Differential Equations and their Deformations. Painleve Hierarchies) [O] . KOIKE Tatsuya 2007

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8. Bifurcation, Geometric Phases and Control in Hamiltonian Systems and Fluid Dynamics. Final report [R] . 2000

机译：哈密顿系统中的分岔，几何相位和控制及流体动力学。总结报告

Study on Complex Geometric Boundary Problems in Hamiltonian system

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