Based on the method of lum-pedmass explicit finite element and local transmitting artificial boundary,pulse displacement is input to the foundation.

The explicit finite element method and the transmitting boundary are used.

To overcome this drawback of the classical fixed/free boundary of finite computational models for structure-foundation systems, a transmitting boundary model has been proposed to account the dynamic inter.

In this paper, the asymptotic traces of Dirac eigenvalue problem with unlocal boundary conditions are researched .

PML technique and non-local boundary conditions for the parabolic equation;

High order parabolic equation algorithm and its application to non-local boundary condition;

Considering a reaction-diffusion equation with non-local boundary conditions in bounded regions, we have found under some conditions the solutions of the equation blow up or exist globally.

Starting from the step by step integral algorithm and considering the coupling between the motion of the boundarynodes and the internal nodes, the authors bring about a method which can give an approximate stability criterion of a local artificial boundary in numerical simulation of multi dimensional wave motion.