Numerical Implementation For Artificial Boundary Of The Perfectly Matched Layer

Appropriately integrating the artificial boundary into the computional domainis the key to numerical simulation of the problems in both infinite and semi-infinitecategories. The commonly used artificial boundaries in the Finite Element Method(FEM) cover the visco-elastic artificial boundary, transmitting boundary etc. In themost commonly used discrete element pogram, UDEC (Universal Distinct ElementCode), the mainly usedr atificial boundary is the viscous boundary. PerfectlyMatched Player (PML) artificial boundary is a new absorbing layer boundary wherethe incident waves could be fully absorbed theoretically. So far, it has beensuccessfully used in the electromagnetism field, and it has been obtained someprogresses in some other engineering arears including civil engineering, however,not yet integrated in the commercial software. In this thesis, the main purpose is tograsp the numerical mechanism and the process of the numerical implementation forthe PML artificial boundary, based on which the PML is tried to integrate in UDEC.(1)In the first step in FEM simulation of the artificial boundary, FEM is used tosolve the static problem, in which the basic steps for solving an engineeringproblem and the theory in FEM are illustratively understood. After that, FEM isused to deal with a dynamic problem by solving the simple fluctuation problem, inwhich the boundary of the model is the hinge joint. In this step, the parameters inthe equations of motion, including stiffness matrix, mass matrix and the matrix ofthe load of the nodes, are solved, therefore the solution of the equation of motion issolved as well. Sequentially, for the purpose of comparison of the effects ofartificial boundaries, the transmission boundary and PML boundary are applied tothe computational domain for a simple fluctuation problem. Finally, theone-dimensional illustration examples in dynamics problems are performed, wherethe hinge joint boundary, the transmission boundary and PML boundary areindividually applied to the boundary of the numerical model respectively. Therefore,in the process of solving both the static and dynamic illustration problems, theeffects in absorbing the outgoing waves for the above mentioned three artificialboundaries are compared and discussed, and the key points in numericalimplementation for PML boundary are grasped. (2) In the first step in simulation of the artificial boundary in UDEC, the filesare coded in the embedded language FISH in UDEC to integrating the viscousboundary in UDEC executive program. The results from the viscous boundarycoded in FISH are compared with those from the viscous boundary supplied by thestandard UDEC code. In this step, the method for numerical implementation of theartificial boundary in UDEC is primarily studied. After that, the FISH files arecoded, integrating the visco-elastic boundary as well, to compare the effects onwave absorption between viscous and visco-elastic boundaries in UDEC.Meanwhile in the process of numerical implementation for the visco-elasticartificial boundary in UDEC, the numerical implementation method by using FISHin UDEC executive program is further probed.(3) Using the numerical implementation method coded in FISH, the PMLartificial boundary is integrated in the discrete program in UDEC.