Coupled Multi-scale Method For Solving Wave Problems

For most complicated problems in scientific computing, we need to know not onlythe changes in micro-scales, but also the situation of macro-scales. Multi-scale methodis the most important method to solve these problems. In multi-scale method, the in-terface matching condition is a very important part as a bridge to connect the microand macro scales. In this thesis, we study the problem of optimal interface matchingconditions of wave equation. Usually, we use the method of minimizing the reflectioncoefcient to decide the optimal matching conditions. In this thesis, we introduce theweight function which is determined by the incident wave. By minimizing the productof the weight function and the reflection coefcient, we get the optimal matching con-ditions again, which is a little more precise than before. Further more, we introduce theself-adaptive method and finite point-method which optimizes the numerical results.