| Boundary Element Method is a numerical method for solving the mathematic and physics equations. This method changes differential equation into integral equation. Then, the boundary of domain is divided into finite units. That is, boundary integral equation is dispersed. We can get a set of equations that only contain unknown boundary nodes. Finely, we can solve the equations so as to fine the numerical solutions. This method has some similar with finite element method and finite differential method that are using intensive at present in disposing problem. But they different in starting point.Finite element method and finite differential method belong to "region method". Their starting point is dividing continue region into many tiny units or grids. Then we can change every unit or grid into easy equivalent model. And combine them together to compute all. That is, we change hybrid distributing parameter system into central parameter system to compute. The basic thought of the methods is that control differential equation is approached by the function satisfied whole boundary condition in definitional domain. Boundary element method turned out contrary to them. It divides many units on boundary in definitional domain. Boundary condition is approached by function that satisfy control differential equation. The function in unit may change with varieties form. This method is similar to finite element method.BEM may be divided into two basic types. They are direct method and indirect method. Indirect method begins with a basic solution that satisfy control differential equation, but it contain some unknown number that is defined by implement boundary condition on many points. Indirect method is that formula is expressed by variable which physics sense do not clear. This method is used to solving elasticity force controlled by Laplace and Helmholtz. And other potential question, direct methods starting point is greens equality. Variable have certainly physics sense, it have priority to use engineering science. This thesis discusses this method.Boundary element method change control equation in domain into integer equation of boundary in domain. Thus it need unit in boundary and combining boundary condition to solve. So dimension that dispute question will be decrease one dimension. This step important is green formation and basic solution. Because this method disperse boundary only, building equation group number will be decrease. Data will decrease largely. Thus, computer internal memory will be decrease.But building equation group coefficient matrix in boundary element method is dense and dissymmetry and matrix elements count quantity is very large. This offset part times saved by matrix after decreasing dimension. In addition boundary element method is difficulty in disposing uneven question.Boundary element method and finite element method will realize to disperse solving domain in a probe function. The two methods take step to variable regular in selecting these functions. A control differential equations basic solving or control differential equations green function in solving domain need to be find in solving boundary value question in boundary element method. This is difficult in some questions. Finite element methods shortcoming is difficult to solving boundary value question of infinite field domain. And only solving finite question, because dispersed infinite domain in finite unit is unlike. Finite element method is difficult to dispose question which have power bizarre. This bizarre often occur in irregular concavity angle and near hold in solid mechanics because bizarre can cause section expanding, it is very important in finding an accurate solving near bizarre. But power is infinite large in theory in bizarre. Result can have not sense in finite element method. Similar situation can occur in centralize load. Such as field question have point source. Under this situation, no matter what divided unit is smaller. Result in finite element method need not reflect rapid change n...
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