Research On The Technic Of Realizing The Direct Current Electric Field Modeling Of With The Quasi-analytical Method

The integral equation method is numerical method based on the integral form of the Maxwell equations. It usually passes to solve surface of the target or the equivalent source in the body of the target, and acquires the solution of the field. The integral equation method has many advantages when using in resolving the 3D D.C field modeling problems, it can avoid the cumulative error in the transmission the field, which is gained in the differential eguation methods. In order to make the 3D modeling more quickly by The integral equation method, some Approximation method was turned up, such as Born method,Extended Born approximation and Quasi-linear Method and so on. Quasi-analytical Method was put forward while resolving the electromagnetic problems. It can be used in the large pertubation problems, and can avoid to solving the large matrix problems, so it was introduced in the numeracal modeling of the D.C. electric field.First of all, this paper studies the formulas which appeared in Sun.J' paper. We derived the integral equations of the D.C. electric field from the basic theory of electric field, using the relation of the normal field and the anomalous field, the integral equation can be derived. Based on the idea of the Quasi-linear method, and analysis the formulas of the Quasi-linear method, the Quasi-analytical method can be put forwared. In this method we get two kinds of apporximation methods by different assumptions. They are called the Scalar Quasi-analytical method and the tensor Quasi-analytical method. According to the Quasi-analytical formulas get the iterative Quasi-analytical equation. Using the iterative Quasi-analytical equation we can make the result more accurately.Next, we have to consider some problems meeting in the process of realizing the Quasi-analytical method. The first is problem of the magnetic dyadic Green's function. The Green's function used in this paper is different from the Green's function before, and it has not explicit expression. So we must study it. We can derive the relationship of the two kinds Green'function from the relation between the potential and the field, and we know the expression of the potentil dyadic Green's function, so the explicit expression can be presented. The second problem is the numeracal integral method. On the study of the Gauss integral method, we find that it has many advantages; especially the method can be extended to multi-dimensions numeracal integral. After experimentding with new method of Gauss integral method, we find that when the number of the nodes is 5, the method has higher precision and higher speed. The third problem is the singularity of the magnetic dyadic Green's function. to make out the problem, we studied the treatment method of the tensor Green's function, which was put forwarded by Yaghjian, and we get the quasi source dyadic method to solve the singularity. This method split the integral area into two parts, which are the small neighbourhood area of the singularity and the non singularity area. We calculate the integral on the neighbourhood area of the singularity to get the quasi source dyadic by methods of mathematics, and calulate the integral on the non singularity area directly. Finally integral on the whole area can be got by adding the two parts integral, and we resoved the problem.Finally, after solving the problems of the Quasi-analytical method, this paper studies the realizing the Quasi-analytical method using to solving the integral equation of the D.C.electic field. In the process, we realize the scalar and tensor Quasi-analytical method make use of the different shape of the anomalous body, and different conductance rate, different type of the field source.In the process of realizing the scalar Quasi-analytical method, first of all, we must confirm that whether this method is feasible or not, and whether this method has high precision or not. At the aim of this, we calculate the anomalous electric field caused by anomalous sphere models which has different conductance rate to the surrounding medium, which is caused by the uniform field and the point source field, because anomalous sphere has analytical solution. Through the numerical analysis of the scalar quasi-analytical result and the analytical solution about the anomalous, also we get the Born approximation result, and analysis its precision, we find that the scalar quasi-analytical method has high precision whether the model with large perturbation. When the perturbation is very large, the iterative scalar Quasi-analytical solution is also accuracy. So we validate the feasible of the the scalar Quasi-analytical method, and make sure that the scalar Quasi-analytical method is excelled than Born approximation. Next we prove this method having better adaptability. So we choose the anomalous ellipsoid and anomalous cube located in the the uniform field and the point source field, and calculate the anomalous field using the scalar Quasi-analytical method and the Born appoximation method. After these researches, we can sum up that the scalar Quasi-analytical method is excellent method for solving the 3D D.C. electric field integral equations.When we carry on realzing of the tensor Quasi-analytical method, we use the same way as the scalar Quasi-analytical method. We get the following conclusions: This method can be applied to large perturbation problems with high precision; it can be used to modeling anomalous body in the uniform field and point source field, the anomalous body can take on sphere, ellipsoid, tube and so on.Through the studies of realizing of the Quasi-analytical method, we can find than this method can be used to solve the integral equations of the 3D D.C. electric field, its application can promote the fast forward and inverse modeling of the D.C. electic field, so it has bright foreground.