1. The project falls into the field of scientific computational technique of the electromagnetic field and electromagnetic Wave.

2. Main contents:

(1) The multi-pole theory, and spherical and rectangular (hexahedral) equivalent source methods are proposed, resulting in creating a theoretical system for the semi-analytic method:

1) Based on the theory and method proposed are built up two sets of united methods for deriving the general solution in the three categories of second order mathematical and physical equations;

2) Based on the theory and method proposed are built up two sets of efficient methods for setting the starting point of the variable, i.e., the position of vertex and quantity in the series expansion equation;

(2) Efficient ideas, methods and techniques in other fields are integrated:

1) For the first time, the evenly and unevenly distributed ring source and spherical equivalent source are grouped into the distribution of the simulation field. The area expansion approach is proposed. The idea of the separate field solution (·ЦУтЅв) , constraint theory, etc. are presented. The computational precision of the axially symmetric field, the three-dimensional field with the axially symmetric structure and the singular point of the electric field are integrated and the scope of the solution of problems is extended.

2) For the first time, the semi-analytic method is used to determine the non-linear field. Due to the derivability and smoothness of the solution of the series, the method is better than the boundary element method.

3) The semi-analytic method, and the finite element method, or the matching method of the boundary element method are developed. The undetermined coefficient in the series expansion equation is determined by use of the least square method, thus omitting the complex subdivision link and facilitating the control of errors.

4) For the first time, the matrix equation in the semi-analytic method is solved by use of the multi-identification analytic technique in the small wave analysis, thus improving the stability in the solution and saving the computational time. The visualization technique is introduced into the semi-analytic method, resulting in reducing the computational time for determining the optimal solution of the order of the variable in the series expansion equation of individual parts in the scope of the complex fields.

3. Specific features

(1) The excessive function in the series expansion equation of the three-dimensional scalar field for the general multi-polar technique is removed, thus reducing the unknown values. A breakthrough is made about the computation of the three-dimensional vector field with the magnetic position as the variable, the axially symmetric field and the field with the rectangular boundary or hexahedral boundary, thus filling the blank for expanding the scope of the solution of problems by use of the semi-analytic method.

(2) Under the guidance of the theory, two sets of methods for determining how to set the starting point, i.e., vertex, of the variable in the expansion equation are developed, thus overcoming the blindness for setting the vertex and tackling the difficult problem to enhance the problem solution efficiency with the semi-analytic method;

(3) Efficient ideas and methods are integrated into the numerical computation, enabling the semi-analytic method not only to possess the advantages of both the analytic and numeric methods but overcome their disadvantages as well.

4. Application and popularization

At present, the method finds its application mainly in the computation of the analysis of the electromagnetic field and wave and it is also extended to other fields delineated by the second order mathematical and physical equations, including elliptic, parabolic and wave equations.