The Particular Solution Method for Potential value Inversion

Wen Zegang; He Jinglin

doi:10.3969/j.issn.1004-4140.2001.02.002

Abstract：In this paper the integral routes of irrotational field are treated as rays, the potential values of the boundary points which be passed by the ray are treated as input and output ，then Laplace Equation can be solved by inverse method. This method is innovatory and applicable, the results are precise and the boundary conditions are easy to be coped with. This is a useful numerical method for a kind of second-order partial differential equations that can be transformed to Laplace Equation. The most of control equations in engineering and physics are Laplace Equation or Poisson Equation, and the analytical solution of the two kinds of equations cannot be gotten generally, so they often be solved by differential method and finite element method. It is too complex to cope with the boundary conditions by differential method and its grids must be square and same size when calculated. We measure the input and output from different directions with instrument through which we can get the total attenuation of every ray. It means that we need some rays and detecting instrument. In this paper the integral routes of irrotational field are treated as rays, the potential values of the boundary points that rays pass by are treated as input and output, then a kind of second-order partial differential equations that can be transformed to Laplace Equation which can be solved by inverse method. This theory is particular and simple, the results are precise and the boundary conditions are easy to be coped with. So we think it has wide applications in physics, numerical mathematics, and specially, may be used in the research of gravity and geoelectric fields.