A method using stochastic response surface method is presented. It solves wave equation with uncertain parameters in shallow water. Uncertain parameters of ocean environment are expressed with standard stochastic variables. And stochastic response of coherent sound field is expressed by Hermite multinomials. An approximate expression of coherent sound field is achieved with coefficients of stochastic muhinomial solved by probabilistic collocation method. It shows that the proposed method is more accurate and efficient than Monte Carlo method and field shifting method.

A 4-layer sphere model of human head is built for the forward problem of magnetic induction tomography.The layers represent the brain,the CFS,the skull,and the scalp respectively.Taking vector magnetic potential as a variable,Helmholtz equation in a spherical coordinates is constructed as a control equation of the forward problem.A variables separation method is used to solve the equations with boundary and interface conditions.Distribution of the magnetic vector potential and eddy current in the model are obtained.Equi-potential lines of the eddy current are given.Influence of frequency and magnitude of the exciting current on the induced voltage is analyzed.The algorithm is validated by solving a forward problem of magnetic induction tomography.It can be used as a fast algorithm to generate sensitivity matrix in an inverse problem.