Induced Magnetic Field Computation for Ships Based on Fast Multipole Method and Integral Equation Method

Abstract

The nonsymmetric and dense coefficient matrix of integral equation method results in low computation efficiency and large memory cost in induced magnetic field computation of large scale ships. In order to improve the computation efficiency, a new method called FMMIEM is developed based on fast multipole method and integral equation method. The basic formulas of the FMMIEM were deduced. The numerical implementations of the multipole expansion, multipole to local translation and local expansion were described in detail. The FMMIEM not only has the virtue of the vector integral equation method which needs only meshing source area and is easy to deal with the infinite domain problems, such as the induced magnetic field modeling, but also has the excellent performance of the fast multipole method in conjunction with iterative solver which can accelerate the matrix vector product. The analytical numerical experiment of the sphere magnetized in the uniform applied magnetic field and the magnetostatic field modeling of the main cabin of the simple submarine mockup were designed and the results showed that the FMMIEM is with the high calculation accuracy and reduces costing time obviously. The proposed method is very helpful in engineering.