The IIM in polar coordinates and its application to electro capacitance tomography problems

In a numerical study of the electric field inside an Electro Capacitance Tomography (ECT) device and other applications, often a Poisson equation with a discontinuous coefficient needs to be solved in polar coordinates. This paper is devoted to the Immersed Interface Method (IIM) in polar coordinates and the application to the solution of the electric potential inside an ECT device. The numerical algorithm is based on a finite difference discretization on a uniform polar coordinates grid. The finite difference scheme is modified at grid points near and on the interface across which the coefficient is discontinuous so that the natural jump conditions are satisfied. The algorithm and analysis here is one step forward in applying the IIM for 3D problems in axisymmetric situations or in the spherical coordinates. Numerical examples against exact solutions and the application to ECT problems are also presented.