| For the applications with moving interfaces, the mesh has to be refinedagain and again according to the varying interface, which prevents theconventional finite difference and finite element method from workingefficiently. For large scale problems, the computational expense for refining themesh again and again is prohibitive. Therefore, many methods have beendeveloped to get rid of this limitation so that interface problems can be solvedwith a mesh independent of interface. A periodic boundary condition isdeveloped based on Dirichlet boundary condition and Neumann boundarycondition. The periodic boundary condition can solve the interface fieldboundary value problem on a Cartesian mesh. It also requires much lesscomputational time.For an interface problem, the fnite elements are set to be body-fttingmeshes in order to obtain the optimal convergence rate, but the immersed finiteelement (IFE) method can achieve the same optimal convergence rate on aCartesian mesh, which is critical to many applications. However, the electricfeld in the conducting body should be zero, which cannot be guaranteed by theexisting IFE method. This paper develops a new IFE method to solve theinterface problem including a conducting body in the simulation domain.Numerical examples are provided to demonstrate the features of the new IFEmethod in this paper. This method can obtain a suitable accuracy for thesimulation domain which includes a charged conducting body.A bilinear axial symmetric immersed finite elements (AIFE) is developed,which was used to build a three-dimensional immersed finite element field solver.The most attractive advantage of the AIFE solver is that it can solve the three-dimensional interface field boundary value problems which are identified asaxisymmetric problems. The error estimation for the interpolation of a functionin a bilinear IFE space indicates that this space has the usual approximationcapability expected from bilinear polynomials, which isO (h~2)inL~2norm andO (h) inH1norm. |
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