Abstract
In this thesis, we propose a new method using volumetric extension to solve PDEs on a curve. The computational domain is a narrow tubular region surrounding the curve. Our method uses Cartesian grids on the narrow tube and the Neumann boundary condition is taken care by interpolation treatment. Therefore it is easy to implement, even for complicated curves without given parametrization. We apply our method for thin-wire model equations. The model combines the telegrapher's equations with the Maxwell's equations, and it describes how an electrical wire reacts with nearby electric and magnetic fields. The Maxwell's equations are solved by Finite-Difference Time-Domain (FD-TD) method with perfectly matched layer (PML) boundary condition and the telegrapher's equations are solved by our approach. Some numerical examples are presented.