A Finite Difference Method On Irregular Grids With Local Second Order Ghost Point Extension For Solving Maxwell’s Equations Around Curved PEC Objects
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Zou, Haiyu
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Abstract
This thesis proposes a new method to solve Maxwell’s equations that involve objects with potentially complicated geometries coupled with perfect electric conductor (PEC) boundary conditions. At its core, it is driven by a simple first order finite difference scheme with the boundary conditions handled by a new higher order ghost value extension tech- nique based on the level-set method and related redistancing and extension methods on lo- cally conforming point-shifted grids. Then the accuracy and stability are further improved by the back and forth error compensation and correction (BFECC) method. The level set method provides a convenient platform for capturing complicated interfaces as well as ex- trapolating certain quantities across an interface using PDE-based methods. The proposed new method is convenient to implement because the perturbed grid is still a “rectangular” grid topologically and all underlying schemes used are first order schemes. And it is second order accurate (in l1 norm) and stable even with the CFL number greater than one in two dimensions.
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2023-07-31
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Dissertation