Scientific Computing Seminar
Abstract: We consider four fourth order accurate compact schemes for numerical solutions of Maxwell's equations. The first one is the Ty(2,4) scheme which is a compact implicit scheme. This scheme is second order in time and fourth order in space. The second scheme is the Ty(4,4) which is forth order both in time and space. The third one is the explicit(2,4) scheme which is an explicit scheme. This scheme is also second order in time and fourth order in space. The Ty(2,4) and the exlicit(2,4) are staggered both in time and space. The Ty(4,4) is staggered only in space. These three schemes use the same mesh stencil as used in the standard Yee scheme. In particular extra information over a wider stencil is not required. This has several advantages. First it is relatively easy to modify an existing code based on the Yee algorithm to make it fourth order accurate. Second, a staggered mesh, without additional mesh location, makes the boundary treatment easier since some of the quantities are located inside the domain rather than on the boundary. Finally, a staggered grid gives a lower error than a similar non-staggered system.
In the fourth scheme we consider fourth order accurate compact scheme for the Maxwell's equations. We base this scheme on the Ty(2,4) scheme. We solve the equations on a Cartesian grid but consider boundaries which do not necessarily conform with the Cartesian grid.
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