Solving the Maxwell Equations with a 2 D Finite VolumeMethod on the CM - 200

The 2D transverse electric (TE) Maxwell equations have been solved by a Finite Volume method. The reconstruction of quantities on the cell interfaces is taken as an average of the values in the two neighbouring cells. We use an explicit three step Runge-Kutta method for the time-stepping. This method is well suited for a SIMD machine because of the locality of references. We run our code on a 16K CM-200. With periodic boundary conditions the code runs in single precision at 2.5 GFLOPS, which is almost half of the peak performance. The use of absorbing boundary conditions reduces this performance with a factor of about 5. The memory size of 2 Gbyte enables us to run problems with 2048*2048 cells in double precision. We have run the test cases C2D 2, BINA2D 4 and O2D 4b using uniform Cartesian grids. This procedure gives a saw-tooth approximation of objects. Uniform Cartesian grids were used because of the simplicity of creating them. All three cases were run on several grid sizes ranging from 512*512 to 2048*2048 cells to check the discretization error. Mesh convergence was accomplished in all three cases.