Such modeling has already been done in rectangular waveguide with semiconductor obstacle placed on a wide wall of the waveguide and in the obstacle under the thin metal diaphragm. To perform investigation it is planned to use internal programs for the modeling of electromagnetic wave propagating in the circular waveguide with the obstacle. Therefore it is also planning to investigate the behavior of the averaged electric field in the semiconductor obstacle when different modes are excited in the waveguide. Since the resistive sensor actually feels the amplitude of electric field, the distribution of electric field component within the waveguide should have a crucial influence on the performance of the sensor and this fact should be taken into account in sensors design. Depending on mode some components of electromagnetic field are suppressed, nevertheless in the vicinity of the obstacle all six components of electromagnetic field might be excited and they should be taken into account when determining averaged electric field in the semiconductor obstacle. Although, the lowest critical frequency in the circular waveguide is characteristic to H11 mode higher modes such as E01 and H01 are also sometimes used. To calculate the average electric field in the semiconductor obstacle the finite difference time domain method will be used. This report results from a contract tasking Semiconductor Physics Institute as follows: To achieve the proposed goals, the modeling of the circular waveguide section containing semiconductor obstacle will be performed. The improved FDTD algorithm is also applied to sonic logging simulations in non-axisymmetric formations and sources.
Results show that the method is accurate and stable at the singularity point. This method is verified by several 3-D numerical examples.
This algorithm has three advantages over the conventional treatment techniques: 1) the excitation source can be directly loaded at r = 0 2) the central difference scheme with second-order accuracy is maintained 3) the stability condition at the axis is consistent with the FDTD in Cartesian coordinates. By rotating the Cartesian coordinate (RCC) system around the z-axis in cylindrical coordinates, the numerical singularity problems in both 2-D and 3-D cylindrical coordinates can be removed.
In this paper, we propose a simple but effective method for the treatment of this numerical singularity problem. For many years this issue has been impeding the accurate numerical solution near the axis. When modelling the propagation of 3-D non-axisymmetric viscoelastic waves in cylindrical coordinates using the finite-difference time-domain (FDTD) method, one encounters a mathematical singularity due to the presence of 1/r terms in the viscoelastic wave equations.
0 kommentar(er)
