In electrical impedance tomography (EIT), a forward solver capable of predicting the voltages on electrodes for a given conductivity distribution is essential for reconstruction. The EIT forward solver is normally based on the conventional finite element method (FEM). One of the major problems of three-dimensional (3-D) EIT is its high demand in computing power and memory since high precision is required for obtaining a small secondary field which is typical for a small anomaly. This accuracy requirement is also set by the level of noise in the real data; although currently the noise level is still an issue, future EIT systems should significantly reduce the noise level to be capable of detecting very small anomalies. To accurately simulate the forward solution with the FEM, a mesh with large number of nodes and elements is usually needed. To overcome this problem, we proposed the spectral element method (SEM) for EIT forward problem. With the introduction of SEM, a smaller number of nodes and hence less computational time and memory are needed to achieve the same or better accuracy in the forward solution than the FEM. Numerical results demonstrate the efficiency of the SEM in 3-D EIT simulation.

A three-dimensional (3-D) spectral-element method (SEM) based on Gauss-Lobatto-Legendre (GLL) polynomials is proposed to solve the Schro/spl uml/dinger equation in nanodevice simulation. Galerkin's method is employed to obtain the system equation. The high-order basis functions employed are orthogonal and the numerical quadrature points are the same as the GLL integration points, leading to a diagonal mass matrix and a more sparse stiffness matrix. Thus, the proposed method leads to a regular eigenvalue problem, rather than a generalized eigenvalue problem, greatly reducing the computer-memory requirement and central-processing-unit (CPU) time in comparison with the conventional finite-element method (FEM). Furthermore, the SEM is implemented for high geometrical orders, where curved structures can be modeled up to the accuracy comparable to the interpolation accuracy afforded by the basis functions. Numerical examples verify a spectral accuracy with the interpolation orders, and confirm that higher geometrical orders are essential for curved structures to achieve overall spectral accuracy. Examples of quantum dots in various structures, including a waveguide, are analyzed with mixed boundary conditions. Numerical results show that the SEM is an efficient alternative to conventional FEM and to the finite-difference method (FDM) for nanodevice simulation.

The effect of changing sampling timing in intermediate frequency (IF) sampling receivers is analyzed for the case when symbol timing recovery is performed by controlling the IF sampling clock. We note that changing the sampling timing in IF sampling causes a phase discontinuity which is detrimental to the stable operation of the phase recovery loop. We propose a new IF sampling scheme which makes it possible to control sampling timing while maintaining the continuous phase of the output samples so that the subsequent phase recovery properly works.