NUMERICAL SOLUTION OF THE PROBLEM FOR POISSON’S EQUATION WITH THE USE OF DAUBECHIES WAVELET DISCRETE-CONTINUAL FINITE ELEMENT METHOD

Numerical solution of the problem for Poisson’s equation with the use of Daubechies wavelet discrete continual finite element method (specific version of wavelet-based discrete-continual finite element method) is under consideration in the distinctive paper. The operational initial continual and discrete-continual formulations of the problem are given, several aspects of finite element approximation are considered. Some information about the numerical implementation and an example of analysis are presented.

On the methodology of calculating volume charge density in a MIFGMOS substrate using Poisson’s equation

Purpose This study aims to present a mathematical method based on Poisson’s equation to calculate the voltage and volume charge density formed in the substrate under the floating gate area of a multiple-input floating-gate metal-oxide semiconductor metal-oxide semiconductor (MOS) transistor. Design/methodology/approach Based on this method, the authors calculate electric fields and electric potentials from the charges generated when voltages are applied to the control gates (CG). This technique allows us to consider cases when the floating gate has any trapped charge generated during the manufacturing process. Moreover, the authors introduce a mathematical function to describe the potential behavior through the substrate. From the resultant electric field, the authors compute the volume charge density at different depths. Findings The authors generate some three-dimensional graphics to show the volume charge density behavior, which allows us to predict regions in which the volume charge density tends to increase. This will be determined by the voltages on terminals, which reveal the relationship between CG and volume charge density and will allow us to analyze some superior-order phenomena. Originality/value The procedure presented here and based on coordinates has not been reported before, and it is an aid to generate a model of the device and to build simulation tools in an analog design environment.

LOCALIZATION OF SOLUTION OF THE PROBLEM FOR POISSON’S EQUATION WITH THE USE OF B-SPLINE DISCRETE-CONTINUAL FINITE ELEMENT METHOD

Localization of solution of the problem for Poisson’s equation with the use of B-spline discrete-continual finiteelement method (specificversion of wavelet-based discrete-continual finiteelement method) is under consideration in the distinctive paper. The original operational continual and discrete-continual formulations of the problem are given, some actual aspects of construction of normalized basis functions of a B-spline are considered, the corresponding local constructions for an arbitrary discrete-continual finiteelement are described, some information about the numerical implementation and an example of analysis are presented.

Grid independent convergence using multilevel circulant preconditioning: Poisson’s equation

We consider the iterative solution of the discrete Poisson’s equation with Dirichlet boundary conditions. The discrete domain is embedded into an extended domain and the resulting system of linear equations is solved using a fixed point iteration combined with a multilevel circulant preconditioner. Our numerical results show that the rate of convergence is independent of the grid’s step sizes and of the number of spatial dimensions, despite the fact that the iteration operator is not bounded as the grid is refined. The embedding technique and the preconditioner is derived with inspiration from theory of boundary integral equations. The same theory is used to explain the behaviour of the preconditioned iterative method.