Modulation of the refractive index of glass using ion exchange is a common fabrication method for various micro-optics components, such as waveguide devices, microlenses, and diiractive elements. The design of elements with complicated optical functions has increased the demand for fast numerical simulation of the nonlinear ion-exchange process of two monovalent ions. In this paper, a linear im...

A new numerical method for the full-wave physical modelling of semiconductor devices using a combination of the meshless and finite-difference time-domain (FDTD) approaches is described. The model consists of the electron equations for the active part and Maxwell’s equations for the electromagnetic effects, which describe the complete behaviour of a high-frequency active device. The uncondition...

A nonlinear Poisson equation (NPE) has been introduced to model and nonlocal hyperpolarisation effects in electrostatic solute-solvent interaction for biomolecular solvation analysis. Due a strong nonlinearity associated with the heterogeneous dielectric media, NPE is difficult solve numerically large protein systems. new pseudo-transient continuation approach proposed this paper efficiently st...

This paper proposes a novel hybrid FDTD method for solving the time-dependent Schrödinger equation, which is fundamental modeling materials and designing nanoscale devices. The wave function propagated on nonuniform grids by applying explicit updates in part of grid implicit elsewhere. latter are based Alternating-Direction Implicit (ADI) scheme while former constructed with central difference ...

In this study, a numerical solution of 2D steady incompressible lid-driven cavity flow is presented. Three different numerical schemes were employed to make a comparison on the practicality of the methods. An alternating direction implicit scheme for the vorticity-stream function formulation, explicit and implicit schemes for the primitive variable formulation of governing Navier-Stokes equatio...

Low-rank versions of the alternating direction implicit (ADI) iteration are popular and well established methods for the numerical solution of large-scale Sylvester and Lyapunov equations. Probably the largest disadvantage of these methods is their dependence on a set of shift parameters that are crucial for a fast convergence. Here we compare existing shifts generation strategies that compute ...

A method, based on a semivectorial finite difference scheme, is described to construct modal fields for any twodimensional refractive-index profile which is constant except at abrupt interfaces. The modal fields correspond to eigenvectors of the matrix equation to be solved. In order to find the eigenvectors and their corresponding eigenvalues, the matrix equation is formulated according to the...

Many temporal discretization methods for linear evolution equations converge uniformly on compact time intervals at the rate 1 nα only for sufficiently smooth initial data. It is shown that these methods can be regularized such that the new schemes converge ‘in the average’ at the rate 1 nα for all initial data. Examples given include the Crank-Nicholson scheme and the alternating direction imp...

Maximum drawdown is a risk measure that plays an important role in portfolio management. In this paper, we address the question of computing the expected value of the maximum drawdown using a partial differential equation (PDE) approach. First, we derive a two-dimensional convection-diffusion pricing equation for the maximum drawdown in the Black-Scholes framework. Due to the properties of the ...

For European plain vanilla options, we investigate the difference between solutions obtained by the full-scale and an approximate Heston-Hull-White (HHW) model. Based on the corresponding two option pricing PDEs, we analyze the quality of the approximation. To confirm the accuracy of the analysis, we solve the HHW PDE, its approximating PDE as well as the PDE for the error, numerically, via a s...