We study domain decomposition counterparts of the classical alternating direction implicit (ADI) and fractional step (FS) methods for solving the large linear systems arising from the implicit time stepping of parabolic equations. In the classical ADI and FS methods for parabolic equations, the elliptic operator is split along coordinate axes; they yield tridiagonal linear systems whenever a un...

This paper describes a new unconditionally stable numerical method for the full-wave physical modeling of semiconductor devices by a combination of the finite-difference Laguerre time-domain (FDLTD) and alternative direction implicit finite-difference time-domain (ADI-FDTD) approaches. The unconditionally stable method by using FDLTD scheme for the electromagnetic model and semi-implicit ADI-FD...

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...

This paper presents the Cholesky factor–alternating direction implicit (CF–ADI) algorithm, which generates a low rank approximation to the solution X of the Lyapunov equation AX + XAT = −BBT . The coefficient matrix A is assumed to be large, and the rank of the righthand side −BBT is assumed to be much smaller than the size of A. The CF–ADI algorithm requires only matrix-vector products and mat...

This paper presents the unified efficient fundamental alternating-direction-implicit finite-difference time-domain (ADIFDTD) schemes for lossy media. The schemes presented include averaging, forward-forward, forward-backward and novel exponential time differencing schemes. Unifications of these schemes in both conventional and efficient fundamental forms of source-incorporated ADIFDTD are provi...

For the approximate representation of large data sets over a parameter domain in IR2, many geological and other applications require the construction of surfaces which have minimal energy, i.e., minimal curvature. One way to achieve this is by solving a fourth order elliptic partial di erential equation. Its discretization by a di erence scheme makes it particularly easy to incorporate (appropr...

To develop a robust and efficient computational flow simulation tool for incompressible flow applications, a number of different implicit multigrid schemes for solving the three-dimensional incompressible Navier–Stokes equations are compared in the current study. These schemes consist of a common full approximation storage (FAS) multigrid algorithm implemented in conjunction with three differen...

Counterparty credit risk (CCR) is a significant factor that financial institutions have to consider in today’s context, and the COVID-19 pandemic military conflicts worldwide heightened concerns about potential default risk. In this work, we investigate changes value of derivatives due counterparty risk, i.e., total adjustment (XVA). We perform XVA for multi-asset option based on multivariate C...

The numerical solution of the time-dependent neutron transport problem in 2-D Cartesian geometry is considered. The problem is described by a coupled system of hyperbolic partial differential equations with the parameters of multiple groups. The system, for given group parameter, is discretized by a discrete ordinate method (SN) in angular direction and adaptive spline wavelet method with alter...