(2014). Fundamental locally one-dimensional method for 3-D thermal simulation. IEICE transactions on electronics, E97.C(7), 636-644. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification o...

In this paper a numerical method is used to study the unsteady state natural convection heat transfer within a confined porous media with uniform internal heat generation. The governing equations based on the Darcy model and Bossiness approximations are solved, using the finite difference Alternating Direction Implicit (ADI) method. The developed program was used to simulate natural convection ...

We present a parallel Alternating Direction Implicit (ADI) solver on GPUs. Our implementation significantly improves existing implementations in two aspects. First, we address the scalability issue of existing Parallel Cyclic Reduction (PCR) implementations by eliminating their hardware resource constraints. As a result, our parallel ADI, which is based on PCR, no longer has the maximum domain ...

Balanced truncation (BT), as applied to date in model order reduction (MOR), is known for its superior accuracy and computable error bounds. Positive-real BT (PRBT) is a particular BT procedure that preserves passivity and stability and imposes no structural constraints on the original state space. However, PRBT requires solving two algebraic Riccati equations (AREs), whose computational comple...

We propose a new high-order alternating direction implicit (ADI) finite difference scheme for the solution of initial-boundary value problems of convection-diffusion type with mixed derivatives and non-constant coefficients, as they arise from stochastic volatility models in option pricing. Our approach combines different high-order spatial discretisations with Hundsdorfer and Verwer’s ADI time...

This paper describes the alternating-direction implicit finite-difference time-domain (ADI-FDTD) method for physical modeling of high-frequency semiconductor devices. The model contains the semiconductor equations in conjunction with the Maxwell’s equations which describe the complete behavior of highfrequency active devices. Using ADI approach leads to a significant reduction of the full-wave ...

Alternating Direction Implicit (ADI) schemes are constructed for the solution of two-dimensional higher-order linear and nonlinear diffusion equations, particularly including the fourth-order thin film equation for surface tension driven fluid flows. First and second-order accurate schemes are derived via approximate factorization of the evolution equations. This approach is combined with itera...

Abstract: We consider three level difference replacements of parabolic equations focusing on the heat equation in two space dimensions. Through a judicious splitting of the approximation, the scheme qualifies as an alternating direction implicit (ADI) method. Using the well known fact of the parabolic-elliptic correspondence, we shall derive a two stage iterative procedure employing a fractiona...

We study accuracy of alternating direction implicit (ADI) methods for parabolic equations. The original ADI method applied to parabolic equations is a perturbation of the Crank-Nicolson di erence equation and has second-order accuracy both in space and time. The perturbation error is on the same order as the discretization error, in terms of mathematical description. However, we often observe i...

In this paper, a new alternating direction implicit (ADI) method is introduced to solve potential driven geometric flow PDEs for biomolecular surface generation. For such PDEs, an extra factor is usually added to stabilize the explicit time integration. However, two existing implicit ADI schemes are also based on the scaled form, which involves nonlinear cross derivative terms that have to be e...