scholarly journals A Comparison of Modern Hyperbolic Methods for Semiconductor Device Simulation: NTK Central Scheme Vs. CLAWPACK

VLSI Design ◽  
2002 ◽  
Vol 15 (4) ◽  
pp. 721-728
Author(s):  
Carl L. Gardner ◽  
Anne Gelb ◽  
Justin Hernandez
Keyword(s):  
Hydrodynamic Model ◽  
Software Package ◽  
Semiconductor Device ◽  
Splitting Method ◽  
Device Simulation ◽  
Second Order ◽  
Godunov Method ◽  
Source Terms ◽  
Central Scheme ◽  
Classical Hydrodynamic

Two modern hyperbolic methods—a second-order Godunov method in the software package CLAWPACK and the second-order Nessyahu–Tadmor–Kurganov (NTK) central scheme—are compared for simulating an electron shock wave in the classical hydrodynamic model for semiconductor devices.The NTK central scheme, which does not employ Riemann problem solutions, is described in detail. Special attention is paid in both methods to handling the source terms in the hydrodynamic model. CLAWPACK incorporates the source terms by a splitting method, while our version of the NTK scheme is unsplit.

scholarly journals A First-Order Explicit-Implicit Splitting Method for a Convection-Diffusion Problem

2020 ◽  
Vol 20 (4) ◽  
pp. 769-782
Author(s):  
Amiya K. Pani ◽  
Vidar Thomée ◽  
A. S. Vasudeva Murthy
Keyword(s):  
Splitting Method ◽  
Diffusion Problem ◽  
Euler Method ◽  
Second Order ◽  
Time Step ◽  
Convection Diffusion ◽  
First Order ◽  
Backward Euler ◽  
Strang Splitting ◽  
Spatially Periodic

AbstractWe analyze a second-order in space, first-order in time accurate finite difference method for a spatially periodic convection-diffusion problem. This method is a time stepping method based on the first-order Lie splitting of the spatially semidiscrete solution. In each time step, on an interval of length k, of this solution, the method uses the backward Euler method for the diffusion part, and then applies a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {\frac{k}{m}} for the convection part. With h the mesh width in space, this results in an error bound of the form {C_{0}h^{2}+C_{m}k} for appropriately smooth solutions, where {C_{m}\leq C^{\prime}+\frac{C^{\prime\prime}}{m}}. This work complements the earlier study [V. Thomée and A. S. Vasudeva Murthy, An explicit-implicit splitting method for a convection-diffusion problem, Comput. Methods Appl. Math. 19 2019, 2, 283–293] based on the second-order Strang splitting.

scholarly journals Topologically Rectangular Grids in the Parallel Simulation of Semiconductor Devices

VLSI Design ◽  
1998 ◽  
Vol 6 (1-4) ◽  
pp. 91-95 ◽  
Author(s):  
A. Asenov ◽  
A. R. Brown ◽  
S. Roy ◽  
J. R. Barker
Keyword(s):  
Simulated Annealing Algorithm ◽  
Semiconductor Device ◽  
Electronic Device ◽  
Device Simulation ◽  
Power Electronic ◽  
Two Dimensional ◽  
Solution Strategy ◽  
Rectangular Grids ◽  
Annealing Algorithm ◽  
2D And 3D

Topologically rectangular grids offer simplicity and efficiency in the design of parallel semiconductor device simulators tailored for mesh connected MIMD platforms. This paper presents several approaches to the generation of topologically rectangular 2D and 3D grids. The effects of the partitioning of such grids on different processor configurations are studied. A simulated annealing algorithm is used to optimise the partitioning of 2D and 3D grids on two dimensional arrays of processors. Problems related to the discretization, parallel matrix generation and solution strategy are discussed. The use of topologically rectangular grids is illustrated through the example of power electronic device simulation.

Element Edge Based Discretization for TCAD Device Simulation

2021 ◽  
Author(s):  
Juan Sanchez ◽  
Qiusong Chen
Keyword(s):  
Computer Aided Design ◽  
Field Effect Transistor ◽  
Semiconductor Device ◽  
Device Simulation ◽  
Polarization Effects ◽  
Effect Transistor ◽  
Edge Based ◽  
Volume Method ◽  
Aided Design ◽  
Novel Devices

<div><div><div><p>Technology computer-aided design (TCAD) semiconductor device simulators solve partial differential equations (PDE) using the finite volume method (FVM), or related methods. While this approach has been in use over several decades, its methods continue to be extended, and are still applicable for investigating novel devices. In this paper, we present an element edge based (EEB) FVM discretization approach suitable for capturing vector-field effects. Drawing from a 2D approach in the literature, we have extended this method to 3D. We implemented this method in a TCAD semiconductor device simulator, which uses a generalized PDE (GPDE) approach to simulate de- vices with the FVM. We describe how our EEB method is compatible with the GPDE approach, allowing the modeling of vector effects using scripting. This method is applied to solve polarization effects in a 3D ferro capacitor, and a 2D ferroelectric field-effect transistor. An example for field- dependent mobility in a 3D MOSFET is also presented.</p></div></div></div>

scholarly journals Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations

2018 ◽  
Author(s):  
Tuomas Kärnä ◽  
Stephan C. Kramer ◽  
Lawrence Mitchell ◽  
David A. Ham ◽  
Matthew D. Piggott ◽  
...  
Keyword(s):  
Discontinuous Galerkin ◽  
Unstructured Grid ◽  
Splitting Method ◽  
Time Integration ◽  
River Estuary ◽  
Coastal Ocean ◽  
Second Order ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Element Discretization

Abstract. Unstructured grid ocean models are advantageous for simulating the coastal ocean and river-estuary-plume systems. However, unstructured grid models tend to be diffusive and/or computationally expensive which limits their applicability to real life problems. In this paper, we describe a novel discontinuous Galerkin (DG) finite element discretization for the hydrostatic equations. The formulation is fully conservative and second-order accurate in space and time. Monotonicity of the advection scheme is ensured by using a strong stability preserving time integration method and slope limiters. Compared to previous DG models advantages include a more accurate mode splitting method, revised viscosity formulation, and new second-order time integration scheme. We demonstrate that the model is capable of simulating baroclinic flows in the eddying regime with a suite of test cases. Numerical dissipation is well-controlled, being comparable or lower than in existing state-of-the-art structured grid models.

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