Efficiency analysis of discontinuous Galerkin approaches for the application onto quantum Liouville-type equations

IF 2.2 4区工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC

Journal of Computational Electronics Pub Date : 2024-06-04 DOI:10.1007/s10825-024-02178-1

Valmir Ganiu, Dirk Schulz

引用次数: 0

Abstract

The simulation of nanodevices is computationally inefficient with current algorithms. The discontinuous Galerkin approach has been demonstrated in the field of computational fluid dynamics to deliver high order accuracy and efficiency due to its reliance on matrix–vector multiplications. Previously, the discontinuous Galerkin approach was successfully used in conjunction with the finite volume technique to solve the Liouville–von Neumann equation in center-mass coordinates and thus simulate nanodevices. To exploit its full potential regarding high-performance computing, this work aims to substitute the aforementioned finite volume technique with the discontinuous Galerkin method. To arrive at the said formalism, a finite element method is implemented as an intermediate step.

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应用于量子刘维尔型方程的非连续伽勒金方法的效率分析

目前的算法对纳米器件的模拟计算效率较低。在计算流体动力学领域，非连续 Galerkin 方法由于依赖矩阵-矢量乘法，已被证明具有高阶精度和效率。在此之前，非连续 Galerkin 方法已成功地与有限体积技术相结合，用于求解中心质量坐标下的 Liouville-von Neumann 方程，从而模拟纳米器件。为了充分发挥非连续伽勒金方法在高性能计算方面的潜力，本研究旨在用非连续伽勒金方法取代上述有限体积技术。为了实现上述形式，作为中间步骤，我们采用了有限元方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational Electronics ENGINEERING, ELECTRICAL & ELECTRONIC-PHYSICS, APPLIED

CiteScore

4.50

自引率

4.80%

发文量

142

审稿时长

>12 weeks

期刊介绍： he Journal of Computational Electronics brings together research on all aspects of modeling and simulation of modern electronics. This includes optical, electronic, mechanical, and quantum mechanical aspects, as well as research on the underlying mathematical algorithms and computational details. The related areas of energy conversion/storage and of molecular and biological systems, in which the thrust is on the charge transport, electronic, mechanical, and optical properties, are also covered. In particular, we encourage manuscripts dealing with device simulation; with optical and optoelectronic systems and photonics; with energy storage (e.g. batteries, fuel cells) and harvesting (e.g. photovoltaic), with simulation of circuits, VLSI layout, logic and architecture (based on, for example, CMOS devices, quantum-cellular automata, QBITs, or single-electron transistors); with electromagnetic simulations (such as microwave electronics and components); or with molecular and biological systems. However, in all these cases, the submitted manuscripts should explicitly address the electronic properties of the relevant systems, materials, or devices and/or present novel contributions to the physical models, computational strategies, or numerical algorithms.