{"title":"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","authors":"Valmir Ganiu, Dirk Schulz","doi":"10.1007/s10825-024-02178-1","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":620,"journal":{"name":"Journal of Computational Electronics","volume":"23 4","pages":"718 - 727"},"PeriodicalIF":2.2000,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10825-024-02178-1.pdf","citationCount":"0","resultStr":"{\"title\":\"Efficiency analysis of discontinuous Galerkin approaches for the application onto quantum Liouville-type equations\",\"authors\":\"Valmir Ganiu, Dirk Schulz\",\"doi\":\"10.1007/s10825-024-02178-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>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.</p></div>\",\"PeriodicalId\":620,\"journal\":{\"name\":\"Journal of Computational Electronics\",\"volume\":\"23 4\",\"pages\":\"718 - 727\"},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-06-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10825-024-02178-1.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational Electronics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10825-024-02178-1\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Electronics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10825-024-02178-1","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
Efficiency analysis of discontinuous Galerkin approaches for the application onto quantum Liouville-type equations
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.
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.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
