Discretization of the drift-diffusion equations with the composite discontinuous Galerkin method

Konrad Sakowski; Leszek Marcinkowski; Pawel Strak; Pawel Kempisty; Stanislaw Krukowski

doi:10.1007/978-3-319-32152-3_37

Discretization of the drift-diffusion equations with the composite discontinuous Galerkin method

Konrad Sakowski, Leszek Marcinkowski, Pawel Strak, Pawel Kempisty, Stanislaw Krukowski

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

3 Citations (Scopus)

Abstract

We present three variants of discretization of the stationary van Roosbroeck equations. They are the Composite Discontinuous Galerkin Methods, in standard symmetric/non-symmetric version, and the Weakly Over-Penalized Symmetric Interior Penalty method. Numerical simulations of gallium nitride semiconductor devices are presented. Results of these simulations serve as a base to perform the convergence analysis of the presented methods. Errors of approximations obtained with these methods are compared with each other.

Original language	English
Title of host publication	Parallel Processing and Applied Mathematics - 11th International Conference, PPAM 2015, Revised Selected Papers
Editors	Kazimierz Wiatr, Konrad Karczewski, Roman Wyrzykowski, Ewa Deelman, Jacek Kitowski, Jack Dongarra
Publisher	Springer Verlag
Pages	391-400
Number of pages	10
ISBN (Print)	9783319321516
DOIs	https://doi.org/10.1007/978-3-319-32152-3_37
Publication status	Published - 2016
Externally published	Yes
Event	11th International Conference on Parallel Processing and Applied Mathematics, PPAM 2015 - Krakow, Poland Duration: Sept 6 2015 → Sept 9 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9574
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	11th International Conference on Parallel Processing and Applied Mathematics, PPAM 2015
Country/Territory	Poland
City	Krakow
Period	9/6/15 → 9/9/15

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-319-32152-3_37

Cite this

Sakowski, K., Marcinkowski, L., Strak, P., Kempisty, P., & Krukowski, S. (2016). Discretization of the drift-diffusion equations with the composite discontinuous Galerkin method. In K. Wiatr, K. Karczewski, R. Wyrzykowski, E. Deelman, J. Kitowski, & J. Dongarra (Eds.), Parallel Processing and Applied Mathematics - 11th International Conference, PPAM 2015, Revised Selected Papers (pp. 391-400). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9574). Springer Verlag. https://doi.org/10.1007/978-3-319-32152-3_37

Discretization of the drift-diffusion equations with the composite discontinuous Galerkin method. / Sakowski, Konrad; Marcinkowski, Leszek; Strak, Pawel et al.
Parallel Processing and Applied Mathematics - 11th International Conference, PPAM 2015, Revised Selected Papers. ed. / Kazimierz Wiatr; Konrad Karczewski; Roman Wyrzykowski; Ewa Deelman; Jacek Kitowski; Jack Dongarra. Springer Verlag, 2016. p. 391-400 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9574).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Sakowski, K, Marcinkowski, L, Strak, P, Kempisty, P & Krukowski, S 2016, Discretization of the drift-diffusion equations with the composite discontinuous Galerkin method. in K Wiatr, K Karczewski, R Wyrzykowski, E Deelman, J Kitowski & J Dongarra (eds), Parallel Processing and Applied Mathematics - 11th International Conference, PPAM 2015, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9574, Springer Verlag, pp. 391-400, 11th International Conference on Parallel Processing and Applied Mathematics, PPAM 2015, Krakow, Poland, 9/6/15. https://doi.org/10.1007/978-3-319-32152-3_37

Sakowski K, Marcinkowski L, Strak P, Kempisty P, Krukowski S. Discretization of the drift-diffusion equations with the composite discontinuous Galerkin method. In Wiatr K, Karczewski K, Wyrzykowski R, Deelman E, Kitowski J, Dongarra J, editors, Parallel Processing and Applied Mathematics - 11th International Conference, PPAM 2015, Revised Selected Papers. Springer Verlag. 2016. p. 391-400. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-32152-3_37

Sakowski, Konrad ; Marcinkowski, Leszek ; Strak, Pawel et al. / Discretization of the drift-diffusion equations with the composite discontinuous Galerkin method. Parallel Processing and Applied Mathematics - 11th International Conference, PPAM 2015, Revised Selected Papers. editor / Kazimierz Wiatr ; Konrad Karczewski ; Roman Wyrzykowski ; Ewa Deelman ; Jacek Kitowski ; Jack Dongarra. Springer Verlag, 2016. pp. 391-400 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{9a7f98231e4f4c44991237c6790a0210,

title = "Discretization of the drift-diffusion equations with the composite discontinuous Galerkin method",

abstract = "We present three variants of discretization of the stationary van Roosbroeck equations. They are the Composite Discontinuous Galerkin Methods, in standard symmetric/non-symmetric version, and the Weakly Over-Penalized Symmetric Interior Penalty method. Numerical simulations of gallium nitride semiconductor devices are presented. Results of these simulations serve as a base to perform the convergence analysis of the presented methods. Errors of approximations obtained with these methods are compared with each other.",

keywords = "Composite discontinuous galerkin method, Drift-diffusion, Van Roosbroeck equations, Weakly Over-Penalized symmetric interior penalty method",

author = "Konrad Sakowski and Leszek Marcinkowski and Pawel Strak and Pawel Kempisty and Stanislaw Krukowski",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.; 11th International Conference on Parallel Processing and Applied Mathematics, PPAM 2015 ; Conference date: 06-09-2015 Through 09-09-2015",

year = "2016",

doi = "10.1007/978-3-319-32152-3_37",

language = "English",

isbn = "9783319321516",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "391--400",

editor = "Kazimierz Wiatr and Konrad Karczewski and Roman Wyrzykowski and Ewa Deelman and Jacek Kitowski and Jack Dongarra",

booktitle = "Parallel Processing and Applied Mathematics - 11th International Conference, PPAM 2015, Revised Selected Papers",

address = "Germany",

}

TY - GEN

T1 - Discretization of the drift-diffusion equations with the composite discontinuous Galerkin method

AU - Sakowski, Konrad

AU - Marcinkowski, Leszek

AU - Strak, Pawel

AU - Kempisty, Pawel

AU - Krukowski, Stanislaw

N1 - Publisher Copyright: © Springer International Publishing Switzerland 2016.

PY - 2016

Y1 - 2016

N2 - We present three variants of discretization of the stationary van Roosbroeck equations. They are the Composite Discontinuous Galerkin Methods, in standard symmetric/non-symmetric version, and the Weakly Over-Penalized Symmetric Interior Penalty method. Numerical simulations of gallium nitride semiconductor devices are presented. Results of these simulations serve as a base to perform the convergence analysis of the presented methods. Errors of approximations obtained with these methods are compared with each other.

AB - We present three variants of discretization of the stationary van Roosbroeck equations. They are the Composite Discontinuous Galerkin Methods, in standard symmetric/non-symmetric version, and the Weakly Over-Penalized Symmetric Interior Penalty method. Numerical simulations of gallium nitride semiconductor devices are presented. Results of these simulations serve as a base to perform the convergence analysis of the presented methods. Errors of approximations obtained with these methods are compared with each other.

KW - Composite discontinuous galerkin method

KW - Drift-diffusion

KW - Van Roosbroeck equations

KW - Weakly Over-Penalized symmetric interior penalty method

UR - http://www.scopus.com/inward/record.url?scp=84964462351&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84964462351&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-32152-3_37

DO - 10.1007/978-3-319-32152-3_37

M3 - Conference contribution

AN - SCOPUS:84964462351

SN - 9783319321516

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 391

EP - 400

BT - Parallel Processing and Applied Mathematics - 11th International Conference, PPAM 2015, Revised Selected Papers

A2 - Wiatr, Kazimierz

A2 - Karczewski, Konrad

A2 - Wyrzykowski, Roman

A2 - Deelman, Ewa

A2 - Kitowski, Jacek

A2 - Dongarra, Jack

PB - Springer Verlag

T2 - 11th International Conference on Parallel Processing and Applied Mathematics, PPAM 2015

Y2 - 6 September 2015 through 9 September 2015

ER -

Discretization of the drift-diffusion equations with the composite discontinuous Galerkin method

Abstract

Publication series

Conference

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this