Adaptive multigrid applied to a bipolar transistor problem:
Abstract: "In this paper an adaptive multigrid method is presented for the solution of the steady 2D semiconductor equations. The discretization is made on an adaptive grid by means of the (hybrid) mixed finite element method on rectangles. The integrals involved are approximated by means of th...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
1991
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| Series: | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM
1991,15 |
| Subjects: | |
| Summary: | Abstract: "In this paper an adaptive multigrid method is presented for the solution of the steady 2D semiconductor equations. The discretization is made on an adaptive grid by means of the (hybrid) mixed finite element method on rectangles. The integrals involved are approximated by means of the trapezoidal rule in order to obtain a generalization in 2D of the well-known Scharfetter-Gummel scheme. We show that the use of the trapezoidal rule does not influence the accuracy of the discretization. The discrete equations thus obtained are solved by means of the dual version of the FAS-FMG algorithm A Vanka-type relaxation is used as a smoother, and a local damping of the restricted residual is introduced in order to be able to use very coarse grids. Consistent with the FAS-FMG algorithm, we use the relative truncation error between coarse and fine grids as a refinement criterion for constructing adaptive grids. We study the relative truncation errors for the semiconductor equations in detail and show how they can be incorporated into a practical grid adaptation scheme. Results are shown for a realistic bipolar transistor problem. |
| Physical Description: | 18 S. |
Staff View
MARC
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| 520 | 3 | |a Abstract: "In this paper an adaptive multigrid method is presented for the solution of the steady 2D semiconductor equations. The discretization is made on an adaptive grid by means of the (hybrid) mixed finite element method on rectangles. The integrals involved are approximated by means of the trapezoidal rule in order to obtain a generalization in 2D of the well-known Scharfetter-Gummel scheme. We show that the use of the trapezoidal rule does not influence the accuracy of the discretization. The discrete equations thus obtained are solved by means of the dual version of the FAS-FMG algorithm | |
| 520 | 3 | |a A Vanka-type relaxation is used as a smoother, and a local damping of the restricted residual is introduced in order to be able to use very coarse grids. Consistent with the FAS-FMG algorithm, we use the relative truncation error between coarse and fine grids as a refinement criterion for constructing adaptive grids. We study the relative truncation errors for the semiconductor equations in detail and show how they can be incorporated into a practical grid adaptation scheme. Results are shown for a realistic bipolar transistor problem. | |
| 650 | 4 | |a Multigrid methods (Numerical analysis) | |
| 650 | 4 | |a Semiconductors | |
| 810 | 2 | |a Afdeling Numerieke Wiskunde: Report NM |t Centrum voor Wiskunde en Informatica <Amsterdam> |v 1991,15 |w (DE-604)BV010177152 |9 1991,15 | |
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Record in the Search Index
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| author | Molenaar, J. |
| author_facet | Molenaar, J. |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:47:58Z |
| institution | BVB |
| language | English |
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| physical | 18 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
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| spelling | Molenaar, J. Verfasser aut Adaptive multigrid applied to a bipolar transistor problem Amsterdam 1991 18 S. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM 1991,15 Abstract: "In this paper an adaptive multigrid method is presented for the solution of the steady 2D semiconductor equations. The discretization is made on an adaptive grid by means of the (hybrid) mixed finite element method on rectangles. The integrals involved are approximated by means of the trapezoidal rule in order to obtain a generalization in 2D of the well-known Scharfetter-Gummel scheme. We show that the use of the trapezoidal rule does not influence the accuracy of the discretization. The discrete equations thus obtained are solved by means of the dual version of the FAS-FMG algorithm A Vanka-type relaxation is used as a smoother, and a local damping of the restricted residual is introduced in order to be able to use very coarse grids. Consistent with the FAS-FMG algorithm, we use the relative truncation error between coarse and fine grids as a refinement criterion for constructing adaptive grids. We study the relative truncation errors for the semiconductor equations in detail and show how they can be incorporated into a practical grid adaptation scheme. Results are shown for a realistic bipolar transistor problem. Multigrid methods (Numerical analysis) Semiconductors Afdeling Numerieke Wiskunde: Report NM Centrum voor Wiskunde en Informatica <Amsterdam> 1991,15 (DE-604)BV010177152 1991,15 |
| spellingShingle | Molenaar, J. Adaptive multigrid applied to a bipolar transistor problem Multigrid methods (Numerical analysis) Semiconductors |
| title | Adaptive multigrid applied to a bipolar transistor problem |
| title_auth | Adaptive multigrid applied to a bipolar transistor problem |
| title_exact_search | Adaptive multigrid applied to a bipolar transistor problem |
| title_full | Adaptive multigrid applied to a bipolar transistor problem |
| title_fullStr | Adaptive multigrid applied to a bipolar transistor problem |
| title_full_unstemmed | Adaptive multigrid applied to a bipolar transistor problem |
| title_short | Adaptive multigrid applied to a bipolar transistor problem |
| title_sort | adaptive multigrid applied to a bipolar transistor problem |
| topic | Multigrid methods (Numerical analysis) Semiconductors |
| topic_facet | Multigrid methods (Numerical analysis) Semiconductors |
| volume_link | (DE-604)BV010177152 |
| work_keys_str_mv | AT molenaarj adaptivemultigridappliedtoabipolartransistorproblem |