EXPERIENCE WITH ADOPTING ONE-PARAMETER IMBEDDING METHODS TOWARD CALCULATION OF COUNTERCURRENT SEPARATION PROCESSES
The one-parameter imbedding method (also called homotopy or continuation) was adopted toward solution of large sets of nonlinear algebraical equations describing counter-current separation processes. Different imbedding functions were tested on a spectrum of difficult distillation problems ranging f...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Bhargava, Ravi [verfasserIn] Hlavacek, Vladimir [verfasserIn] |
|---|
| Format: |
E-Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2011 |
|---|
| Übergeordnetes Werk: |
Enthalten in: Chemical engineering communications - London [u.a.] : Taylor & Francis, 1973, 28(1984), 1-3 vom: 01. Juni, Seite 165-179 |
|---|---|
| Übergeordnetes Werk: |
number:1-3 ; volume:28 ; year:1984 ; month:06 ; day:01 ; pages:165-179 |
| Links: |
|---|
| DOI / URN: |
10.1080/00986448408940130 |
|---|
| Katalog-ID: |
NLEJ252494431 |
|---|
| LEADER | 01000naa a22002652 4500 | ||
|---|---|---|---|
| 001 | NLEJ252494431 | ||
| 003 | DE-627 | ||
| 005 | 20231206142356.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 231206s2011 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1080/00986448408940130 |2 doi | |
| 035 | |a (DE-627)NLEJ252494431 | ||
| 035 | |a (TFO)777918100 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rda | ||
| 041 | |a eng | ||
| 100 | 1 | |a Bhargava, Ravi |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a EXPERIENCE WITH ADOPTING ONE-PARAMETER IMBEDDING METHODS TOWARD CALCULATION OF COUNTERCURRENT SEPARATION PROCESSES |
| 264 | 1 | |c 2011 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 520 | |a The one-parameter imbedding method (also called homotopy or continuation) was adopted toward solution of large sets of nonlinear algebraical equations describing counter-current separation processes. Different imbedding functions were tested on a spectrum of difficult distillation problems ranging from distillation of hydrocarbons to strongly nonideal distillation problems. For the one-parameter imbedding functions studied in this report the classical Newton-Raphson Formula can be easily generated after an appropriate selection of the control parameters. Two different approaches were used to solve the homotopy equations: i) marching integration, ii) sequential use of the Newton-Raphson method. The one-parameter imbedding technique represents a trade-off between robustness and computation time. The algorithm is more robust than the Newton-Raphson technique, however, the computational time is usually higher. A combination of the one-parameter imbedding and the Newton-Raphson approach seems to be a very efficient method, the solution is approached by the one-parameter imbedding technique and the Newton-Raphson method is used to finish the iteration process. Geometrical interpretation of convergence is presented. | ||
| 700 | 1 | |a Hlavacek, Vladimir |e verfasserin |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Chemical engineering communications |d London [u.a.] : Taylor & Francis, 1973 |g 28(1984), 1-3 vom: 01. Juni, Seite 165-179 |h Online-Ressource |w (DE-627)NLEJ252478002 |w (DE-600)2040030-5 |w (DE-576)27388056X |x 1563-5201 |7 nnns |
| 773 | 1 | 8 | |g number:1-3 |g volume:28 |g year:1984 |g month:06 |g day:01 |g pages:165-179 |
| 856 | 4 | 0 | |u https://www.tib.eu/de/suchen/id/tandf%3A3b545db1c585d064550c50604af3ef691d4ab3fa |x Digitalisierung |z Deutschlandweit zugänglich |
| 912 | |a ZDB-1-TFO | ||
| 912 | |a GBV_NL_ARTICLE | ||
| 951 | |a AR | ||
| 952 | |e 1-3 |d 28 |j 1984 |c 6 |b 01 |h 165-179 | ||
| author_variant |
r b rb v h vh |
|---|---|
| matchkey_str |
article:15635201:2011----::xeineihdpignprmtrmednmtosoadacltoocut |
| hierarchy_sort_str |
2011 |
| publishDate |
2011 |
| allfields |
10.1080/00986448408940130 doi (DE-627)NLEJ252494431 (TFO)777918100 DE-627 ger DE-627 rda eng Bhargava, Ravi verfasserin aut EXPERIENCE WITH ADOPTING ONE-PARAMETER IMBEDDING METHODS TOWARD CALCULATION OF COUNTERCURRENT SEPARATION PROCESSES 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The one-parameter imbedding method (also called homotopy or continuation) was adopted toward solution of large sets of nonlinear algebraical equations describing counter-current separation processes. Different imbedding functions were tested on a spectrum of difficult distillation problems ranging from distillation of hydrocarbons to strongly nonideal distillation problems. For the one-parameter imbedding functions studied in this report the classical Newton-Raphson Formula can be easily generated after an appropriate selection of the control parameters. Two different approaches were used to solve the homotopy equations: i) marching integration, ii) sequential use of the Newton-Raphson method. The one-parameter imbedding technique represents a trade-off between robustness and computation time. The algorithm is more robust than the Newton-Raphson technique, however, the computational time is usually higher. A combination of the one-parameter imbedding and the Newton-Raphson approach seems to be a very efficient method, the solution is approached by the one-parameter imbedding technique and the Newton-Raphson method is used to finish the iteration process. Geometrical interpretation of convergence is presented. Hlavacek, Vladimir verfasserin aut Enthalten in Chemical engineering communications London [u.a.] : Taylor & Francis, 1973 28(1984), 1-3 vom: 01. Juni, Seite 165-179 Online-Ressource (DE-627)NLEJ252478002 (DE-600)2040030-5 (DE-576)27388056X 1563-5201 nnns number:1-3 volume:28 year:1984 month:06 day:01 pages:165-179 https://www.tib.eu/de/suchen/id/tandf%3A3b545db1c585d064550c50604af3ef691d4ab3fa Digitalisierung Deutschlandweit zugänglich ZDB-1-TFO GBV_NL_ARTICLE AR 1-3 28 1984 6 01 165-179 |
| spelling |
10.1080/00986448408940130 doi (DE-627)NLEJ252494431 (TFO)777918100 DE-627 ger DE-627 rda eng Bhargava, Ravi verfasserin aut EXPERIENCE WITH ADOPTING ONE-PARAMETER IMBEDDING METHODS TOWARD CALCULATION OF COUNTERCURRENT SEPARATION PROCESSES 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The one-parameter imbedding method (also called homotopy or continuation) was adopted toward solution of large sets of nonlinear algebraical equations describing counter-current separation processes. Different imbedding functions were tested on a spectrum of difficult distillation problems ranging from distillation of hydrocarbons to strongly nonideal distillation problems. For the one-parameter imbedding functions studied in this report the classical Newton-Raphson Formula can be easily generated after an appropriate selection of the control parameters. Two different approaches were used to solve the homotopy equations: i) marching integration, ii) sequential use of the Newton-Raphson method. The one-parameter imbedding technique represents a trade-off between robustness and computation time. The algorithm is more robust than the Newton-Raphson technique, however, the computational time is usually higher. A combination of the one-parameter imbedding and the Newton-Raphson approach seems to be a very efficient method, the solution is approached by the one-parameter imbedding technique and the Newton-Raphson method is used to finish the iteration process. Geometrical interpretation of convergence is presented. Hlavacek, Vladimir verfasserin aut Enthalten in Chemical engineering communications London [u.a.] : Taylor & Francis, 1973 28(1984), 1-3 vom: 01. Juni, Seite 165-179 Online-Ressource (DE-627)NLEJ252478002 (DE-600)2040030-5 (DE-576)27388056X 1563-5201 nnns number:1-3 volume:28 year:1984 month:06 day:01 pages:165-179 https://www.tib.eu/de/suchen/id/tandf%3A3b545db1c585d064550c50604af3ef691d4ab3fa Digitalisierung Deutschlandweit zugänglich ZDB-1-TFO GBV_NL_ARTICLE AR 1-3 28 1984 6 01 165-179 |
| allfields_unstemmed |
10.1080/00986448408940130 doi (DE-627)NLEJ252494431 (TFO)777918100 DE-627 ger DE-627 rda eng Bhargava, Ravi verfasserin aut EXPERIENCE WITH ADOPTING ONE-PARAMETER IMBEDDING METHODS TOWARD CALCULATION OF COUNTERCURRENT SEPARATION PROCESSES 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The one-parameter imbedding method (also called homotopy or continuation) was adopted toward solution of large sets of nonlinear algebraical equations describing counter-current separation processes. Different imbedding functions were tested on a spectrum of difficult distillation problems ranging from distillation of hydrocarbons to strongly nonideal distillation problems. For the one-parameter imbedding functions studied in this report the classical Newton-Raphson Formula can be easily generated after an appropriate selection of the control parameters. Two different approaches were used to solve the homotopy equations: i) marching integration, ii) sequential use of the Newton-Raphson method. The one-parameter imbedding technique represents a trade-off between robustness and computation time. The algorithm is more robust than the Newton-Raphson technique, however, the computational time is usually higher. A combination of the one-parameter imbedding and the Newton-Raphson approach seems to be a very efficient method, the solution is approached by the one-parameter imbedding technique and the Newton-Raphson method is used to finish the iteration process. Geometrical interpretation of convergence is presented. Hlavacek, Vladimir verfasserin aut Enthalten in Chemical engineering communications London [u.a.] : Taylor & Francis, 1973 28(1984), 1-3 vom: 01. Juni, Seite 165-179 Online-Ressource (DE-627)NLEJ252478002 (DE-600)2040030-5 (DE-576)27388056X 1563-5201 nnns number:1-3 volume:28 year:1984 month:06 day:01 pages:165-179 https://www.tib.eu/de/suchen/id/tandf%3A3b545db1c585d064550c50604af3ef691d4ab3fa Digitalisierung Deutschlandweit zugänglich ZDB-1-TFO GBV_NL_ARTICLE AR 1-3 28 1984 6 01 165-179 |
| allfieldsGer |
10.1080/00986448408940130 doi (DE-627)NLEJ252494431 (TFO)777918100 DE-627 ger DE-627 rda eng Bhargava, Ravi verfasserin aut EXPERIENCE WITH ADOPTING ONE-PARAMETER IMBEDDING METHODS TOWARD CALCULATION OF COUNTERCURRENT SEPARATION PROCESSES 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The one-parameter imbedding method (also called homotopy or continuation) was adopted toward solution of large sets of nonlinear algebraical equations describing counter-current separation processes. Different imbedding functions were tested on a spectrum of difficult distillation problems ranging from distillation of hydrocarbons to strongly nonideal distillation problems. For the one-parameter imbedding functions studied in this report the classical Newton-Raphson Formula can be easily generated after an appropriate selection of the control parameters. Two different approaches were used to solve the homotopy equations: i) marching integration, ii) sequential use of the Newton-Raphson method. The one-parameter imbedding technique represents a trade-off between robustness and computation time. The algorithm is more robust than the Newton-Raphson technique, however, the computational time is usually higher. A combination of the one-parameter imbedding and the Newton-Raphson approach seems to be a very efficient method, the solution is approached by the one-parameter imbedding technique and the Newton-Raphson method is used to finish the iteration process. Geometrical interpretation of convergence is presented. Hlavacek, Vladimir verfasserin aut Enthalten in Chemical engineering communications London [u.a.] : Taylor & Francis, 1973 28(1984), 1-3 vom: 01. Juni, Seite 165-179 Online-Ressource (DE-627)NLEJ252478002 (DE-600)2040030-5 (DE-576)27388056X 1563-5201 nnns number:1-3 volume:28 year:1984 month:06 day:01 pages:165-179 https://www.tib.eu/de/suchen/id/tandf%3A3b545db1c585d064550c50604af3ef691d4ab3fa Digitalisierung Deutschlandweit zugänglich ZDB-1-TFO GBV_NL_ARTICLE AR 1-3 28 1984 6 01 165-179 |
| allfieldsSound |
10.1080/00986448408940130 doi (DE-627)NLEJ252494431 (TFO)777918100 DE-627 ger DE-627 rda eng Bhargava, Ravi verfasserin aut EXPERIENCE WITH ADOPTING ONE-PARAMETER IMBEDDING METHODS TOWARD CALCULATION OF COUNTERCURRENT SEPARATION PROCESSES 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The one-parameter imbedding method (also called homotopy or continuation) was adopted toward solution of large sets of nonlinear algebraical equations describing counter-current separation processes. Different imbedding functions were tested on a spectrum of difficult distillation problems ranging from distillation of hydrocarbons to strongly nonideal distillation problems. For the one-parameter imbedding functions studied in this report the classical Newton-Raphson Formula can be easily generated after an appropriate selection of the control parameters. Two different approaches were used to solve the homotopy equations: i) marching integration, ii) sequential use of the Newton-Raphson method. The one-parameter imbedding technique represents a trade-off between robustness and computation time. The algorithm is more robust than the Newton-Raphson technique, however, the computational time is usually higher. A combination of the one-parameter imbedding and the Newton-Raphson approach seems to be a very efficient method, the solution is approached by the one-parameter imbedding technique and the Newton-Raphson method is used to finish the iteration process. Geometrical interpretation of convergence is presented. Hlavacek, Vladimir verfasserin aut Enthalten in Chemical engineering communications London [u.a.] : Taylor & Francis, 1973 28(1984), 1-3 vom: 01. Juni, Seite 165-179 Online-Ressource (DE-627)NLEJ252478002 (DE-600)2040030-5 (DE-576)27388056X 1563-5201 nnns number:1-3 volume:28 year:1984 month:06 day:01 pages:165-179 https://www.tib.eu/de/suchen/id/tandf%3A3b545db1c585d064550c50604af3ef691d4ab3fa Digitalisierung Deutschlandweit zugänglich ZDB-1-TFO GBV_NL_ARTICLE AR 1-3 28 1984 6 01 165-179 |
| language |
English |
| source |
Enthalten in Chemical engineering communications 28(1984), 1-3 vom: 01. Juni, Seite 165-179 number:1-3 volume:28 year:1984 month:06 day:01 pages:165-179 |
| sourceStr |
Enthalten in Chemical engineering communications 28(1984), 1-3 vom: 01. Juni, Seite 165-179 number:1-3 volume:28 year:1984 month:06 day:01 pages:165-179 |
| format_phy_str_mv |
Article |
| institution |
findex.gbv.de |
| isfreeaccess_bool |
false |
| container_title |
Chemical engineering communications |
| authorswithroles_txt_mv |
Bhargava, Ravi @@aut@@ Hlavacek, Vladimir @@aut@@ |
| publishDateDaySort_date |
1984-06-01T00:00:00Z |
| hierarchy_top_id |
NLEJ252478002 |
| id |
NLEJ252494431 |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">NLEJ252494431</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20231206142356.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">231206s2011 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1080/00986448408940130</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)NLEJ252494431</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(TFO)777918100</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bhargava, Ravi</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">EXPERIENCE WITH ADOPTING ONE-PARAMETER IMBEDDING METHODS TOWARD CALCULATION OF COUNTERCURRENT SEPARATION PROCESSES</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2011</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The one-parameter imbedding method (also called homotopy or continuation) was adopted toward solution of large sets of nonlinear algebraical equations describing counter-current separation processes. Different imbedding functions were tested on a spectrum of difficult distillation problems ranging from distillation of hydrocarbons to strongly nonideal distillation problems. For the one-parameter imbedding functions studied in this report the classical Newton-Raphson Formula can be easily generated after an appropriate selection of the control parameters. Two different approaches were used to solve the homotopy equations: i) marching integration, ii) sequential use of the Newton-Raphson method. The one-parameter imbedding technique represents a trade-off between robustness and computation time. The algorithm is more robust than the Newton-Raphson technique, however, the computational time is usually higher. A combination of the one-parameter imbedding and the Newton-Raphson approach seems to be a very efficient method, the solution is approached by the one-parameter imbedding technique and the Newton-Raphson method is used to finish the iteration process. Geometrical interpretation of convergence is presented.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Hlavacek, Vladimir</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Chemical engineering communications</subfield><subfield code="d">London [u.a.] : Taylor & Francis, 1973</subfield><subfield code="g">28(1984), 1-3 vom: 01. Juni, Seite 165-179</subfield><subfield code="h">Online-Ressource</subfield><subfield code="w">(DE-627)NLEJ252478002</subfield><subfield code="w">(DE-600)2040030-5</subfield><subfield code="w">(DE-576)27388056X</subfield><subfield code="x">1563-5201</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">number:1-3</subfield><subfield code="g">volume:28</subfield><subfield code="g">year:1984</subfield><subfield code="g">month:06</subfield><subfield code="g">day:01</subfield><subfield code="g">pages:165-179</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.tib.eu/de/suchen/id/tandf%3A3b545db1c585d064550c50604af3ef691d4ab3fa</subfield><subfield code="x">Digitalisierung</subfield><subfield code="z">Deutschlandweit zugänglich</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-1-TFO</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_NL_ARTICLE</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="e">1-3</subfield><subfield code="d">28</subfield><subfield code="j">1984</subfield><subfield code="c">6</subfield><subfield code="b">01</subfield><subfield code="h">165-179</subfield></datafield></record></collection>
|
| author |
Bhargava, Ravi |
| spellingShingle |
Bhargava, Ravi EXPERIENCE WITH ADOPTING ONE-PARAMETER IMBEDDING METHODS TOWARD CALCULATION OF COUNTERCURRENT SEPARATION PROCESSES |
| authorStr |
Bhargava, Ravi |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)NLEJ252478002 |
| format |
electronic Article |
| delete_txt_mv |
keep |
| author_role |
aut aut |
| collection |
NL |
| remote_str |
true |
| illustrated |
Not Illustrated |
| issn |
1563-5201 |
| topic_title |
EXPERIENCE WITH ADOPTING ONE-PARAMETER IMBEDDING METHODS TOWARD CALCULATION OF COUNTERCURRENT SEPARATION PROCESSES |
| format_facet |
Elektronische Aufsätze Aufsätze Elektronische Ressource |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
cr |
| hierarchy_parent_title |
Chemical engineering communications |
| hierarchy_parent_id |
NLEJ252478002 |
| hierarchy_top_title |
Chemical engineering communications |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)NLEJ252478002 (DE-600)2040030-5 (DE-576)27388056X |
| title |
EXPERIENCE WITH ADOPTING ONE-PARAMETER IMBEDDING METHODS TOWARD CALCULATION OF COUNTERCURRENT SEPARATION PROCESSES |
| ctrlnum |
(DE-627)NLEJ252494431 (TFO)777918100 |
| title_full |
EXPERIENCE WITH ADOPTING ONE-PARAMETER IMBEDDING METHODS TOWARD CALCULATION OF COUNTERCURRENT SEPARATION PROCESSES |
| author_sort |
Bhargava, Ravi |
| journal |
Chemical engineering communications |
| journalStr |
Chemical engineering communications |
| lang_code |
eng |
| isOA_bool |
false |
| recordtype |
marc |
| publishDateSort |
2011 |
| contenttype_str_mv |
txt |
| container_start_page |
165 |
| author_browse |
Bhargava, Ravi Hlavacek, Vladimir |
| container_volume |
28 |
| format_se |
Elektronische Aufsätze |
| author-letter |
Bhargava, Ravi |
| doi_str_mv |
10.1080/00986448408940130 |
| author2-role |
verfasserin |
| title_sort |
experience with adopting one-parameter imbedding methods toward calculation of countercurrent separation processes |
| title_auth |
EXPERIENCE WITH ADOPTING ONE-PARAMETER IMBEDDING METHODS TOWARD CALCULATION OF COUNTERCURRENT SEPARATION PROCESSES |
| abstract |
The one-parameter imbedding method (also called homotopy or continuation) was adopted toward solution of large sets of nonlinear algebraical equations describing counter-current separation processes. Different imbedding functions were tested on a spectrum of difficult distillation problems ranging from distillation of hydrocarbons to strongly nonideal distillation problems. For the one-parameter imbedding functions studied in this report the classical Newton-Raphson Formula can be easily generated after an appropriate selection of the control parameters. Two different approaches were used to solve the homotopy equations: i) marching integration, ii) sequential use of the Newton-Raphson method. The one-parameter imbedding technique represents a trade-off between robustness and computation time. The algorithm is more robust than the Newton-Raphson technique, however, the computational time is usually higher. A combination of the one-parameter imbedding and the Newton-Raphson approach seems to be a very efficient method, the solution is approached by the one-parameter imbedding technique and the Newton-Raphson method is used to finish the iteration process. Geometrical interpretation of convergence is presented. |
| abstractGer |
The one-parameter imbedding method (also called homotopy or continuation) was adopted toward solution of large sets of nonlinear algebraical equations describing counter-current separation processes. Different imbedding functions were tested on a spectrum of difficult distillation problems ranging from distillation of hydrocarbons to strongly nonideal distillation problems. For the one-parameter imbedding functions studied in this report the classical Newton-Raphson Formula can be easily generated after an appropriate selection of the control parameters. Two different approaches were used to solve the homotopy equations: i) marching integration, ii) sequential use of the Newton-Raphson method. The one-parameter imbedding technique represents a trade-off between robustness and computation time. The algorithm is more robust than the Newton-Raphson technique, however, the computational time is usually higher. A combination of the one-parameter imbedding and the Newton-Raphson approach seems to be a very efficient method, the solution is approached by the one-parameter imbedding technique and the Newton-Raphson method is used to finish the iteration process. Geometrical interpretation of convergence is presented. |
| abstract_unstemmed |
The one-parameter imbedding method (also called homotopy or continuation) was adopted toward solution of large sets of nonlinear algebraical equations describing counter-current separation processes. Different imbedding functions were tested on a spectrum of difficult distillation problems ranging from distillation of hydrocarbons to strongly nonideal distillation problems. For the one-parameter imbedding functions studied in this report the classical Newton-Raphson Formula can be easily generated after an appropriate selection of the control parameters. Two different approaches were used to solve the homotopy equations: i) marching integration, ii) sequential use of the Newton-Raphson method. The one-parameter imbedding technique represents a trade-off between robustness and computation time. The algorithm is more robust than the Newton-Raphson technique, however, the computational time is usually higher. A combination of the one-parameter imbedding and the Newton-Raphson approach seems to be a very efficient method, the solution is approached by the one-parameter imbedding technique and the Newton-Raphson method is used to finish the iteration process. Geometrical interpretation of convergence is presented. |
| collection_details |
ZDB-1-TFO GBV_NL_ARTICLE |
| container_issue |
1-3 |
| title_short |
EXPERIENCE WITH ADOPTING ONE-PARAMETER IMBEDDING METHODS TOWARD CALCULATION OF COUNTERCURRENT SEPARATION PROCESSES |
| url |
https://www.tib.eu/de/suchen/id/tandf%3A3b545db1c585d064550c50604af3ef691d4ab3fa |
| remote_bool |
true |
| author2 |
Hlavacek, Vladimir |
| author2Str |
Hlavacek, Vladimir |
| ppnlink |
NLEJ252478002 |
| mediatype_str_mv |
c |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| doi_str |
10.1080/00986448408940130 |
| up_date |
2024-07-06T12:55:09.502Z |
| _version_ |
1803834369772617728 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">NLEJ252494431</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20231206142356.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">231206s2011 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1080/00986448408940130</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)NLEJ252494431</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(TFO)777918100</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bhargava, Ravi</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">EXPERIENCE WITH ADOPTING ONE-PARAMETER IMBEDDING METHODS TOWARD CALCULATION OF COUNTERCURRENT SEPARATION PROCESSES</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2011</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The one-parameter imbedding method (also called homotopy or continuation) was adopted toward solution of large sets of nonlinear algebraical equations describing counter-current separation processes. Different imbedding functions were tested on a spectrum of difficult distillation problems ranging from distillation of hydrocarbons to strongly nonideal distillation problems. For the one-parameter imbedding functions studied in this report the classical Newton-Raphson Formula can be easily generated after an appropriate selection of the control parameters. Two different approaches were used to solve the homotopy equations: i) marching integration, ii) sequential use of the Newton-Raphson method. The one-parameter imbedding technique represents a trade-off between robustness and computation time. The algorithm is more robust than the Newton-Raphson technique, however, the computational time is usually higher. A combination of the one-parameter imbedding and the Newton-Raphson approach seems to be a very efficient method, the solution is approached by the one-parameter imbedding technique and the Newton-Raphson method is used to finish the iteration process. Geometrical interpretation of convergence is presented.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Hlavacek, Vladimir</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Chemical engineering communications</subfield><subfield code="d">London [u.a.] : Taylor & Francis, 1973</subfield><subfield code="g">28(1984), 1-3 vom: 01. Juni, Seite 165-179</subfield><subfield code="h">Online-Ressource</subfield><subfield code="w">(DE-627)NLEJ252478002</subfield><subfield code="w">(DE-600)2040030-5</subfield><subfield code="w">(DE-576)27388056X</subfield><subfield code="x">1563-5201</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">number:1-3</subfield><subfield code="g">volume:28</subfield><subfield code="g">year:1984</subfield><subfield code="g">month:06</subfield><subfield code="g">day:01</subfield><subfield code="g">pages:165-179</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.tib.eu/de/suchen/id/tandf%3A3b545db1c585d064550c50604af3ef691d4ab3fa</subfield><subfield code="x">Digitalisierung</subfield><subfield code="z">Deutschlandweit zugänglich</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-1-TFO</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_NL_ARTICLE</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="e">1-3</subfield><subfield code="d">28</subfield><subfield code="j">1984</subfield><subfield code="c">6</subfield><subfield code="b">01</subfield><subfield code="h">165-179</subfield></datafield></record></collection>
|
| score |
7.3982677 |