Numerical validation methods

In the last years, numerical simulation has seen a great development thanks to costs reduction and speed increases of the computational systems. With these improvements, the mathematical algorithms are able to work properly with more realistic problems. Nowadays, the solution of a problem using nume...

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Detalles Bibliográficos
Autores: Jauregui Tellería, Ricardo, Silva Martínez, Fernando|||0000-0003-3019-3993
Tipo de recurso: capítulo de libro
Fecha de publicación:2011
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/13404
Acceso en línea:https://hdl.handle.net/2117/13404
Access Level:acceso abierto
Palabra clave:Numerical analysis -- Simulation methods
Anàlisi numèrica -- Processament de dades
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
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spelling Numerical validation methodsJauregui Tellería, RicardoSilva Martínez, Fernando|||0000-0003-3019-3993Numerical analysis -- Simulation methodsAnàlisi numèrica -- Processament de dadesÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèricaIn the last years, numerical simulation has seen a great development thanks to costs reduction and speed increases of the computational systems. With these improvements, the mathematical algorithms are able to work properly with more realistic problems. Nowadays, the solution of a problem using numerical simulation is not just finding a result, but also to ensure the quality. However, can we say that the model results are correct regarding the behaviour of the system? In other words, how could we quantify the similarity between reality and simulations? To answer these questions, it is necessary to establish a validation criterion that allows an objective quantification of the difference between the results and the reality. Another way to say this is, how “true” our results are. In the case of numerical methods, the main objective is to replicate as closely as possible the behaviour of the "real" world through numbers. Normally, the results of the numerical methods are expressed in terms of graphics, pictures, etc. These results represent the view of reality that the chosen method provides. In order to affirm that the result of a numerical solution is fully consistent with the reality, it must be satisfied that: a. The mathematical model must incorporate all aspects of the real world. b. The numerical method has to solve exactly the equations of the mathematical modelling. The problem starts with these two conditions that guarantee the "truth" of the results, since none of them are fully accomplished and it must be admitted that the numerical prediction never completely matches the "real" world behaviour. Then you can only be sure that the numerical solution is a good approximation of the reality. Now, new questions arise: How much does the result obtained by a numerical method resemble the reality? How can we objectively quantify this similarity? The answers to these questions are those that give rise to the validation methods.Peer ReviewedINTECH20112011-09-0120112011-10-03book parthttp://purl.org/coar/resource_type/c_3248VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/bookPartapplication/pdfhttps://hdl.handle.net/2117/13404reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengEuropean Commission http://dx.doi.org/10.13039/100011102 Seventh Framework Programme 205294 HIRF Synthetic Environmentopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/134042026-05-27T15:37:01Z
dc.title.none.fl_str_mv Numerical validation methods
title Numerical validation methods
spellingShingle Numerical validation methods
Jauregui Tellería, Ricardo
Numerical analysis -- Simulation methods
Anàlisi numèrica -- Processament de dades
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
title_short Numerical validation methods
title_full Numerical validation methods
title_fullStr Numerical validation methods
title_full_unstemmed Numerical validation methods
title_sort Numerical validation methods
dc.creator.none.fl_str_mv Jauregui Tellería, Ricardo
Silva Martínez, Fernando|||0000-0003-3019-3993
author Jauregui Tellería, Ricardo
author_facet Jauregui Tellería, Ricardo
Silva Martínez, Fernando|||0000-0003-3019-3993
author_role author
author2 Silva Martínez, Fernando|||0000-0003-3019-3993
author2_role author
dc.subject.none.fl_str_mv Numerical analysis -- Simulation methods
Anàlisi numèrica -- Processament de dades
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
topic Numerical analysis -- Simulation methods
Anàlisi numèrica -- Processament de dades
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
description In the last years, numerical simulation has seen a great development thanks to costs reduction and speed increases of the computational systems. With these improvements, the mathematical algorithms are able to work properly with more realistic problems. Nowadays, the solution of a problem using numerical simulation is not just finding a result, but also to ensure the quality. However, can we say that the model results are correct regarding the behaviour of the system? In other words, how could we quantify the similarity between reality and simulations? To answer these questions, it is necessary to establish a validation criterion that allows an objective quantification of the difference between the results and the reality. Another way to say this is, how “true” our results are. In the case of numerical methods, the main objective is to replicate as closely as possible the behaviour of the "real" world through numbers. Normally, the results of the numerical methods are expressed in terms of graphics, pictures, etc. These results represent the view of reality that the chosen method provides. In order to affirm that the result of a numerical solution is fully consistent with the reality, it must be satisfied that: a. The mathematical model must incorporate all aspects of the real world. b. The numerical method has to solve exactly the equations of the mathematical modelling. The problem starts with these two conditions that guarantee the "truth" of the results, since none of them are fully accomplished and it must be admitted that the numerical prediction never completely matches the "real" world behaviour. Then you can only be sure that the numerical solution is a good approximation of the reality. Now, new questions arise: How much does the result obtained by a numerical method resemble the reality? How can we objectively quantify this similarity? The answers to these questions are those that give rise to the validation methods.
publishDate 2011
dc.date.none.fl_str_mv 2011
2011-09-01
2011
2011-10-03
dc.type.none.fl_str_mv book part
http://purl.org/coar/resource_type/c_3248
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/bookPart
format bookPart
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/13404
url https://hdl.handle.net/2117/13404
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv European Commission http://dx.doi.org/10.13039/100011102 Seventh Framework Programme 205294 HIRF Synthetic Environment
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv INTECH
publisher.none.fl_str_mv INTECH
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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