# This Collection

By Defense Date By Authors By Titles By Subject

# Statistics

View Statistics All RECERCAT

# My RECERCAT

To access the full text documents, please follow this link: http://hdl.handle.net/2117/13404

 Title: Numerical validation methods Jauregui Tellería, Ricardo; Silva Martínez, Fernando Universitat Politècnica de Catalunya. Departament d'Enginyeria Electrònica; Universitat Politècnica de Catalunya. IEB - Instrumentació Electrònica i Biomèdica 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. Peer Reviewed Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèricaNumerical analysis -- Simulation methodsAnàlisi numèrica -- Processament de dades info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/bookPart INTECH

# Related documents

## Other documents of the same author

Jauregui Tellería, Ricardo; Ventosa Llopart, Oriol; Silva Martínez, Fernando; Kunze, Marco
Jauregui Tellería, Ricardo; Riu Costa, Pere Joan; Silva Martínez, Fernando
Jauregui Tellería, Ricardo; Pous Solà, Marc; Fernández Chimeno, Mireya; Silva Martínez, Fernando
Jauregui Tellería, Ricardo; Rojas, Julio; Silva Martínez, Fernando
Jauregui Tellería, Ricardo; Silva Martínez, Fernando; Heras, Miguel

Coordination

Supporters