Matches in SemOpenAlex for { <https://semopenalex.org/work/W2493181255> ?p ?o ?g. }
Showing items 1 to 76 of
76
with 100 items per page.
- W2493181255 endingPage "41" @default.
- W2493181255 startingPage "25" @default.
- W2493181255 abstract "This chapter describes two computational methods for solving sensitivity equations. Note that the model problems given in Chapter 3 are defined on parameter-dependent domains. We address this issue here, and suggestions for dealing with this situation in the context of numerical sensitivity approximations are given. In particular, mapping techniques are discussed, and we show how these techniques can be blended with SEMs to numerically approximate sensitivities. We also show that there are some pitfalls associated with combining these techniques.4.1 The Method of MappingsThe examples introduced in Chapter 3 belong to a class of elliptic boundary value problems defined on domains that depend on a parameter. For many engineering applications, a typical approach to such problems is to begin by transforming the problem to a fixed computational domain that is not parameter dependent. This computational domain is often more regular in shape, which simplifies grid generation and can improve the accuracy of numerical calculations. This mapping technique is very common for problems involving complex geometries that occur in fluid dynamics. The book [53] is an excellent source of information about these topics, and [32] provides some examples with computational details.4.1.1 Transformation TechniquesWe begin with some comments concerning the theoretical aspects of the method of mappings. The technique of mapping a given domain to one with a different coordinate system is used extensively in the theory of partial differential equations. We briefly summarize the theoretical results that provide the mathematical foundation for the use of this technique. The transformation theorem on page 80 of [54] gives the conditions under which Sobolev spaces defined on the physical domain, Ωp, are equivalent to those defined on the computational space Ω. Let T : Ωp → Ω be a Ck,λ diffeomorphism between the domains." @default.
- W2493181255 created "2016-08-23" @default.
- W2493181255 creator A5008588323 @default.
- W2493181255 creator A5028921522 @default.
- W2493181255 date "2002-01-01" @default.
- W2493181255 modified "2023-09-26" @default.
- W2493181255 title "4. Computational Algorithms" @default.
- W2493181255 doi "https://doi.org/10.1137/1.9780898717556.ch4" @default.
- W2493181255 hasPublicationYear "2002" @default.
- W2493181255 type Work @default.
- W2493181255 sameAs 2493181255 @default.
- W2493181255 citedByCount "0" @default.
- W2493181255 crossrefType "book-chapter" @default.
- W2493181255 hasAuthorship W2493181255A5008588323 @default.
- W2493181255 hasAuthorship W2493181255A5028921522 @default.
- W2493181255 hasConcept C104317684 @default.
- W2493181255 hasConcept C11413529 @default.
- W2493181255 hasConcept C127413603 @default.
- W2493181255 hasConcept C134306372 @default.
- W2493181255 hasConcept C151730666 @default.
- W2493181255 hasConcept C182310444 @default.
- W2493181255 hasConcept C185592680 @default.
- W2493181255 hasConcept C187691185 @default.
- W2493181255 hasConcept C204241405 @default.
- W2493181255 hasConcept C21200559 @default.
- W2493181255 hasConcept C24326235 @default.
- W2493181255 hasConcept C2524010 @default.
- W2493181255 hasConcept C2779343474 @default.
- W2493181255 hasConcept C28826006 @default.
- W2493181255 hasConcept C33923547 @default.
- W2493181255 hasConcept C36503486 @default.
- W2493181255 hasConcept C41008148 @default.
- W2493181255 hasConcept C55493867 @default.
- W2493181255 hasConcept C80444323 @default.
- W2493181255 hasConcept C86803240 @default.
- W2493181255 hasConcept C93779851 @default.
- W2493181255 hasConceptScore W2493181255C104317684 @default.
- W2493181255 hasConceptScore W2493181255C11413529 @default.
- W2493181255 hasConceptScore W2493181255C127413603 @default.
- W2493181255 hasConceptScore W2493181255C134306372 @default.
- W2493181255 hasConceptScore W2493181255C151730666 @default.
- W2493181255 hasConceptScore W2493181255C182310444 @default.
- W2493181255 hasConceptScore W2493181255C185592680 @default.
- W2493181255 hasConceptScore W2493181255C187691185 @default.
- W2493181255 hasConceptScore W2493181255C204241405 @default.
- W2493181255 hasConceptScore W2493181255C21200559 @default.
- W2493181255 hasConceptScore W2493181255C24326235 @default.
- W2493181255 hasConceptScore W2493181255C2524010 @default.
- W2493181255 hasConceptScore W2493181255C2779343474 @default.
- W2493181255 hasConceptScore W2493181255C28826006 @default.
- W2493181255 hasConceptScore W2493181255C33923547 @default.
- W2493181255 hasConceptScore W2493181255C36503486 @default.
- W2493181255 hasConceptScore W2493181255C41008148 @default.
- W2493181255 hasConceptScore W2493181255C55493867 @default.
- W2493181255 hasConceptScore W2493181255C80444323 @default.
- W2493181255 hasConceptScore W2493181255C86803240 @default.
- W2493181255 hasConceptScore W2493181255C93779851 @default.
- W2493181255 hasLocation W24931812551 @default.
- W2493181255 hasOpenAccess W2493181255 @default.
- W2493181255 hasPrimaryLocation W24931812551 @default.
- W2493181255 hasRelatedWork W1559336379 @default.
- W2493181255 hasRelatedWork W2062274034 @default.
- W2493181255 hasRelatedWork W2136492660 @default.
- W2493181255 hasRelatedWork W2352349437 @default.
- W2493181255 hasRelatedWork W2365767001 @default.
- W2493181255 hasRelatedWork W2380963126 @default.
- W2493181255 hasRelatedWork W2920887911 @default.
- W2493181255 hasRelatedWork W2951985102 @default.
- W2493181255 hasRelatedWork W7229105 @default.
- W2493181255 hasRelatedWork W2805391225 @default.
- W2493181255 isParatext "false" @default.
- W2493181255 isRetracted "false" @default.
- W2493181255 magId "2493181255" @default.
- W2493181255 workType "book-chapter" @default.