From eb845a8f3ba956e565846ee8e62e248f331d629e Mon Sep 17 00:00:00 2001 From: bruneton Date: Wed, 6 Mar 2013 12:48:41 +0000 Subject: [PATCH] Doc fix - extensive field interpolation differs from intensive field interpolation, even if the meshes perfectly overlapp. --- doc/doxygen/interptheory.dox | 11 ++++++----- doc/doxygen/medcoupling.dox | 24 ++++++++++++++---------- 2 files changed, 20 insertions(+), 15 deletions(-) diff --git a/doc/doxygen/interptheory.dox b/doc/doxygen/interptheory.dox index f53984c82..4fd32b8bb 100644 --- a/doc/doxygen/interptheory.dox +++ b/doc/doxygen/interptheory.dox @@ -8,8 +8,8 @@ For fields with polynomial representation on each cell, the components of the di \f] \f$W\f$ is called the \anchor interpolationmatrix interpolation matrix. -The objectives of interpolators is to compute the matrix W depending on their physical -properties (\ref IntExtFields) and their mesh discretisation (P0, P1,...). +The objective of interpolators is to compute the matrix W depending on their physical +properties (\ref IntExtFields) and their mesh discretisation (on cells P0, on nodes P1,...). \section ConsInterp Conservative interpolation @@ -42,9 +42,10 @@ fully overlapped by cells of S that is \sum_{S_j} Vol(T_i\cap S_j) = Vol(T_i),\hspace{1cm} and \hspace{1cm} \sum_{T_i} Vol(S_j\cap T_i) = Vol(S_j) \f] then the meshes S and T are said to be \b -overlapping and all the algorithms will return the same results. +overlapping. In this case the two formulas in a given column in the table below give the same +result. All intensive formulas result in the same output, and all the extensive formulas give also the same output. -The ideal interpolation algorithm should be conservative and respect the maximum principle. However such an algorithm can be impossible to design if the two meshes do not overlap. When the meshes do not overlap, using either \f$Vol(T_i)\f$ or \f$\sum_{S_j} Vol(T_i\cap S_j)\f$ in the formula one obtains an algorithm that respects either conservativity either the maximum principle (see the nature of field \ref TableNatureOfField "summary table"). +The ideal interpolation algorithm should be conservative and respect the maximum principle. However such an algorithm can be impossible to design if the two meshes do not overlap. When the meshes do not overlap, using either \f$Vol(T_i)\f$ or \f$\sum_{S_j} Vol(T_i\cap S_j)\f$ one obtains an algorithm that respects either the conservativity or the maximum principle (see the nature of field \ref TableNatureOfField "summary table"). \section InterpKerRemapInt Linear conservative remapping of P0 (cell based) fields @@ -109,7 +110,7 @@ given by the formula : \f] \section TableNatureOfField Summary -In the case of fields with P0 representation, if the meshes do not overlap the scheme is either conservative or maximum preserving (not both) and depending on the prioritised property and the \ref NatureOfField the interpolation coefficients take the following value +In the case of fields with a P0 representation (cell based) and when the meshes do not overlap, the scheme is either conservative or maximum preserving (not both). Depending on the \ref NatureOfField the interpolation coefficients take the following value: * * diff --git a/doc/doxygen/medcoupling.dox b/doc/doxygen/medcoupling.dox index b8293f96e..6c49ae303 100644 --- a/doc/doxygen/medcoupling.dox +++ b/doc/doxygen/medcoupling.dox @@ -638,28 +638,32 @@ Let's consider DataArrayDouble instance \c ddd constituted with 4 tuples contain \section IntExtFields Overview: intensive and extensive field -\c NatureOfField is an enum which helps determining some physical significance of the field and affects the choice of interpolation formula ( see \ref TableNatureOfField). +\c NatureOfField is an enum which helps determining some physical significance of the field and affects the choice of the interpolation formula (see \ref TableNatureOfField). It has five possible values: -- "NoNature", the default value, does not allow the use of interpolation tools +- "NoNature", the default value, does not allow the use of any interpolation tools - \ref TableNatureOfFieldExampleConservVol "ConservativeVolumic", for intensive field with the maximum principle favored over conservativity. Relevant for temperature, pression fields. +- \ref TableNatureOfFieldExampleRevIntegral "RevIntegral", for intensive field with the conservativity favored over maximum principle. Relevant for power density fields. + - \ref TableNatureOfFieldExampleIntegral "Integral", for extensive field with the maximum principle favored over conservativity. Relevant for power fields. - \ref TableNatureOfFieldExampleIntegralGlobConstraint "IntegralGlobConstraint", for extensive fields with conservativity favored over the maximum principle. Relevant for power fields. -- \ref TableNatureOfFieldExampleRevIntegral "RevIntegral", for intensive field with the conservativity favored over maximum principle. Relevant for power density fields. +The first two correspond to intensive fields, the last two correspond to extensive fields. -By an intensive field we mean a field that represent volumetric or intensive physical variable such as density (\f$kg.m^{-3}\f$), power density (\f$W.m^{-3}\f$), temperature (\f$K\f$) or pressure (\f$Pa\f$). -By extensive (or integral) field we mean a field that represents an extensive physical quantity sych as mass (\f$kg\f$), volume (\f$m^3\f$), a momentum (\f$kg.m.s^{-1}\f$) or power \f$(W\f$). -For fields with a P0 representation, conservativity formulas are different depending on whether the field is extensive or intensive (see \ref InterpKerP0P0Int and \ref InterpKerP0P0Ext). -In some cases such a non \ref MeshOverlap "overlapping meshes", it is impossible to fulfill both conservation and maximum principle during the interpolation. The nature of the fields determines the formula to be used for non overlapped cells and thus the property that we will be satisfied. -We consider that fields with P1 or P2 representations are necessarily intensive. +By an intensive field we mean a field that represent an intensive physical variable such as density (\f$kg.m^{-3}\f$), power density (\f$W.m^{-3}\f$), temperature (\f$K\f$) or pressure (\f$Pa\f$). Typically the physical value doesn't scale with the size of the underlying geometry. +By extensive (or integral) field we mean a field that represents an extensive physical quantity such as mass (\f$kg\f$), volume (\f$m^3\f$), a momentum (\f$kg.m.s^{-1}\f$) or power \f$(W\f$). +Typically the field value scales linearly with respect to the underlying geometry size. +For fields with a P0 representation (cell based), conservativity formulas are different depending on whether the field is extensive or intensive (see \ref InterpKerP0P0Int and \ref InterpKerP0P0Ext). +Those two notions are themselves split into two sub-categories. +Indeed in some cases (e.g. non \ref MeshOverlap "overlapping meshes"), it is impossible to fulfill both the conservation principle and the maximum principle during the interpolation. The nature of the fields determine the formula to be used for non overlapping cells and thus the property that we will be satisfied. +Finally we consider that fields with P1 or P2 representations are necessarily intensive. \section Usage -In order to employ the various \ref interptools, it is important to specify the nature of your field. -In case the sources and target meshes do not overlap different treatments will be employed, depending on the nature of the source and target fields. +In order to employ the various \ref interptools, you have to specify the nature of your field. +When the source and target meshes do not overlap, different treatments will be employed depending on the nature of the source and target fields. You can specify the nature of the field when you create a \ref medcoupling field with the following constructor: \code MEDCouplingFieldDouble(NatureOfField n, MEDCouplingTimeDiscretization *td, MEDCouplingFieldDiscretization *type); -- 2.39.2
Intensive extensive