From 5259d0bcd125a9dbc44309fdd8c074bb46ffd481 Mon Sep 17 00:00:00 2001 From: "stefan.girke" <stefan.girke@4028485c-44d9-4cde-a312-5a4635ee2db9> Date: Fri, 11 Feb 2011 09:06:25 +0000 Subject: [PATCH] Added a small figure showing applyLocal() for the systemMatrix/RHS. Suggestion for a interface class Assemble. git-svn-id: https://dune.mathematik.uni-freiburg.de/svn/dune-fem-functionals/trunk@18 4028485c-44d9-4cde-a312-5a4635ee2db9 --- doc/latex/dune-fem-functionals.pdf | Bin 183334 -> 185716 bytes doc/latex/dune-fem-functionals.tex | 511 ++++++++++++++++++++++++++++- 2 files changed, 509 insertions(+), 2 deletions(-) diff --git a/doc/latex/dune-fem-functionals.pdf b/doc/latex/dune-fem-functionals.pdf index 9d30118c7c04da25f76112fc1175c2487a346feb..ee2815201e3395b42ec90d53bd80e6141db70610 100644 GIT binary patch literal 185716 zcmY!laB<T$)HC5yJ^rSD5tosXf`LMQQWlqujlNH6UV2G}f|0R;fkKeJTV_s4YLSAz zTTWt0s!M8eeoCsH9anKlQEFl?SH+yS(KjcB92fjr+<y4}g@@wh)>o$A61R_ZQh4~G zX-VM^#~+CjvlgB`vw^2KrGD@Em8+sdxBoU$ki6MZAYfoxs-1n(W@cs9!=phwMVddB z|FPK}bLUso%%?xUI_c~`aR2ks?p7b&X-|*eeEMm#@U~6fFWFVsM$WT|ODWtr<s6Tq z&RpT<!qbyaAKkwC{Pm&^N3Y#gJMW!1=#qWrRmtAK<_%suu0H<i#_#ARAGSU~L}>1> ztDCPq;F3*{c>BNZ6Fc9V-;IXzK3q)xFxfqG1FsvOoy6W-%QsDk+T0%!c5l|zX{pN> 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b/doc/latex/dune-fem-functionals.tex @@ -14,6 +14,10 @@ \usepackage{xspace} \usepackage{relsize} +\usepackage[usenames,dvipsnames]{pstricks} +\usepackage{epsfig} + + \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amsthm} @@ -769,7 +773,7 @@ First of all we give an overview on the various classes that are required in our %added by Stefan %---------------------- \item[$\circ$] incorporates something like:\\ - \CodeT{assembleSystemMatrix(); constraints.apply( systemMatrix() );} + \CodeT{SystemMatrix(); constraints.apply( systemMatrix() );}, \CodeT{algebraic(); constraints.apply( algebraic() );} respectively \end{itemize} %------------------------- @@ -781,7 +785,7 @@ First of all we give an overview on the various classes that are required in our \item[$\circ$] assembles the right hand side in our system of equations \item[$\circ$] {\it Algebraic representation:} get assembled functional with \CodeT{functional.algebraic()} \item[$\circ$] incorporates something like:\\ -\CodeT{assembleFunctional(); constraints.apply( functional );} +\CodeT{algebraicl(); constraints.apply( functional );} \end{itemize} Both classes (\CodeT{DifferentialOperator} and \CodeT{FunctionalAssembler}) might be incorporated in a general \CodeT{FunctionalSolverInterface}, so that the user does not need to care about the system assemblers. @@ -805,6 +809,72 @@ Both classes (\CodeT{DifferentialOperator} and \CodeT{FunctionalAssembler}) migh %Both classes might be incorporated in a general \CodeT{FunctionalSolverInterface}, so that the user does not need to care about the system assemblers. +%---------------------- +%added by Stefan +%---------------------- +\subsubsection{Suggestion for an alternative ''Assembler`` design} + +Maybe we should think about the operator and ''assembled functional'' design again. Here is another abstract approach:\\ + +\begin{remark}[Conceptual class tree]\theoremNewline + \begin{tikzpicture} + \tikzstyle{boxs} = [draw, %text width=4em, + fill=blue!5, minimum height=2em, rounded corners] + \tikzstyle{boxsG} = [draw, %text width=4em, + fill=green!5, minimum height=2em, rounded corners ] + \tikzstyle{line} = [draw,->,thick] + \tikzstyle{lineR} = [draw,<-,thick] + + \node(Assembler)[boxs]{\CodeT{Assembler}}; + \tikzset{node distance = 25mm} + \node(dummy1)[below of = Assembler]{}; + \node(OperatorAssembler)[boxs,left of = dummy1]{\CodeT{OperatorAssembler}} edge[line] (Assembler.south); + \node(FunctionalAssembler)[boxs,right of = dummy1]{\CodeT{FunctionalAssembler}} edge[line] (Assembler.south); + \tikzset{node distance = 15mm} + + \end{tikzpicture} + \end{remark}\theoremEndLine + +\noindent\CodeT{typedef Assembler < AssemblerTraits > AssemblerType;} +\begin{itemize} + \item[$\circ$] Assembler interface class. + \item[$\circ$] Each class derived from this interface defines a type \CodeT{AlgebraicRepresentationType}, which defines how the algebraic representation is stored - for example a vector or matrix. + \item[$\circ$] A method \CodeT{algebraic()} with return type \CodeT{AlgebraicRepresentationType} is introduced here. +\end{itemize} + +\noindent\CodeT{typedef OperatorAssembler< LinearSubspaceType, AffineSubspaceType>}\\ +\CodeT{OperatorAssemblerType;} +\begin{itemize} + \item[$\circ$] Derived from \CodeT{Assembler}. + \item[$\circ$] \CodeT{typedef MatrixObject AlgebraicRepresentationType}. + \item[$\circ$] The method \CodeT{algebraic()} represents the algebraic representation for the system matrix, i.e. the assembled system matrix. +\end{itemize} + +\noindent\CodeT{typedef FunctionalAssembler < FunctionalType, AffineSubspace >}\\ +\CodeT{FunctionalAssemblerType;} +\begin{itemize} + \item[$\circ$] Derived from \CodeT{Assembler}. + \item[$\circ$] \CodeT{typedef VectorObject AlgebraicRepresentationType}. + \item[$\circ$] The method \CodeT{algebraic()} represents the algebraic representation, i.e. the assembled functional. +\end{itemize} + +\noindent No we can define the \CodeT{Operator} and \CodeT{FunctionalAssembler} in a different way: + +\noindent\CodeT{typedef Operator< FunctionalType, AffineSubspace,} +\CodeT{AssemblerType > DifferentialOperatorType;}\\ +Note: We can also define \CodeT{typedef Operator< AssemblerType > DifferentialOperatorType } by extracting the space types from the assembler. +\begin{itemize} + \item[$\circ$] Same properties as above\ldots + \item[$\circ$] Define a private method \CodeT{void applyConstraints(algebraicRepresentation)} where the constraints are extracted and applied to the algebraic representation. Now we can implement a general assemble method just by writing \CodeT{applyConstraints(operator.algebraic())}. +\end{itemize} + +\noindent\CodeT{typedef FunctionalAssembler< FunctionalType, AffineSubspace, AssemblerType >}\\ +\CodeT{FunctionalAssemblerType;}\\ +Note: We can also define \CodeT{typedef FunctionalAssembler< AssemblerType > FunctionalAssemblerType} by extracting the space types from the assembler. +\begin{itemize} + \item[$\circ$] Same properties as above\ldots + \item[$\circ$] Define a private method \CodeT{applyConstraints(algebraicRepresentation)} where the constraints are extracted and applied to the algebraic representation. Now we can implement a general assemble method just by writing \CodeT{applyConstraints(functional.algebraic())}. +\end{itemize} \subsection{Draft} @@ -1064,6 +1134,443 @@ The essential difference is that the (differential)operator already knows the co \end{tikzpicture} \end{remark}\theoremEndLine + \begin{remark}[SingleConstraint vs. ConstraintsInterface]\theoremNewline + The next figure shows the class concept again - concentrating on the difference between a single constraint and classes derived from the class \CodeT{ConstraintsInterface}. Here we should discuss about some implementation details, especially about the Interface class. 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Mainly, this class is the formal implementation of \ref{definition::abstract_concept::constraint}. This class is the basic class for all other classes dealing with constraints. Normally this class is not used directly because an efficient implementation is not possible.\\ Shortly said, a single constraint presents a pair of a \emph{functional} (defining the constraint) and \emph{row number} determing the row which has to be deleted in the system matrix.\\ -- GitLab