From d64f409ec29879fdd3694dbfcc83da764ad7f45a Mon Sep 17 00:00:00 2001 From: Peter Schaefer Date: Mon, 27 May 2013 13:21:49 +0200 Subject: [PATCH] =?utf8?q?[doc]=20alle=20Fehler=20beseitigt=20und=20Kommen?= =?utf8?q?tare=20entfernt=20[src]=20Code=20noch=20mal=20=C3=BCberpr=C3=BCf?= =?utf8?q?t=20[doc]=20Plots=20aktualisiert?= MIME-Version: 1.0 Content-Type: text/plain; charset=utf8 Content-Transfer-Encoding: 8bit --- .cproject | 4 +- .settings/org.eclipse.cdt.codan.core.prefs | 67 +++++++-------- doc/doc.pdf | Bin 753776 -> 747507 bytes doc/doc.tex | 91 ++++++++++----------- doc/fig/132t05n05_2DQuad_cond.eps | 8 +- doc/fig/132t05n05_2DQuad_error.eps | 8 +- doc/fig/132t05n05_2DQuad_hminmax.eps | 8 +- doc/fig/132t05n05_2DQuad_time.eps | 2 +- doc/fig/132t05n05_3DFichCube_cond.eps | 8 +- doc/fig/132t05n05_3DFichCube_error.eps | 8 +- doc/fig/132t05n05_3DFichCube_hminmax.eps | 8 +- doc/fig/132t05n05_3DFichCube_time.eps | 2 +- src/A_plots.m | 2 +- src/compute.m | 28 +++---- src/export_exmpl.m | 5 +- src/mark.m | 6 +- src/mex_build_V.cpp | 14 ++-- src/refineQuad.m | 50 +++++------ src/slpRectangle.cpp | 17 +--- src/slpRectangle.hpp | 7 +- 20 files changed, 165 insertions(+), 178 deletions(-) diff --git a/.cproject b/.cproject index 13bd80b..be5a581 100644 --- a/.cproject +++ b/.cproject @@ -38,7 +38,7 @@ @@ -116,7 +116,7 @@ diff --git a/.settings/org.eclipse.cdt.codan.core.prefs b/.settings/org.eclipse.cdt.codan.core.prefs index a54da21..77386c2 100644 --- a/.settings/org.eclipse.cdt.codan.core.prefs +++ b/.settings/org.eclipse.cdt.codan.core.prefs @@ -1,66 +1,67 @@ -#Thu Dec 01 19:22:52 CET 2011 eclipse.preferences.version=1 org.eclipse.cdt.codan.checkers.errnoreturn=Warning -org.eclipse.cdt.codan.checkers.errnoreturn.params={implicit\=>false} +org.eclipse.cdt.codan.checkers.errnoreturn.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true},implicit\=>false} org.eclipse.cdt.codan.checkers.errreturnvalue=Error -org.eclipse.cdt.codan.checkers.errreturnvalue.params={} +org.eclipse.cdt.codan.checkers.errreturnvalue.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} org.eclipse.cdt.codan.checkers.noreturn=Error -org.eclipse.cdt.codan.checkers.noreturn.params={implicit\=>false} +org.eclipse.cdt.codan.checkers.noreturn.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true},implicit\=>false} org.eclipse.cdt.codan.internal.checkers.AbstractClassCreation=Error -org.eclipse.cdt.codan.internal.checkers.AbstractClassCreation.params={launchModes\=>{RUN_ON_FULL_BUILD\=>false,RUN_ON_INC_BUILD\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} +org.eclipse.cdt.codan.internal.checkers.AbstractClassCreation.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} org.eclipse.cdt.codan.internal.checkers.AmbiguousProblem=Error -org.eclipse.cdt.codan.internal.checkers.AmbiguousProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>false,RUN_ON_INC_BUILD\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} +org.eclipse.cdt.codan.internal.checkers.AmbiguousProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} org.eclipse.cdt.codan.internal.checkers.AssignmentInConditionProblem=Warning -org.eclipse.cdt.codan.internal.checkers.AssignmentInConditionProblem.params={} +org.eclipse.cdt.codan.internal.checkers.AssignmentInConditionProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} org.eclipse.cdt.codan.internal.checkers.AssignmentToItselfProblem=Error -org.eclipse.cdt.codan.internal.checkers.AssignmentToItselfProblem.params={} +org.eclipse.cdt.codan.internal.checkers.AssignmentToItselfProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} org.eclipse.cdt.codan.internal.checkers.CaseBreakProblem=Warning -org.eclipse.cdt.codan.internal.checkers.CaseBreakProblem.params={no_break_comment\=>"no break",last_case_param\=>true,empty_case_param\=>false} +org.eclipse.cdt.codan.internal.checkers.CaseBreakProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true},no_break_comment\=>"no break",last_case_param\=>false,empty_case_param\=>false} org.eclipse.cdt.codan.internal.checkers.CatchByReference=Warning -org.eclipse.cdt.codan.internal.checkers.CatchByReference.params={unknown\=>false,exceptions\=>()} +org.eclipse.cdt.codan.internal.checkers.CatchByReference.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true},unknown\=>false,exceptions\=>()} org.eclipse.cdt.codan.internal.checkers.CircularReferenceProblem=Error -org.eclipse.cdt.codan.internal.checkers.CircularReferenceProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>false,RUN_ON_INC_BUILD\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} +org.eclipse.cdt.codan.internal.checkers.CircularReferenceProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} +org.eclipse.cdt.codan.internal.checkers.ClassMembersInitialization=Warning +org.eclipse.cdt.codan.internal.checkers.ClassMembersInitialization.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true},skip\=>true} org.eclipse.cdt.codan.internal.checkers.FieldResolutionProblem=Error -org.eclipse.cdt.codan.internal.checkers.FieldResolutionProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>false,RUN_ON_INC_BUILD\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} +org.eclipse.cdt.codan.internal.checkers.FieldResolutionProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} org.eclipse.cdt.codan.internal.checkers.FunctionResolutionProblem=Error -org.eclipse.cdt.codan.internal.checkers.FunctionResolutionProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>false,RUN_ON_INC_BUILD\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} +org.eclipse.cdt.codan.internal.checkers.FunctionResolutionProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} org.eclipse.cdt.codan.internal.checkers.InvalidArguments=Error -org.eclipse.cdt.codan.internal.checkers.InvalidArguments.params={launchModes\=>{RUN_ON_FULL_BUILD\=>false,RUN_ON_INC_BUILD\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} +org.eclipse.cdt.codan.internal.checkers.InvalidArguments.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} org.eclipse.cdt.codan.internal.checkers.InvalidTemplateArgumentsProblem=Error -org.eclipse.cdt.codan.internal.checkers.InvalidTemplateArgumentsProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>false,RUN_ON_INC_BUILD\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} +org.eclipse.cdt.codan.internal.checkers.InvalidTemplateArgumentsProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} org.eclipse.cdt.codan.internal.checkers.LabelStatementNotFoundProblem=Error -org.eclipse.cdt.codan.internal.checkers.LabelStatementNotFoundProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>false,RUN_ON_INC_BUILD\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} +org.eclipse.cdt.codan.internal.checkers.LabelStatementNotFoundProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} org.eclipse.cdt.codan.internal.checkers.MemberDeclarationNotFoundProblem=Error -org.eclipse.cdt.codan.internal.checkers.MemberDeclarationNotFoundProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>false,RUN_ON_INC_BUILD\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} +org.eclipse.cdt.codan.internal.checkers.MemberDeclarationNotFoundProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} org.eclipse.cdt.codan.internal.checkers.MethodResolutionProblem=Error -org.eclipse.cdt.codan.internal.checkers.MethodResolutionProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>false,RUN_ON_INC_BUILD\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} +org.eclipse.cdt.codan.internal.checkers.MethodResolutionProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} org.eclipse.cdt.codan.internal.checkers.NamingConventionFunctionChecker=-Info -org.eclipse.cdt.codan.internal.checkers.NamingConventionFunctionChecker.params={pattern\=>"^[a-z]",macro\=>true,exceptions\=>()} +org.eclipse.cdt.codan.internal.checkers.NamingConventionFunctionChecker.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true},pattern\=>"^[a-z]",macro\=>true,exceptions\=>()} org.eclipse.cdt.codan.internal.checkers.NonVirtualDestructorProblem=Warning -org.eclipse.cdt.codan.internal.checkers.NonVirtualDestructorProblem.params={} +org.eclipse.cdt.codan.internal.checkers.NonVirtualDestructorProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} org.eclipse.cdt.codan.internal.checkers.OverloadProblem=Error -org.eclipse.cdt.codan.internal.checkers.OverloadProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>false,RUN_ON_INC_BUILD\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} +org.eclipse.cdt.codan.internal.checkers.OverloadProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} org.eclipse.cdt.codan.internal.checkers.RedeclarationProblem=Error -org.eclipse.cdt.codan.internal.checkers.RedeclarationProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>false,RUN_ON_INC_BUILD\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} +org.eclipse.cdt.codan.internal.checkers.RedeclarationProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} org.eclipse.cdt.codan.internal.checkers.RedefinitionProblem=Error -org.eclipse.cdt.codan.internal.checkers.RedefinitionProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>false,RUN_ON_INC_BUILD\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} +org.eclipse.cdt.codan.internal.checkers.RedefinitionProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} org.eclipse.cdt.codan.internal.checkers.ReturnStyleProblem=-Warning -org.eclipse.cdt.codan.internal.checkers.ReturnStyleProblem.params={} +org.eclipse.cdt.codan.internal.checkers.ReturnStyleProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} org.eclipse.cdt.codan.internal.checkers.ScanfFormatStringSecurityProblem=-Warning -org.eclipse.cdt.codan.internal.checkers.ScanfFormatStringSecurityProblem.params={} +org.eclipse.cdt.codan.internal.checkers.ScanfFormatStringSecurityProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} org.eclipse.cdt.codan.internal.checkers.StatementHasNoEffectProblem=Warning -org.eclipse.cdt.codan.internal.checkers.StatementHasNoEffectProblem.params={macro\=>true,exceptions\=>()} +org.eclipse.cdt.codan.internal.checkers.StatementHasNoEffectProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true},macro\=>true,exceptions\=>()} org.eclipse.cdt.codan.internal.checkers.SuggestedParenthesisProblem=Warning -org.eclipse.cdt.codan.internal.checkers.SuggestedParenthesisProblem.params={paramNot\=>false} +org.eclipse.cdt.codan.internal.checkers.SuggestedParenthesisProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true},paramNot\=>false} org.eclipse.cdt.codan.internal.checkers.SuspiciousSemicolonProblem=Warning -org.eclipse.cdt.codan.internal.checkers.SuspiciousSemicolonProblem.params={else\=>false,afterelse\=>false} +org.eclipse.cdt.codan.internal.checkers.SuspiciousSemicolonProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true},else\=>false,afterelse\=>false} org.eclipse.cdt.codan.internal.checkers.TypeResolutionProblem=Error -org.eclipse.cdt.codan.internal.checkers.TypeResolutionProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>false,RUN_ON_INC_BUILD\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} +org.eclipse.cdt.codan.internal.checkers.TypeResolutionProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} org.eclipse.cdt.codan.internal.checkers.UnusedFunctionDeclarationProblem=Warning -org.eclipse.cdt.codan.internal.checkers.UnusedFunctionDeclarationProblem.params={macro\=>true} +org.eclipse.cdt.codan.internal.checkers.UnusedFunctionDeclarationProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true},macro\=>true} org.eclipse.cdt.codan.internal.checkers.UnusedStaticFunctionProblem=Warning -org.eclipse.cdt.codan.internal.checkers.UnusedStaticFunctionProblem.params={macro\=>true} +org.eclipse.cdt.codan.internal.checkers.UnusedStaticFunctionProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true},macro\=>true} org.eclipse.cdt.codan.internal.checkers.UnusedVariableDeclarationProblem=Warning -org.eclipse.cdt.codan.internal.checkers.UnusedVariableDeclarationProblem.params={macro\=>true,exceptions\=>("@(\#)","$Id")} +org.eclipse.cdt.codan.internal.checkers.UnusedVariableDeclarationProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true},macro\=>true,exceptions\=>("@(\#)","$Id")} org.eclipse.cdt.codan.internal.checkers.VariableResolutionProblem=Error -org.eclipse.cdt.codan.internal.checkers.VariableResolutionProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>false,RUN_ON_INC_BUILD\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} +org.eclipse.cdt.codan.internal.checkers.VariableResolutionProblem.params={launchModes\=>{RUN_ON_FULL_BUILD\=>true,RUN_ON_INC_BUILD\=>true,RUN_ON_FILE_OPEN\=>false,RUN_ON_FILE_SAVE\=>false,RUN_AS_YOU_TYPE\=>true,RUN_ON_DEMAND\=>true}} diff --git a/doc/doc.pdf b/doc/doc.pdf index 057566d36a7bb662b689efd8f6573f4a39f67fae..5e27c3364d0ac1ae88fd3b55cf992cd63da98919 100644 GIT binary patch delta 532355 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z)&dtc+(MEzzwPi|$1n%>yO-(?2%QWIFPfoT&5^ZNe@Q%m!CC&KfL}a%up<0X#-Qa+ zv;bSv3C@zxF%D`%z2bFf)eF57Wp>L2~tYVB@7f)<4Xxyf^$S zC$npQWOmIp&wbwbc~@Vv96#r|vum!#;rJuZd+ya&{H?!{;$^)nuIRn~))Tkf`V+U@ U_^KZ9Bf@sQOD=idi>~SYe``v>3IG5A diff --git a/doc/doc.tex b/doc/doc.tex index de9ca99..d111223 100644 --- a/doc/doc.tex +++ b/doc/doc.tex @@ -149,23 +149,23 @@ \psfrag{min hmin/hmax 1t05n05 A}{\tiny $\min (h_{\min}/h_{\max})$} -\psfrag{tmu 132t05n05 A}{\tiny $\tilde \mu$ analytisch} -\psfrag{eta 132t05n05 A}{\tiny $\eta$ analytisch} -\psfrag{fehler 132t05n05 A}{\tiny Fehler analytisch} -\psfrag{Zeit 132t05n05 A}{\tiny Zeit analytisch} -\psfrag{cond 132t05n05 A}{\tiny Kondition analytisch} +\psfrag{tmu 142t05n05 A}{\tiny $\tilde \mu$ analytisch} +\psfrag{eta 142t05n05 A}{\tiny $\eta$ analytisch} +\psfrag{fehler 142t05n05 A}{\tiny Fehler analytisch} +\psfrag{Zeit 142t05n05 A}{\tiny Zeit analytisch} +\psfrag{cond 142t05n05 A}{\tiny Kondition analytisch} -\psfrag{tmu 132t05n05 QEQA}{\tiny $\tilde \mu$ semianalytisch QE} -\psfrag{eta 132t05n05 QEQA}{\tiny $\eta$ semianalytisch QE} -\psfrag{fehler 132t05n05 QEQA}{\tiny Fehler semianalytisch QE} -\psfrag{Zeit 132t05n05 QEQA}{\tiny Zeit semianalytisch QE} -\psfrag{cond 132t05n05 QEQA}{\tiny Kondition semianalytisch QE} +\psfrag{tmu 142t05n05 QE}{\tiny $\tilde \mu$ semianalytisch QE} +\psfrag{eta 142t05n05 QE}{\tiny $\eta$ semianalytisch QE} +\psfrag{fehler 142t05n05 QE}{\tiny Fehler semianalytisch QE} +\psfrag{Zeit 142t05n05 QE}{\tiny Zeit semianalytisch QE} +\psfrag{cond 142t05n05 QE}{\tiny Kondition semianalytisch QE} -\psfrag{tmu 132t05n05 QA}{\tiny $\tilde \mu$ volle Quadratur} -\psfrag{eta 132t05n05 QA}{\tiny $\eta$ volle Quadratur} -\psfrag{fehler 132t05n05 QA}{\tiny Fehler volle Quadratur} -\psfrag{Zeit 132t05n05 QA}{\tiny Zeit volle Quadratur} -\psfrag{cond 132t05n05 QA}{\tiny Kondition volle Quadratur} +\psfrag{tmu 142t05n05 QA}{\tiny $\tilde \mu$ volle Quadratur} +\psfrag{eta 142t05n05 QA}{\tiny $\eta$ volle Quadratur} +\psfrag{fehler 142t05n05 QA}{\tiny Fehler volle Quadratur} +\psfrag{Zeit 142t05n05 QA}{\tiny Zeit volle Quadratur} +\psfrag{cond 142t05n05 QA}{\tiny Kondition volle Quadratur} \pagestyle{fancy} @@ -174,7 +174,7 @@ % \lhead{\bf \large Aufgabe \thesubsection} % \chead{\thesection. Übung ZtuA} -\rhead{\todo{ \scriptsize \today}} +% \rhead{\todo{ \scriptsize \today}} \cfoot{\thepage} % \setlength{\headheight}{4\baselineskip} @@ -2289,11 +2289,11 @@ In der letzten Strategie "`volle Quadratur"' berechnen wir alle $\zeta_Q$-zuläs \begin{figure}[ht] \centering -\subfloat[Fehler und Fehlerschätzer für das Quadrat \label{fig:2DQuad:sem:err}]{\includegraphics[width=0.5\textwidth]{fig/132t05n05_2DQuad_error}} +\subfloat[Fehler und Fehlerschätzer für das Quadrat \label{fig:2DQuad:sem:err}]{\includegraphics[width=0.5\textwidth]{fig/142t05n05_2DQuad_error}} % \subfloat[Seitenverhältnisse auf dem Quadrat \label{fig:2DQuad:quad:hminmax}]{\includegraphics[width=0.5\textwidth]{fig/132t05n05_2DQuad_hminmax}} \\ -\subfloat[Kondition der $\hat V_{\ell}$ Matrix \label{fig:2DQuad:sem:cond}]{\includegraphics[width=0.5\textwidth]{fig/132t05n05_2DQuad_cond}} -\subfloat[Berechnungszeit für das Quadrat \label{fig:2DQuad:sem:time}]{\includegraphics[width=0.5\textwidth]{fig/132t05n05_2DQuad_time}} +\subfloat[Kondition der $\hat V_{\ell}$ Matrix \label{fig:2DQuad:sem:cond}]{\includegraphics[width=0.5\textwidth]{fig/142t05n05_2DQuad_cond}} +\subfloat[Berechnungszeit für das Quadrat \label{fig:2DQuad:sem:time}]{\includegraphics[width=0.5\textwidth]{fig/142t05n05_2DQuad_time}} \caption{Vergleich der Berechnungsarten von $\hat V_{\ell}$ auf dem Quadrat} \label{fig:2DQuad:sem} \end{figure} @@ -2303,13 +2303,13 @@ In Abbildung \ref{fig:2DQuad:sem:err} haben wir die Ergebnisse des Fehlers gegen 2000 Elemente eine gute Konvergenzrate von $N^{-3/4}$. \noindent -In Abbildung \ref{fig:2DQuad:sem:cond} vergleichen wir noch einmal die Konditionszahlen der $\hat V_{\ell}$ Matrix für die verschiedenen Strategien. Auch hier wurde die \figErr[e] Grenzlinie bei etwa 2000 Elementen eingezeichnet. Anhand der Linie in \figLineA[] erkennen wir deutlich, dass ab der 2000 Elemente Grenze die Konditionszahlen für die analytische Berechnung sprunghaft gegenüber den Konditionszahlen der beiden Quadraturn in \figLineB[] und \figLineC[] ansteigen. Wir erkennen an dieser Stelle aber auch, dass die Kondtionszahlen der "`analytischen"' Berechnung schon ab 1000 Elementen von den Quadraturen geringfügig Abweichen und damit auf eine ungünstige Berechnung hindeuten. +In Abbildung \ref{fig:2DQuad:sem:cond} vergleichen wir noch einmal die Konditionszahlen der $\hat V_{\ell}$ Matrix für die verschiedenen Strategien. Auch hier wurde die \figErr[e] Grenzlinie bei etwa 2000 Elementen eingezeichnet. Anhand der Linie in \figLineA[] erkennen wir deutlich, dass ab der 2000 Elemente Grenze die Konditionszahlen für die analytische Berechnung sprunghaft gegenüber den Konditionszahlen der beiden Quadraturen in \figLineB[] und \figLineC[] ansteigen. Wir erkennen an dieser Stelle aber auch, dass die Kondtionszahlen der "`analytischen"' Berechnung schon ab 1000 Elementen von den Quadraturen geringfügig abweichen und damit auf eine ungünstige Berechnung hindeuten. \noindent -Weiterhin wollen wir noch einmal die Laufzeit der drei Strategien in Abbildung \ref{fig:2DQuad:sem:time} betrachten. Gemessen wurde die Zeit eines Berechnungsschritt, welches wieder das Aufstellen der Matritzen und Lösen des Gleichungssystems beinhaltet. Hier erkennen wir, dass sich die Laufzeiten der drei Strategien nur minimal von einander unterscheiden. Für fast $10^4$ Elemente benötigen alle drei Berechnungsarten etwa $4*10^4$ Sekunden, was etwa elf Stunden entspricht. Da die Zeit zum Aufstellen im Vergleich der Quadraturgrade wesentlich kürzer war, können wir daraus schließen, dass die meiste Zeit beim Lösen und berechnen der Konditionszahlen verloren geht. +Weiterhin wollen wir noch einmal die Laufzeit der drei Strategien in Abbildung \ref{fig:2DQuad:sem:time} betrachten. Gemessen wurde die Zeit eines Berechnungsschritts, welches wieder das Aufstellen der Matritzen und Lösen des Gleichungssystems beinhaltet. Hier erkennen wir, dass sich die Laufzeiten der drei Strategien nur minimal voneinander unterscheiden. Für fast $10^4$ Elemente benötigen alle drei Berechnungsarten etwa $4*10^4$ Sekunden, was etwa elf Stunden entspricht. Da die Zeit zum Aufstellen im Vergleich der Quadraturgrade wesentlich kürzer ist, können wir daraus schließen, dass die meiste Zeit beim Lösen und Berechnen der Konditionszahlen verloren geht. \noindent -Die Ergebnisse zeigen, dass wir durch Gauss-Quadratur über das kleinere Element auf $\zeta_E$-zulässigen Elementen bis an die Speichergrenze stabil rechnen können und es nicht nötig ist alle Integrale durch Quadratur zu ersetzen. Weiterhin nimmt die Art der Berechnung von $\hat V_{\ell}$ kaum Einfluss auf die Laufzeit. +Die Ergebnisse zeigen, dass wir durch Gauss-Quadratur über das kleinere Element auf $\zeta_E$-zulässigen Elementen bis an die Speichergrenze stabil rechnen können und es nicht nötig ist, alle Integrale durch Quadratur zu ersetzen. Weiterhin nimmt die Art der Berechnung von $\hat V_{\ell}$ kaum Einfluss auf die Laufzeit. Damit haben wir in der semianalytischen Berechnung und adaptiv anisotroper Verfeinerung ein stabile Strategie für parallele Elemente gefunden. \subsection{Beispiel Fischer Würfel} @@ -2337,9 +2337,9 @@ Auch hier wurde die Energienorm $\enorm{\phi}^2 \approx 16.2265$ der exakten Lö \end{figure} \noindent -Bei den folgenden Berechnungen werden wir wieder den Algorithmus \ref{alg:adapt} mit Parametern $\theta=0.5,\nu=0.5$ zum Lösen von \eqref{math:bsp:FichCube:gls} verwenden, wobei für alle auftretenden Gauss-Quadraturen der Grad 4 gewählt wurde. Alle Berechnungsarten werden auf den selben Netzen ausgeführt um die Ergebnisse nicht durch die Wahl des Netzes zu beeinflussen.\\ +Bei den folgenden Berechnungen werden wir wieder den Algorithmus \ref{alg:adapt} mit Parametern $\theta=0.5,\nu=0.5$ zum Lösen von \eqref{math:bsp:FichCube:gls} verwenden, wobei für alle auftretenden Gauss-Quadraturen der Grad 4 gewählt wurde. Alle Berechnungsarten werden auf den selben Netzen ausgeführt, um die Ergebnisse nicht durch die Wahl des Netzes zu beeinflussen.\\ Wir werden nun die Matrix $\hat V_{\ell}$ in der "`analytischen"' Strategie durch die in Kapitel \ref{sec:analyt} vorgestellten Stammfunktionen analytisch berechnen. -\todo{Strategie SEMIANALYTISCH} +Dann werden wir für $\zeta_E$-zulässige Elemente wie in Kapitel \ref{sec:semi:QE} das Integral über das kleinere Element durch Gauss-Quadratur ersetzen. Alle anderen Elemente werden bei dieser "`semianalytischen QE"' Strategie weiterhin analytisch berechnet. Weiterhin werden wir in der Strategie "`volle Quadratur"' alle auftretenden Integrale für $\zeta_Q$ zulässige Elemente durch Gauss-Quadratur ersetzen. Da wir annehmen, dass diese Strategie wieder die zuverlässigste sein wird, werden wir den zugehörigen $\tilde \mu$ Schätzer zum Steuern der Netzverfeinerung verwenden. \begin{figure}[ht] @@ -2361,28 +2361,27 @@ Weiterhin werden wir in der Strategie "`volle Quadratur"' alle auftretenden Inte In Abbildung \ref{fig:3DFichCube:sem:err} betrachten wir den Fehler und die Fehlerschätzer $\eta,\tilde \mu$ der Galerkin-Lösung für die verschiedenen Strategien. Gerechnet wurde hierbei bis zu einer Elementanzahl von etwa 8000. Anhand der Linien in \figLineA[] erkennen wir für die "`analytische"' Berechnung wieder die erwartete Konvergenzrate von $N^{-3/4}$. Da die Kurven des $\tilde \mu$ und $\eta$ Schätzers wieder parallel zum Fehler verlaufen, sind die Fehlerschätzer $\tilde \mu$ und $\eta$ effektiv und zuverlässig. Ab 4000 Elementen beobachten wir am $\tilde \mu$ Schätzer, dass die Lösung instabil wird. Diese Grenze haben wir in \figErr[] eingezeichnet. Weiterhin erkennen wir anhand der Linien in \figLineB[] und \figLineC[], dass die Berechnungen mithilfe von Quadratur weiterhin stabil bleiben und wir dadurch einen Fehler der Energienorm von etwa 0.01 erreichen. \noindent -Die Konditionszahlen der $\hat V_{\ell}$ Matrix sehen wir in Abbildung \ref{fig:3DFichCube:sem:cond}. Bis zu der Elementanzahl 4000 steigt die Kondition der Matrix für alle Strategien auf $10^9$ an. Für feinere Netze, erkennen wir ab der Grenze von 4000 Elementen wieder den sprunghaften Anstieg der Konditionszahl für die "`analytische"' Berechnung in \figLineA[]. +Die Konditionszahlen der $\hat V_{\ell}$ Matrix sehen wir in Abbildung \ref{fig:3DFichCube:sem:cond}. Bis zu der Elementanzahl 4000 steigt die Kondition der Matrix für alle Strategien auf $10^9$ an. Für feinere Netze erkennen wir ab der Grenze von 4000 Elementen wieder den sprunghaften Anstieg der Konditionszahl für die "`analytische"' Berechnung in \figLineA[]. \noindent -Diese Beobachtungen zeigen für dreidimensionalen Geometrien, dass die analytische Berechnung auf feinen Netzen instabil wird. -Vergleichen wir unsere Ergebnisse mit denen aus dem Paper \cite[Figur 13]{fer:errbem}, so erreichen wir mit der "`analytischen"' Strategie die gleiche Genauigkeit. Dass das Netz die Ergebnisse beeinflusst können wir fast ausschließen, da wir vergleichbare Forderungen und Parameter an die Netzverfeinerung gestellt haben. -Durch geeignetes ersetzen der Integrale durch Gauss-Quadratur können wir jedoch die Genauigkeit der Lösung beliebig erhöhen und erreichen bis zur Netzgröße von 9000 Elementen einen Fehler der Galerkin-Lösung von 0.01. Wenn wir den Fehler für feinere Netze berechnen wollen, müssten wir entweder einen größeren Arbeitsspeicher verwenden oder andere Strategien entwickeln, welche zum Beispiel unter Verwendung von $h$-Matrizen, durch Approximation eine Komprimierung der Matrix zulassen. +Diese Beobachtungen zeigen für dreidimensionale Geometrien, dass die analytische Berechnung auf feinen Netzen instabil wird. +Vergleichen wir unsere Ergebnisse mit denen aus dem Paper \cite[Figur 13]{fer:errbem}, so erreichen wir mit der "`analytischen"' Strategie die gleiche Genauigkeit. Dass das Netz die Ergebnisse beeinflusst, können wir fast ausschließen, da wir vergleichbare Forderungen und Parameter an die Netzverfeinerung gestellt haben. +Durch geeignetes Ersetzen der Integrale durch Gauss-Quadratur können wir jedoch die Genauigkeit der Lösung beliebig erhöhen und erreichen bis zur Netzgröße von 9000 Elementen einen Fehler der Galerkin-Lösung von 0.01. Wenn wir den Fehler für feinere Netze berechnen wollen, müssten wir entweder einen größeren Arbeitsspeicher verwenden oder andere Strategien entwickeln, welche zum Beispiel unter Verwendung von $h$-Matrizen durch Approximation eine Komprimierung der Matrix zulassen. \subsection{Beispielnetz mit Verfeinerung} -An dieser Stellen wollen wir noch einmal das Netz des Quadrats aus Abbildung \ref{fig:mesh:2DQuad:start} betrachten. Wir wenden dazu die Netzverfeinerung aus Kapitel \ref{sec:implement:refine} mit dem Markierungsvektor $marked = (2, 3, 1, 3)$ auf das Startnetz an und erhalten dadurch das Netz aus Abbildung \ref{exmpl12:lage}. Die drei zugehörigen Matrizen $COO$, $ELE$ und $NEI$, welche in Kapitel \ref{sec:implement:daten} genauer beschrieben wurden, finden wir in den Abbildungen \ref{exmpl12:coo},\ref{exmpl12:ele},\ref{exmpl12:nei}.\\ - -\begin{figure}[ht] +An dieser Stelle wollen wir noch einmal das Netz des Quadrats aus Abbildung \ref{fig:mesh:2DQuad:start} betrachten. Wir wenden dazu die Netzverfeinerung aus Kapitel \ref{sec:implement:refine} mit dem Markierungsvektor $marked = (2, 3, 1, 3)$ auf das Startnetz an und erhalten dadurch das Netz aus Abbildung \ref{exmpl12:lage}. Die drei zugehörigen Matrizen $COO$, $ELE$ und $NEI$, welche in Kapitel \ref{sec:implement:daten} genauer beschrieben wurden, finden wir in den Abbildungen \ref{exmpl12:coo},\ref{exmpl12:ele},\ref{exmpl12:nei}. +\begin{figure}[h!t] \centering \subfloat[Lage \label{exmpl12:lage}]{\includegraphics[width=0.55\textwidth]{fig/exmpl12_ref}} \subfloat[Koordinatenmatrix]{\input{fig/exmpl12_coo}}\\ \subfloat[Elementmatrix]{\input{fig/exmpl12_ele}} \subfloat[Nachbarschaftsrelationen]{\input{fig/exmpl12_nei}} -\caption{{\scriptsize Dieses Beispielnetz entsteht durch die Verfeinerung von Netz \ref{fig:mesh:2DQuad} mit dem Markierungsvektor $marked = (2,3,1,3)$. Zum Verfeinern wurde der Algorithmus \ref{alg:refine} mit der Implementierung aus \ref{code:refineQuad} verwendet. In Schwarz wurde der Index der Elemente und in rot der Index der Koordinaten eingezeichnet.}} +\caption{{\scriptsize Dieses Beispielnetz entsteht durch die Verfeinerung von Netz \ref{fig:mesh:2DQuad} mit dem Markierungsvektor $marked = (2,3,1,3)$. Zum Verfeinern wurde der Algorithmus \ref{alg:refine} mit der Implementierung aus \ref{code:refineQuad} verwendet. In schwarz wurde der Index der Elemente und in rot der Index der Koordinaten eingezeichnet.}} \label{exmpl12} \end{figure} \noindent -Wenn wir nun in diesem Netz das Element 7 durch ein Teilung vom Typ 2 weiter verfeinern, muss auch das Element 4 geteilt werden. Abbildung \ref{exmpl13:lage} stellt dieses neue Netz dar und zeigt das der Algorithmus \ref{alg:refine} die nötigen Teilungen vornimmt. +Wenn wir nun in diesem Netz das Element 7 durch eine Teilung vom Typ 2 weiter verfeinern, muss auch das Element 4 geteilt werden. Abbildung \ref{exmpl13:lage} stellt dieses neue Netz dar und zeigt, dass der Algorithmus \ref{alg:refine} die nötigen Teilungen vornimmt. \begin{figure}[ht] \centering @@ -2392,7 +2391,7 @@ Wenn wir nun in diesem Netz das Element 7 durch ein Teilung vom Typ 2 weiter ver % \subfloat[Koordinaten]{\input{fig/exmpl13_coo}}\\ % \subfloat[Elemente]{\input{fig/exmpl13_ele}} % \subfloat[Nachbarn]{\input{fig/exmpl13_nei}} -\caption{\scriptsize Dieses Netz entsteht durch die Verfeinerung von Element 7 aus dem Netz \ref{exmpl12}. In Schwarz wurde der Index der Elemente und in rot der Index der Koordinaten eingezeichnet. Es zeigt, dass zusätzlich Elemente verfeinert werden um die Forderung von maximal drei Knoten auf einer Kante zu erfüllen.} +\caption{\scriptsize Dieses Netz entsteht durch die Verfeinerung von Element 7 aus dem Netz \ref{exmpl12}. In schwarz wurde der Index der Elemente und in rot der Index der Koordinaten eingezeichnet. Es zeigt, dass zusätzlich Elemente verfeinert werden, um die Forderung von maximal drei Knoten auf einer Kante zu erfüllen.} \label{exmpl13:lage}\label{exmpl13} \end{figure} @@ -2437,7 +2436,7 @@ Wenn wir nun in diesem Netz das Element 7 durch ein Teilung vom Typ 2 weiter ver % \end{enumerate} % } \noindent -Abschließend werden wir die für die Numerischen Experimente verwendeten Funktionen vorstellen. Hierbei wollen wir anmerken, dass wir im Laufe der Untersuchungen eine Erweiterung eingeführt haben auf die wir in den vorherigen Kapiteln nicht eingegangen sind.\\ +Abschließend werden wir die für die numerischen Experimente verwendeten Funktionen vorstellen. Hierbei wollen wir anmerken, dass wir im Laufe der Untersuchungen eine Erweiterung eingeführt haben, auf die wir in den vorherigen Kapiteln nicht eingegangen sind.\\ Um Berechnungsfehler für die Seitenlängen und Flächeninhalte in \Matlab~zu vermeiden, haben wir die zusätzliche Matrix $sites\in\N^{N\times2}$ eingeführt. Eine Zeile $sites_j = (a_{j},b_{j})$ mit $j\in \{1,\ldots,N\}$ der Matrix entspricht der Anzahl der Halbierungen der Seitenlängen $a,b$ aus Definition \ref{thm:def:T} vom Element $T_j$, gelten muss hierbei $a = 2^{-a_j}$ und $b = 2^{-b_j}$. Dadurch können wir den Flächeninhalt von $T_j$ durch $\abs{T_j} = 2^{-(a_j+b_j)}$ bestimmen.\\ In der Implementierung für die Berechnung der Matrixeinträge $A_{jk} = \int_{T_j} \int_{T_k} \frac{1}{\abs{\bs x -\bs y}}ds_{\bs y} ds_{\bs x}$ wurde diese Erweiterung nicht verwendet. \subsection[C++]{\Cpp} @@ -2448,14 +2447,14 @@ Dadurch können wir den Flächeninhalt von $T_j$ durch $\abs{T_j} = 2^{-(a_j+b_j \begin{lstlisting}[language=M,numbers=none] [A] = mex_build_V(coo,ele,zeta,typ); \end{lstlisting} - Hierbei ist \lstinline!coo! $\in \R^{M\times3}$ die Koordinatenmatrix aus Kapitel \ref{sec:implement:daten} und \lstinline!ele! $\in \N^{N\times4}$ die zugehörige Elementmatrix in der die Zeilenindizes der Koordinaten \lstinline!coo! stehen. Eine Zeile der Koordinatenmatrix entspricht einer Koordinate und eine Zeile aus der Elementmatrix steht für die Indizes der Koordinaten eines Elements. Weiterhin steht \lstinline!zeta! $ = (p, \zeta_Q, \zeta_E)$ für den Koordinatenvektor. Mithilfe des Parameters $q \in \{0,1,2,3,4,5\}$ kann die Anzahl $2^q$ der Auswertungsstellen für die Gauss-Quadratur gewählt werden. Die beiden Parameter $\zeta_Q,\zeta_E \in \R^+$ werden in den Zulässigkeitsbedingungen verwendet. Der Parameter \lstinline!typ! $\in \{1,2,3\}$ steht für die Art der Berechnung aus Kapitel \ref{sec:implement:A}. Zurück gegeben wird die zur Parametrisierung gehörende Matrix $A \in\R^{N\times N}$. + Hierbei ist \lstinline!coo! $\in \R^{M\times3}$ die Koordinatenmatrix aus Kapitel \ref{sec:implement:daten} und \lstinline!ele! $\in \N^{N\times4}$ die zugehörige Elementmatrix, in der die Zeilenindizes der Koordinaten \lstinline!coo! stehen. Eine Zeile der Koordinatenmatrix entspricht einer Koordinate und eine Zeile aus der Elementmatrix steht für die Indizes der Koordinaten eines Elements. Weiterhin steht \lstinline!zeta! $ = (p, \zeta_Q, \zeta_E)$ für den Koordinatenvektor. Mithilfe des Parameters $q \in \{0,1,2,3,4,5\}$ kann die Anzahl $2^q$ der Auswertungsstellen für die Gauss-Quadratur gewählt werden. Die beiden Parameter $\zeta_Q,\zeta_E \in \R^+$ werden in den Zulässigkeitsbedingungen verwendet. Der Parameter \lstinline!typ! $\in \{1,2,3\}$ steht für die Art der Berechnung aus Kapitel \ref{sec:implement:A}. Zurückgegeben wird die zur Parametrisierung gehörende Matrix $A \in\R^{N\times N}$. \lstinputlisting[language=C++,firstline=29,firstnumber=29]{../src/mex_build_V.cpp} \subsubsection{slpRectangle.hpp}\label{code:slpRectangle.hpp} Diese Datei stellt die Funktionen zur Berechnung eines Matrixeintrages $A_{jk}$ bereit, welcher dann für parallele Elemente über \begin{lstlisting}[language=C++,numbers=none] double cParO1(b,d,t,v,d1,d2,d3,zeta*); \end{lstlisting} - berechnet werden kann. \lstinline!b,d! entspricht den Seitenlängen des Elements $T_j$ und \lstinline!t,v! denen des Elements $T_k$ und $\bs \delta =$\lstinline!(d1,d2,d3)! dem Abstandsvektor, wie in Kapitel \ref{sec:analyt:int}. Hierbei ist zu beachten, dass \lstinline!b,t! in der selben Dimension liegen wie auch \lstinline!d1! und wie auch \lstinline!d,v,d2! in der selben Dimension liegen. Die Zulässigkeitsbedingungen werden durch \lstinline!zeta*! = $(\zeta_Q,\zeta_E)$ bestimmt. Für Ortogonale Elemente steht analog die Funktion + berechnet werden kann. \lstinline!b,d! entspricht den Seitenlängen des Elements $T_j$ und \lstinline!t,v! denen des Elements $T_k$ und $\bs \delta =$\lstinline!(d1,d2,d3)! dem Abstandsvektor, wie in Kapitel \ref{sec:analyt:int}. Hierbei ist zu beachten, dass \lstinline!b,t! in der selben Dimension liegen, wie auch \lstinline!d1! und wie auch \lstinline!d,v,d2! in der selben Dimension liegen. Die Zulässigkeitsbedingungen werden durch \lstinline!zeta*! = $(\zeta_Q,\zeta_E)$ bestimmt. Für orthogonale Elemente steht analog die Funktion \begin{lstlisting}[language=C++,numbers=none] double cOrtO1(b,d,t,v,d1,d2,d3,zeta*); \end{lstlisting} @@ -2481,25 +2480,25 @@ for(int i=0;i=0,1) +first = 0 +find(([ (G_D(2:end,2+rows*i)-G_D(1:end-1,2+rows*i))./G_D(2:end,2+rows*i)])>=0,1) Ferr = (X(first,i+1)+X(first-1,i+1))/2; loglog(X(:,i+1),G_D(:,2+rows*i),type2sym(i*3+1), ... diff --git a/src/compute.m b/src/compute.m index 9ba527a..8cae628 100644 --- a/src/compute.m +++ b/src/compute.m @@ -19,7 +19,7 @@ function [data er fileo] = compute(file,times,zeta,typ,theta,nu,vcon) % Datei laden load(file) -% Kontainer fuer Messungen initialisieren +% Container fuer Messungen initialisieren if(~exist('data','var')) data=[]; end @@ -28,7 +28,7 @@ kap3 = 0; %times mal verfeinern oder bis Elementanzahl fuer times > 40 for j = 1:times - %Beende Schleife wenn Element Anzahl erreicht + %beende Schleife wenn Elementanzahl erreicht if(times>40 && size(elements,1) > times) break; end @@ -41,11 +41,11 @@ for j = 1:times old_x_fine = x_fine; end - %uniformIsotrop Verfeinern + %uniformIsotrop verfeinern [coo_fine,ele_fine,neigh_fine,f2s,sit_fine]... =refineQuad(coordinates,elements,neigh,sites,2); - %Flaecheninhalte Berechnen (rhs) + %Flaecheninhalte berechnen (rhs) b_fine = 2.^-sum(sit_fine,2); b = 2.^-sum(sites,2); @@ -56,7 +56,7 @@ for j = 1:times %data -> ErgebnisVektor dataS = size(elements,1); - %zeta Vorbereiten + %zeta vorbereiten if(~iscell(zeta)) zeta_tmp = zeta; clear zeta; @@ -65,14 +65,14 @@ for j = 1:times end end - %Alle MatrixBrechenungsArten mit dem selben Netz berechnen + %alle MatrixBrechenungsArten mit dem selben Netz berechnen for i = 1:length(typ) start_time = toc; disp([num2str(size(elements,1)) ' : ' t2str(toc) ' ->' num2str(i)]) %Matrix aufbauen -> MEX V_fine = mex_build_V(coo_fine,ele_fine,zeta{i},typ(i)); build_time = toc; - %Testet auf Fehlerhafte Eintraege (NaN +/-Inf) + %testet auf fehlerhafte Eintraege (NaN +/-Inf) [r c] = find(isnan(V_fine)~=isinf(V_fine)); if(~isempty(r)) figure(9) @@ -82,7 +82,7 @@ for j = 1:times end if(~vcon) - %Loesung Berechnen + %Loesung berechnen x_fine = V_fine\b_fine; con = cond(V_fine); else @@ -125,14 +125,14 @@ for j = 1:times mu = hmin.*b.*sum((x_fine(f2s)'-repmat(x',4,1)).^2)'/4; - %Energienorm^2 Berechnen |||h||| & |||h/2||| + %Energienorm^2 berechnen |||h||| & |||h/2||| % xe_fine = x_fine'*A_fine*x_fine; xe_fine = b_fine'*x_fine; % xe = x'*A*x; xe = b'*x; - %Enorm^2 Elementweise Vergleich + %Enorm^2 Elementweise vergleichen if(exist('old_F_fine','var')) for k = 1:size(ele_fine,1) e_f = find(sum(k==f2s,2)); @@ -191,10 +191,10 @@ for j = 1:times ]; end - % Markieren mit gewaehlten Parametern + % markieren mit gewaehlten Parametern marked = mark(x_fine(f2s)',tmu,theta,nu); - % Netz bunt Plotten! + % Netz bunt plotten! % figure(1) % plotShape(G_C,G_E,'s',tmu); % title('Elemente mit Fehlerschaetzer') @@ -209,7 +209,7 @@ for j = 1:times old_E = elements; old_S = sites; - %Netz Verfeinern, wie durch marked bestimmt + %Netz verfeinern, wie durch marked bestimmt [coordinates, elements, neigh, f, sites, er]... = refineQuad(coordinates,elements,neigh,sites,marked); @@ -243,7 +243,7 @@ for j = 1:times p2(2) = p2(2) -2; end - %ErgebnisWerte Speichern + %ErgebnisWerte speichern data(size(data,1)+1,1:length(dataS)) = dataS; typeN = int2str(typ); fileo = [typeN(typeN~=' ')... diff --git a/src/export_exmpl.m b/src/export_exmpl.m index f6b3002..fb83974 100644 --- a/src/export_exmpl.m +++ b/src/export_exmpl.m @@ -166,10 +166,11 @@ A_plots({'meshSave/1t1n0_2DQuad_6',... %% Semianalytisch A_plots({'meshSave/132t05n05_2DQuad_30'},'../doc/fig/132t05n05_2DQuad') +A_plots({'meshSave/142t05n05_2DQuad_30'},'../doc/fig/142t05n05_2DQuad') A_plots({'meshSave/142t05n05_3DFichCube_22'},'../doc/fig/132t05n05_3DFichCube') -A_plots({'meshSave/1432t05n05_3DFichCube_21'},'../doc/fig/1432t05n05_3DFichCube') -A_plots({'meshSave/1432t05n05_2DQuad_29'},'../doc/fig/1432t05n05_2DQuad') +% A_plots({'meshSave/1432t05n05_3DFichCube_21'},'../doc/fig/1432t05n05_3DFichCube') +% A_plots({'meshSave/1432t05n05_2DQuad_29'},'../doc/fig/1432t05n05_2DQuad') % A_plots({'meshSave/2222t05n05_2DQuad_30'},'../doc/fig/2222t05n05_2DQuad') diff --git a/src/mark.m b/src/mark.m index 17ba062..93a56ca 100644 --- a/src/mark.m +++ b/src/mark.m @@ -18,7 +18,7 @@ t3 =0; t4 = 0; Ct = T4*xF2S; -%% Muss ueberhaupt verfeinert werden (welche sollen nicht verfeinert werden) +%% muss ueberhaupt verfeinert werden (welche sollen nicht verfeinert werden) if(theta <1) [s_ind idx] = sort(ind,'descend'); @@ -33,14 +33,14 @@ if(theta <1) end -%% Wie muss verfeinert werden +%% wie muss verfeinert werden if(nu > 0) % Horizontal oder Vertikal t3 = (nu*abs(Ct(3,:)) >= sqrt(Ct(2,:).^2+Ct(4,:).^2)); REF(t3-t1==1) = 3; t4 = (nu*abs(Ct(4,:)) >= sqrt(Ct(2,:).^2+Ct(3,:).^2)); REF(t4-t1==1) = 4; end -REF(~(t4+t3+t1)) = 2; % Rest wird Horizontal UND Vertikal geteilt +REF(~(t4+t3+t1)) = 2; % Rest wird horizontal UND vertikal geteilt end diff --git a/src/mex_build_V.cpp b/src/mex_build_V.cpp index 332915a..f0b5641 100644 --- a/src/mex_build_V.cpp +++ b/src/mex_build_V.cpp @@ -27,7 +27,7 @@ /***************************************************************************/ /* - * wenn gesetzt wird paralleles Rechnen benutzt + * wenn gesetzt wird, paralleles Rechnen benutzt */ #define PARALLEL #include @@ -209,7 +209,7 @@ double inline distT_ort(double b, double d, double t, double v, double d1, } /* - * mexFunktion zum aufbauen der Galerkin Matrix + * mexFunktion zum Aufbauen der Galerkin Matrix */ void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { @@ -294,19 +294,19 @@ void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { double*); switch (type) { - default: // Voll Analytisch + default: // voll analytisch ctypeP = cParO1; ctypeO = cOrtO1; break; - case 2: // Analytisch oder Qadratur + case 2: // analytisch oder Qadratur ctypeP = cParO2; ctypeO = cOrtO2; break; - case 3: // Analytisch oder Qadratur oder Qy[1]x2 + case 3: // analytisch oder Qadratur oder Qy[1]x2 ctypeP = cParO3; ctypeO = cOrtO3; break; - case 4: // Analytisch oder Qy[1]x2 + case 4: // analytisch oder Qy[1]x2 ctypeP = cParO4; ctypeO = cOrtO4; // ctypeO = cOrtO2; @@ -317,7 +317,7 @@ void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { break; } - //LageInformationen + //Lageinformationen int rx, rxa, rxb, ry, rya, ryb; double tmp; double x[4][3] = { { 0, 0, 0 }, { 0, 0, 0 }, { 0, 0, 0 }, { 0, 0, 0 } }; diff --git a/src/refineQuad.m b/src/refineQuad.m index 8ee43f2..a405677 100644 --- a/src/refineQuad.m +++ b/src/refineQuad.m @@ -17,7 +17,7 @@ function [coo,ele,nei,f2s,sit,err] = refineQuad(coordinates,elements,neigh,sites err = []; -%Type wenn nur ein Wert: aufblaehen +%Type: wenn nur ein Wert: aufblaehen if([1 1] == size(typ)) typ = repmat(typ, size(elements,1),1); end @@ -31,12 +31,12 @@ global G_ref_E; global G_ref_C; global G_ref_N; global G_ref_S; -global G_ref_f2s; %Finale Beziehung (VaterSohn) +global G_ref_f2s; %finale Beziehung (VaterSohn) global G_ref_t; %wie soll verfeinert werden global G_ref_tD; %wie wurde bereits verfeinert (in diesem Durchlauf) -global G_ref_f2sT; %Temporaere Beziehung +global G_ref_f2sT; %temporaere Beziehung -%INTERNE Globale Variablen zuweisen +%INTERNE globale Variablen zuweisen G_ref_E = elements; G_ref_C = coordinates; G_ref_N = neigh; @@ -45,7 +45,7 @@ G_ref_t = typ; G_ref_f2s = repmat((1:size(elements,1))',1,4); G_ref_tD = ones(size(elements,1),1); -%Parameter Freigeben (Speicher...) +%Parameter freigeben (Speicher...) clear elements coordinates neigh typ % figure(11) @@ -57,17 +57,17 @@ clear elements coordinates neigh typ ref_old = []; ref_old2 = []; -%Jedes Element verfeinern +%jedes Element verfeinern while(1==1) - %jeden 4ten 2er durch schrittweise Verfeinerung (5) ersetzen + %jeden vierten 2er durch schrittweise Verfeinerung (5) ersetzen t_ref=find(G_ref_t==2); G_ref_t(t_ref(2:4:end)) = 5; - %Welche Elemente muessen bearbeitet werden + %welche Elemente muessen bearbeitet werden ref = find(G_ref_t>1); ref = reshape(ref,1,length(ref)); - %Muss noch weiter Verfeinert werden? + %muss noch weiter Verfeinert werden? if(isequal(ref,ref_old)) assert(~isequal(ref_old2,G_ref_t,'Markierte sind verschieden')); break; @@ -78,7 +78,7 @@ while(1==1) break; end - % Elementeweise Bearbeiten + % Elementeweise bearbeiten for ele = ref % ref(randperm(length(ref))) % HangingNode Check @@ -95,7 +95,7 @@ while(1==1) N2 = N2(mod(N2tt,2)==1); end - %Hat noch zu teilende Nachbarn? + %hat noch zu teilende Nachbarn? if(~isempty(N2)) N3t = mod(find((G_ref_N(N2',:)==ele)')-1,4)+1; %Nachbarseiten N4t = find(diag(G_ref_N(N2',(N3t + 4)'))~=0)'; %Nachbarn mit 2Nachbarn @@ -122,16 +122,16 @@ while(1==1) end - % Da Nachbarn noch Verfeinert werden muessen erst mal weiter + % Da Nachbarn noch verfeinert werden muessen, erst mal weiter continue; end end - % Wenn Alle Ueberpruefungen durchgelaufen sind + % Wenn alle Ueberpruefungen durchgelaufen sind assert(G_ref_tD(ele)~=2,'Element ist schon verfeinert') assert(G_ref_t(ele)>1,'Element ist nicht Markiert') G_ref_f2sT = ones(1,4)*ele; - refineE(ele); %Element Teilen + refineE(ele); %Element teilen updateN(ele); %Nachbarn des Elements aktualisieren updateF2S(ele); %VaterSohn Relation setzen end @@ -144,16 +144,16 @@ nei = G_ref_N; f2s = G_ref_f2s; sit = G_ref_S; -%Doppelte Koordinaten loeschen +%doppelte Koordinaten loeschen [coo , ~, pos] = unique(coo,'rows'); pos = pos'; ele = pos(ele); - %INTERNE Globale Variablen freigeben + %INTERNE globale Variablen freigeben clear G_ref_E G_ref_C G_ref_N G_ref_f2s G_ref_t G_ref_tD G_ref_s end -%% Element Verfeinern ! sollte nur ausgefuehrt werden wenn wirklich moeglich +%% Element verfeinern ! sollte nur ausgefuehrt werden wenn wirklich moeglich function refineE(ele) % Element wird gnadenlos Verfeinert @@ -219,11 +219,11 @@ global G_ref_f2sT; global G_ref_t; this = G_ref_N(ele,:); -%An welchen Kanten habe ich Nachbarn -S = find(mod((this(1:4)~=0).*(this(5:8)==0),2))'; %Einen Nachbar (Single) -D = find(this(5:8)~=0)'; %Zwei Nachbarn (Double) +%an welchen Kanten habe ich Nachbarn +S = find(mod((this(1:4)~=0).*(this(5:8)==0),2))'; %einen Nachbar (Single) +D = find(this(5:8)~=0)'; %zwei Nachbarn (Double) -%An welchen Kanten bin ich Nachbar +%an welchen Kanten bin ich Nachbar MSt = mod(find((G_ref_N(this(S),:)==ele)')-1,8)+1; MS = mod(MSt-1,4)+1; % (Single) %OHNE MOD???? MD = mod(find((G_ref_N(this([D D+4]),:)==ele)')-1,4)+1; @@ -329,15 +329,15 @@ end end -%% Aktualisieren der VaterSohn Beziehung ! sollte nur ausgefuehrt werden wenn wirklich moeglich +%% aktualisieren der VaterSohn Beziehung ! sollte nur ausgefuehrt werden wenn wirklich moeglich function updateF2S(ele) -%Vater Sohn Beziehungen richtig Setzen +%VaterSohn Beziehungen richtig Setzen global G_ref_f2s; global G_ref_f2sT; global G_ref_t; global G_ref_tD; - if(G_ref_tD(ele)==1) %Wenn Element zum ersten Mal verfeinert wird + if(G_ref_tD(ele)==1) %wenn Element zum ersten Mal verfeinert wird G_ref_f2s(ele,:) = G_ref_f2sT; if(G_ref_t(ele)<5) G_ref_tD(G_ref_f2sT) = G_ref_t(ele); @@ -346,7 +346,7 @@ function updateF2S(ele) G_ref_tD(G_ref_f2sT) = 3; G_ref_t(G_ref_f2sT) = 4; end - else %Wenn Element zum zweiten Mal verfeinert wird + else %wenn Element zum zweiten Mal verfeinert wird G_ref_tD(G_ref_f2sT) = 2; org=floor((find(G_ref_f2s'==ele,1)-1)/4)+1; pos=find(G_ref_f2s(org,:)==ele,1); diff --git a/src/slpRectangle.cpp b/src/slpRectangle.cpp index c7e9b7f..294d50f 100644 --- a/src/slpRectangle.cpp +++ b/src/slpRectangle.cpp @@ -21,8 +21,6 @@ int GAUSS_size = GAUSS_SIZE[2]; gauss * GAUSS_nodes = GAUSS_NODES[2]; -double count[][2] = {{0,0},{0,0}}; - /* * setzt den Quadraturgrad, also 2^q Auswertungsstellen @@ -34,14 +32,7 @@ int setQuad(int q) { } /* - * gibt die count Matrix zurueck - */ -double ** getCount(){ - return (double **) count; -} - -/* - * gibt das signum von x zurueck + * gibt das Signum von x zurueck */ int inline sign(double x) { return x > 0 ? 1 : (x < 0 ? -1 : 0); @@ -55,7 +46,7 @@ double inline max(double x, double y) { } /* - * gibt das minimum der beiden Zahlen x,y zurueck + * gibt das Minimum der beiden Zahlen x,y zurueck */ double inline min(double x, double y) { return x > y ? y : x; @@ -496,7 +487,7 @@ double inline intA4(double b, double d, double t, double v, double d1, /* * fuer parallele Elemente - * voll Analytisch + * voll analytisch */ double cParO1(double b, double d, double t, double v, double d1, double d2, double d3, double* zeta) { @@ -504,7 +495,7 @@ double cParO1(double b, double d, double t, double v, double d1, double d2, } /* * fuer orthogonale Elemente - * voll Analytisch + * voll analytisch */ double cOrtO1(double b, double d, double t, double v, double d1, double d2, double d3, double* zeta) { diff --git a/src/slpRectangle.hpp b/src/slpRectangle.hpp index 5a8516a..4982fe8 100644 --- a/src/slpRectangle.hpp +++ b/src/slpRectangle.hpp @@ -14,7 +14,7 @@ #define HILBERT3D_LAPLACE_SLPRECTANGLE_HPP_GUARD_ /* - * voll Analytisch rechnen + * voll analytisch rechnen */ double cParO1(double, double, double, double, double, double, double, double*); double cOrtO1(double, double, double, double, double, double, double, double*); @@ -46,9 +46,4 @@ double cOrtO4(double, double, double, double, double, double, double, double*); */ int setQuad(int); -/* - * gibt die count Matrix zurueck - */ -double ** getCount(); - #endif -- 2.47.3